# Real-time Manipulation of Liquid Droplets using Photo-responsive Surfactant

Xichen Liang  Department of Chemical Engineering, University of California at
Santa Barbara, Santa Barbara, California 93106-5070, USA  X.L.and K.K.
contributed equally to this work.  Kseniia M. Karnaukh  Department of
Chemistry, University of California at Santa Barbara, Santa Barbara,
California 93106-5070, USA  X.L.and K.K. contributed equally to this work.
Lei Zhao  Department of Mechanical Engineering, University of California at
Santa Barbara, Santa Barbara, California 93106-5070, USA  Serena Seshadri
Department of Chemistry, University of California at Santa Barbara, Santa
Barbara, California 93106-5070, USA  Austin J. DuBose  Department of
Chemistry, University of California at Santa Barbara, Santa Barbara,
California 93106-5070, USA  Sophia J. Bailey  Department of Chemistry,
University of California at Santa Barbara, Santa Barbara, California
93106-5070, USA  Qixuan Cao  Department of Physics, University of California
at Santa Barbara, Santa Barbara, California 93106-5070, USA  Marielle Cooper
Department of Mechanical Engineering, University of California at Santa
Barbara, Santa Barbara, California 93106-5070, USA  Hao Xu  Department of
Mechanical Engineering, University of California at Santa Barbara, Santa
Barbara, California 93106-5070, USA  Michael Haggmark  Department of Chemical
Engineering, University of California at Santa Barbara, Santa Barbara,
California 93106-5070, USA  Matthew E. Helgeson  Department of Chemical
Engineering, University of California at Santa Barbara, Santa Barbara,
California 93106-5070, USA  Michael Gordon  Department of Chemical
Engineering, University of California at Santa Barbara, Santa Barbara,
California 93106-5070, USA  Paolo Luzzatto-Fegiz  Department of Mechanical
Engineering, University of California at Santa Barbara, Santa Barbara,
California 93106-5070, USA  To whom correspondence should be addressed.
E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>Javier Read de
Alaniz  Department of Chemistry, University of California at Santa Barbara,
Santa Barbara, California 93106-5070, USA  To whom correspondence should be
addressed. E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>Yangying Zhu  Department of Mechanical Engineering, University of California
at Santa Barbara, Santa Barbara, California 93106-5070, USA  To whom
correspondence should be addressed. E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Fast and programmable transport of liquid droplets on a solid substrate is
desirable in microfluidic, thermal, biomedical, and energy devices. Past
research has focused on designing substrates with asymmetric structures or
gradient wettability where droplet behaviors are passively controlled, or by
applying external electric, thermal, magnetic, or acoustic stimuli that either
require the fabrication of electrodes or a strong applied field. In this work,
we demonstrate tunable and programmable droplet motion on liquid-infused
surfaces (LIS) and inside solid-surface capillary channels using low-intensity
light and photo-responsive surfactants. When illuminated by the light of
appropriate wavelengths, the surfactants can reversibly change their molecular
conformation thereby tuning interfacial tensions in a multi-phase fluid
system. This generates a Marangoni flow that drives droplet motions. With two
novel surfactants that we synthesized, we demonstrate fast linear and complex
2D movements of droplets on liquid surfaces, on LIS, and inside microchannels.
We also visualized the internal flow pattern using tracer particles and
developed simple scaling arguments to explain droplet-size-dependent velocity.
The method demonstrated in this study serves as a simple and exciting new
approach for the dynamic manipulation of droplets for microfluidic, thermal,
and water harvesting devices.

## Introduction

Manipulating droplets on surfaces and interfaces is critical for the
efficiency and tunability of water desalination [1], condensation [2, 3, 4,
5], liquid transport in microfluidics [6], and digital bioassay [7]. For
example, condensation, a key process in power generation and thermal
management, requires fast removal of droplets from the substrates for
efficient heat transfer [4, 8]. Passive methods to transport droplets on
surfaces have focused on engineering asymmetric surface structures [9, 10, 11,
12, 13, 14, 15] and gradient chemistry [16, 17, 18, 19]. However, these
surfaces typically require complex fabrication and do not offer real-time
control capability. Active methods that can dynamically tune droplet motions
have been developed using electric [6, 20, 21, 22], magnetic [23, 24, 25, 26],
acoustic [27], chemical [28, 29], thermal [30, 31], and photo-thermal [32]
stimuli. While electric, magnetic and photo-thermal systems may require a high
voltage (100-1000 V for electrowetting), magnetic field ($\sim$ 0.1 T), or
light intensity ($\sim$ 1 W/mm2) to actuate droplet motion, chemical and
thermal systems can have a slow response due to mass diffusion and thermal
mass. To realize spatial control, some of these methods still require
patterning of microstructures, which limits their spatial resolution [33].

Manipulation methods based purely on light stimuli are attractive as light
offers spatial resolution down to the diffraction limit, can be easily
reconfigured, and does not require the fabrication of microstructures such as
electrode arrays [34]. Several studies have investigated photo-sensitive
substrates such as TiO2 or ZnO [35, 36]. Although the contact angle of water
on these surfaces can decrease by 70-100∘ upon UV illumination, direct
manipulation of droplet movement has not been reported. Optical tweezers based
on the transfer of photon momentum have been extensively studied to trap and
manipulate solid microparticles [37]. They have also not been used to control
liquid droplets directly. Alternatively, photo-responsive surfactants have
recently been applied to manipulate multi-phase fluid systems. These are
surfactants that can switch their molecular conformation when illuminated by
light with appropriate wavelengths. The photoswitch of surfactants results in
a local change of the surface tension or interfacial tension, which can
further generate a Marangoni flow. Compared to photo-thermal effects (i.e.,
using light to heat fluid for liquid motion based on Marangoni-flow or
temperature-dependent surface tension force), photo-responsive surfactants
require a significantly lower light intensity to generate a comparable surface
tension change [38], and no light-absorbing substrates or nanoparticle
additives are needed. Using photo-responsive surfactants, recent works have
demonstrated dynamically reconfigurable emulsions [39], trapping and
manipulation of solid objects [40], moving droplets immersed in [41] and on
the surface of an immiscible liquid [41, 42], and bubble departure from solid
surfaces [38]. However, moving liquid droplets on solid or liquid-infused
surfaces using photo-responsive surfactants has not been achieved so far,
which is of particular practical interest to many applications.

In this work, we demonstrate fast and programmable 2D motions of liquid
droplets on liquid-infused surfaces (LIS), inside solid-wall microchannels,
and on liquid substrates using two types of light-sensitive surfactants (SP-
DA-PEG and MCH-para) that can induce large changes in the interfacial tension
in the opposite directions. The surfactants are activated by light whose
intensity is 1-2 orders of magnitude lower than the laser intensities used in
thermal-capillary actuation. We characterize the magnitude and rate of change
in interfacial tensions of various fluid-fluid systems and demonstrate linear
movement, merging, and complex 2D patterns of liquid droplets on various
substrates. Furthermore, we present simple scaling arguments to explain the
observed droplet-size-dependent velocity. The internal Marangoni flow is
visualized via tracer particles and a simplified numerical model. The results
demonstrated in this work open exciting doors for the use of photo-responsive
surfactants for dynamic manipulation of multiphase fluid systems for energy,
building, thermal management, and microfluidics applications.

Figure 1: Mechanisms of liquid movement driven by photo-responsive
surfactants, molecular structures of the photo-responsive surfactants, and
surface tension response. (A) Schematic of a lubricant-cloaked droplet on a
liquid-infused surface (LIS). The interfacial tension increases under
illumination, causing a Marangoni flow from the unilluminated region to the
illuminated region, and a net shear force away from the light. (B) Schematic
of a lubricant-cloaked droplet on LIS. The interfacial tension decreases under
illumination, causing a Marangoni flow from the illuminated region to the
unilluminated region, and a net shear force toward the light. (C) Schematic of
liquid in a microchannel or capillary tube. The surface tension changes under
illumination, which results in an unbalanced total surface tension force on
the liquid column and the subsequent liquid movement. Molecular structures and
photoswitching of (D) SP-DA-PEG and (E) MCH-para. (F) The change of color of
SP-DA-PEG in toluene under UV illumination and MCH-para in aqueous solution
(phosphate buffer, pH 3) under 470 nm illumination. (G) Surface tension
response of SP-DA-PEG in water under UV (365 nm) illumination with an optical
intensity of 37.1 mW/cm2. (H) Surface tension response of MCH-para in water at
various pH levels under blue light (470 nm) illumination with an optical
intensity of 31.8 mW/cm2.

## Results

### Working principle and characterization of surfactants

Photo-responsive surfactants or molecules are synthesized by attaching a
photoswitchable molecule to a surfactant carrier. The photoswitchable moiety
typically exists as a thermodynamically stable isomer in the dark. Upon
illumination with a specific wavelength, the isomer will undergo a
conformational switch to a metastable isomer.

When light is removed or a different wavelength of light is applied, the
metastable isomer can switch back to the original thermodynamically stable
isomer. This reversible isomer conversion can cause a change in the surface
tension or interfacial tension of a solution containing the photo-responsive
surfactant or molecule. We utilize this change in surface or interfacial
tension to drive liquid motion on liquid-infused surfaces (LIS), inside
microchannels with solid walls, and to form complex patterns on liquid
surfaces.

The working principle for driving fluid motion can be explained by two
different mechanisms: interfacial shear caused by a photo-Marangoni (or
chromo-capillary) flow and unbalanced surface tension forces. As illustrated
in Fig. 1A and 1B, for a droplet on LIS consisting of a porous hydrophobic
surface infused with lubricant oil, applying light on one side of the droplet
will cause the photo-responsive surfactants or molecules under illumination to
switch to the metastable isomer. This causes the local surface tension or
interfacial tension $\gamma$ to increase (Fig. 1A) or decrease (Fig. 1B),
which depends on the choice of surfactants and solvents. Meanwhile, the
surfactants on the unilluminated side remain in the thermodynamically stable
form. For droplets cloaked by the lubricant, an interfacial tension gradient
will establish, generating a Marangoni flow from the low interfacial tension
side to the high interfacial tension side. The interfacial flow generates a
net shear force on the droplet, which causes it to move in the direction
opposite to the interfacial flow direction. By adjusting the concentration of
the surfactants, pH of the solution, and light intensity, the gradient in
$\gamma$ can be quantitatively adjusted. On the other hand, for the liquid
inside microfluidic channels with solid walls (Fig. 1C), no Marangoni flow is
present since there is no fluid-fluid interface. Rather, light causes the
surface tension on the illuminated side of the liquid column to increase or
decrease. The unbalanced surface tension force acting on the liquid along the
channel direction becomes the main driving force.

To investigate photo-responsive surfactants with different characteristics, we
selected two types of surfactants: SP-DA-PEG containing an electron-
withdrawing nitro group (Fig. 1D) which has been previously reported in our
work [38], and a newly synthesized merocyanine photoacid with two electron-
donating methoxy groups incorporated at the _para_ -positions in the indolium
and the phenolic moiety (MCH-para, Fig. 1E). These molecules have different
reaction timescales, are soluble in various types of solvents (aqueous and
organic), and, as we show later, result in significant changes in the surface
and interfacial tensions in the opposite directions due to differences in the
photoswitching pathway. As shown in Fig. 1D, SP-DA-PEG can be tuned between
neutral spiropyran (SP) and charged merocyanine (MC) forms upon 365 nm light
irradiation; the reverse reaction occurs when the UV source is removed and can
be accelerated by applying green light ($\sim$ 532 nm). In an aqueous
solution, the photoswitch is accompanied by a change in color from transparent
(SP form) to light pink (MC form) [38]. In toluene, the solution changes from
transparent (SP form) to dark blue (MC form) (Fig. 1F). The photoswitching
mechanism of merocyanine photoacids is multi-step and depends on the
equilibrium between the photoreactive states, solvent choice, pH of an aqueous
solution, and substituent pattern [43, 44]. Recently, J. Beves et al.
described a detailed switching mechanism of merocyanine photoacids [45]. In
the absence of light, merocyanine photoacids exist in three states: protonated
merocyanine (MCH), deprotonated merocyanine (MC), and spiropyran (SP). At low
pHs, MCH is the dominant form, while at basic conditions, the equilibrium
shifts to MC which can undergo thermal ring-closure to form SP (SI Appendix,
Fig. S7 A). For consistency, we investigated the aqueous solutions with a 1 to
4 pH range, where equilibrium completely shifted to the MCH form (SI Appendix,
Fig. S7 B). At low pHs, the MCH-para switches instantaneously between _trans_
-MCH and the more acidic _cis_ -MCH form upon application and removal of blue
light ($\sim$ 470 nm), respectively (Fig. 1E and SI Appendix, Fig. S7 B). Such
fast-switching kinetics is beneficial to result in a fast response of surface
tension change, and maintain the surface tension gradient within a droplet.
Fig. 1F shows that 1 mM MCH-para aqueous solution bleaches from dark orange to
yellow upon irradiation of 470 nm light, using a low-power fiber-coupled blue
LED (5.6 mW/mm2, Thorlabs M470F3). Moreover, we demonstrate that MCH-para has
incredible hydrolytic stability at low pHs compared to previously reported
merocyanine photoacids, which tend to hydrolyze due to the nucleophilic attack
of water (SI Appendix, Fig. S6 A and B) [46]. MCH-para was stable at pH 1-3 at
room temperature for more than one month in aqueous media (SI Appendix, Fig.
S7 C and D). This can be attributed to para- substitution with electron-
donating methoxy groups both in indolium and phenolic moiety. Previously,
Pezzato et al. reported that the para- substitution with electron-donating
groups of either indolium or the chromene moiety increases hydrolytic
stability [47]. However, combinatory effects have not been previously
investigated. We measured the surface tension responses of SP-DA-PEG and MCH-
para aqueous solutions using a standard pendant drop method on a commercial
tensiometer (Theta Flex, Biolin Scientific). Under light illumination, the
surface tension of SP-DA-PEG increases (Fig. 1G and SI Appendix, Fig. S11)
while the surface tension of MCH-para solution decreases (Fig. 1H). Fig. 1G
shows that the change in surface tension of the SP-DA-PEG aqueous solution can
be tuned by varying the surfactant concentration. In this case, a 0.1 mM
solution demonstrated a 5.6 mN/m change in surface tension within 8 s under
37.1 mW/cm2 illumination. Under the same illumination, increasing the
concentrations to 0.2 mM and 0.4 mM reduced the response time to 7 s and 4 s,
respectively, but also resulted in smaller surface tension changes (3.9 mN/m
and 2.9 mN/m, respectively). In addition, the surface tension response can
also be tuned by the light intensity (SI Appendix, Fig. S11). The change in
surface tension of a 0.2 mM SP-DA-PEG aqueous solution increases from 2.1 mN/m
to 3.9 mN/m when the light intensity increases from 7.7 mW/cm2 to 37.1 mW/cm2.
These optical intensities are approximately 102 times lower compared to those
used for thermocapillary actuation [48, 49]. The reverse switching was slower
compared to forward switching. Compared to SP-DA-PEG, the surface tension
response of MCH-para in water at various pH levels (phosphate buffer solution)
is almost instantaneous (1.1 s for the forward reaction and 1.7 s for the
reverse reaction), as illustrated in Fig. 1H ($\sim$ 470 nm, 31.8 mW/cm2). We
demonstrate multiple cycles of surface tension switching under repetitive
pulsed blue light within a short period of time. The change in surface tension
varies slightly from 3.6 mN/m at pH 1 to 5.7 mN/m at pH 4.

### Droplet movement on LIS

We first demonstrate and characterize droplet movement on a liquid-infused
surface (LIS) using SP-DA-PEG and MCH-para (Fig. 2A). LIS offers the
advantages of high droplet mobility and low contact angle hysteresis, which
make it particularly suitable as a microfluidic platform for fluid
manipulation, as an anti-icing and anti-fouling surface, and as a condensation
surface for power generation, thermal management, and desalination. The LIS
used in this study consists of a porous PTFE membrane (SI Appendix, Fig. S12)
infused with Krytox. As water droplets containing 0.2 mM SP-DA-PEG and 1 mM
MCH-para (pH 3) respectively, were deposited on the LIS, we observed
interference diffraction fringes on the surface of both droplets (SI Appendix,
Fig. S13 A). This suggests that the droplets were cloaked by Krytox. In the
absence of Krytox, the surface of the droplet shows no interference patterns
(SI Appendix, Fig. S13 B).

Since both SP-DA-PEG and MCH-para are non-soluble in Krytox, they were
anticipated to adsorb to the water-Krytox interface. For SP-DA-PEG, the water-
Krytox interfacial tension was measured to increase from 18.2 mN/m to 21.8
mN/m ($\sim$20% increase) after UV illumination (365 nm, 110 mW/cm2), as shown
in Fig. 2B. The increase in interfacial tension is consistent with the
increase of surface tension of water under UV (Fig. 1G). Therefore, the
application of UV light to one side of the droplet containing SP-DA-PEG will
increase the interfacial tension locally. This generates a Marangoni flow from
the unilluminated side to the illuminated side on both the top and bottom
interfaces of the droplet, and two vortices form inside the droplet. A
velocity gradient develops in the Krytox in LIS as a result of the interfacial
flow, which exerts a net shear force on the droplet in the direction away from
the light (Fig. 1A).

Figure 2: Droplet movement (linear and 2D) and merging on liquid-infused
surfaces (LIS) using SP-DA-PEG. (A) Schematic of a liquid droplet on LIS. (B)
The interfacial tension response of water-Krytox interface with SP-DA-PEG when
illuminated with 365 nm UV at 37.1 mW/cm2 optical intensity. (C) Time-lapse
optical images (side view) of linear movement of a water droplet containing
SP-DA-PEG on LIS directed by UV light with an intensity gradient. Light
intensity is stronger on the left side and weaker on the right side. The line
plot shows the displacement of the droplet and its velocity as functions of
time. Time-lapse optical images (top-down view) of water droplets containing
SP-DA-PEG on LIS (D) changing moving directions on demand, and (E) merging.

The mechanism described above for SP-DA-PEG is confirmed in Fig. 2C. and Movie
S1. When a water droplet containing SP-DA-PEG is placed in an environment
where the light intensity is stronger on the left side and weaker on the right
side realized using a continuously variable neutral density filter (Thorlabs
NDL-10C-2) and a UV lamp (Analytik Jena, UVP BLAK-RAY B-100AP ALMP), the
droplet moves toward the darker region (i.e., away from the light). Although
the velocity is relatively slow ($\sim$250 $\mu$m/s, Fig. 2C solid line plot),
this is the first demonstration of droplet movement on LIS activated by photo-
responsive surfactants. The output optical intensity after the UV light passed
through the center of the filter was very low (6.1 mW/cm2). In comparison, an
equal-sized water droplet containing no surfactants remained stationary under
the same illumination conditions (SI Appendix, Fig. S15), suggesting that
droplet movement was not caused by the thermal-Marangoni effect from UV
heating. Furthermore, the moving direction of the droplet can be controlled on
the fly. As shown in Fig. 2D and Movie S2, a water droplet was initially
moving in the $+y$ direction driven by a UV laser (351.1 nm and 363.8 nm, beam
diameter of 1.3 mm, optical power of 101 mW). Upon changing the laser
position, the droplet immediately moved in the $-x$ direction. The photo-
Marangoni effect can also achieve controlled merging of multiple droplets. As
illustrated in Fig. 2E and Movie S3, the same UV laser can drive a droplet to
move toward and merge with another droplet. Since the left side of the as-
formed droplet is rich in MC (pink), and the right side of the droplet
contains only SP (transparent), a surface tension gradient remained in the
merged droplet which caused it to move further even without UV light.

We further investigated the movement and the internal flow field of water
droplets (pH 3) containing 1 mM MCH-para on LIS. In contrast to SP-DA-PEG, the
water-Krytox interfacial tension with MCH-para decreased from 42.9 mN/m to
37.9 mN/m (Fig. 3A, 470 nm, 31.8 mW/cm2), which is also consistent with
surface tension measurement (Fig. 1H). This reduction in the interfacial
tension is also evident in the contact angle measurement (SI Appendix, Fig.
S14), where the contact angle of an MCH-para water droplet on LIS reduced from
117∘ to 113∘ upon blue light (470 nm, 31.8 mW/cm2) irradiation. Due to the
opposite trend of interfacial tension change, we expect that the droplet
containing MCH-para will move in the opposite direction, as shown in Fig. 1B.
As shown in Fig. 3B, when the droplet is subject to a light intensity gradient
(470 nm, stronger on the right side and weaker on the left side realized by
the continuously variable neutral density filter, Thorlabs NDL-10C-2), the
droplet moved toward the light in contrast to a droplet containing SP-DA-PEG
moving away from the light. This indicates that we are able to precisely
control the moving direction of the droplet by tuning the direction of surface
tension response.

We confirmed the internal flow field using tracer particles (Cospheric,
sliver-coated hollow glass microsphere 25 - 65 $\mu$m, 0.9 g/cm3). As shown in
Fig. 3C, when blue light (470 nm) illuminates the right side of the droplet,
the local interfacial tension decreases. This causes a Marangoni flow as
indicated by Fig. 1B. The trajectory of tracer particles in Fig. 3C and Movie
S4 clearly showed that fluid indeed traveled from the low $\gamma$ side
(illuminated region) to the high $\gamma$ side (un-illuminated region) along
the water-Krytox interfaces. The directions and lengths of arrows on a few
labeled tracer particles indicate the directions and magnitudes of the
velocity of the tracer particles. We further developed a simplified numerical
model to qualitatively illustrate the internal flow field using COMSOL
Multiphysics. The model assumes that a shear stress is imposed on the top and
bottom interfaces of a droplet on a thin lubricant layer. The flow is steady
in a reference frame moving with the droplet. Fig. 3D shows two opposite-
signed recirculation regions in the mid-plane of the droplet, which is
consistent with the experimental observations in Fig. 3C. The detailed
description of the numerical model is presented in the SI Appendix.

Figure 3: Droplet movement on liquid-infused surfaces (LIS) using MCH-para.
(A) The interfacial tension response of water-Krytox interface containing MCH-
para when illuminated with 470 nm UV at 31.8 mW/cm2 optical intensity. (B)
Time-lapse optical images (side view) of linear movement of a water droplet
containing MCH-para on LIS directed by blue light with an intensity gradient.
(C) Time-lapse optical images (side view) of the internal flow field indicated
by tracer particles of a water droplet containing MCH-para. Blue light was
illuminated on the right side of the droplet. The directions and lengths of
arrows indicate the directions and magnitudes of the velocity of the tracer
particles. (D) Computational results of light driven droplet motion on LIS by
photo-Marangoni effect.

### Droplet transport on liquids

We further investigate liquid motion directly on another immiscible liquid as
a limiting case where there is no porous PTFE in the substrate (Fig. 4A).
Although linear droplet motions on a liquid substrate have been previously
investigated by Xiao et al. [41] and Diguet et al. [42], we demonstrate the
ability to drive liquid in any arbitrary direction to form complex patterns
and 2.5 times higher maximum droplet velocity. Water droplets containing 0.2
mM of SP-DA-PEG were placed on a thick layer ($>$ 1 cm) of higher-density
Krytox lubricant. As shown in Fig. 4B and Movie S5, the application of a UV
laser (351.1 nm and 363.8 nm, beam diameter of 1.3 mm, optical power of 101
mW) can actuate droplet motion and switch its moving direction repeatedly.
Moreover, we show in Fig. 4C and Movie S6 that the same laser can precisely
drive droplets to describe a complex pattern, shown here by spelling the
letters ‘UCSB’. Fig. 4C comprises overlaid time-lapse images to illustrate the
trajectory of the droplet. Consistently with our previous experiments,
droplets containing SP-DA-PEG move away from the light, as shown in Figs.
4B-C, whereas droplets containing MCH-para move towards the light (450 nm, 354
mW/cm2), as indicated in Fig. 4D.

Figure 4: Liquid movement (linear and 2D) on another immiscible liquid and
inside solid-wall microchannels. (A) Schematic and optical image of a liquid
droplet floating at the surface of an immiscible liquid. (B) Time-lapse
optical images (top-down view) of linear movement and switching of the
direction of a water droplet containing SP-DA-PEG on Krytox, directed by a UV
laser. (C) Overlaid images (top-down view) of SP-DA-PEG droplet trajectories
spelling the letters ’UCSB’, driven by a UV laser. The time interval between
images is 10 seconds. (D) Time-lapse optical images (top-down view) of linear
movement of a water droplet containing MCH-para on Krytox, directed by a blue
laser. (E) The average moving velocity of SP-DA-PEG droplets as a function of
droplet volume and light intensity under UV illumination. Scalings for small
and large drops are shown by dotted and dashed lines; a composite is shown by
the continuous line. The results of [41, 42] are shown for reference. (F)
Time-lapse optical images (side view) of a toluene liquid column containing
SP-DA-PEG moving inside a glass capillary tube directed by a UV laser.

Furthermore, we studied how velocity depends on size and light intensity. Fig.
4E shows the average moving velocity of SP-DA-PEG droplets as a function of
droplet volume and light intensity. The maximum velocity was observed when the
droplet volume was approximately 20 $\mu$L, which is 2.5 times higher compared
to previous studies [41, 42]. Velocity decreases gradually as drop volume is
increased past 20 $\mu$L.

We suggest simple scaling arguments to explain the observed maximum in drop
velocity. Within the drop, interfacial tension increases rapidly for fluid
within the laser spot; as the fluid moves away from the light, its interfacial
tension gradually returns towards its ‘dark’ value (as shown earlier in Fig.
2B). For smaller volumes, fluid takes less time to travel the drop length,
leading to an incomplete reverse photo-reaction and therefore a smaller
decrease in interfacial tension. As a result, the interfacial tension
difference across the drop becomes weaker. Balancing this Marangoni force and
the fluid resistance (see SI Scaling theory) we obtain the dotted curve for
the velocity $V$ in Fig. 4E. For small drops

$V\sim\sqrt{\frac{\Delta\gamma}{\mu}\frac{2R-d}{t_{\mathrm{rev}}}}\quad\quad\text{if}\quad\quad
2R-d\ll Vt_{\mathrm{rev}}$ (1)

where $\mu$ is the viscosity of Krytox, $R$ the drop radius, $d$ the beam
diameter, $t_{\mathrm{rev}}$ the reverse reaction timescale, and
$\Delta\gamma$ the maximum surface tension change achievable under the given
illumination (see Supplementary Material). For larger drops, there are several
contributing factors that could explain the decrease in velocity with
increasing volume. We note for example that the largest drops have Reynolds
numbers $Re=\frac{\rho V2R}{\mu}\approx 4$, such that some of the Marangoni
force is expended to overcome the inertia of the surrounding fluid, thereby
decreasing propulsive efficiency. A scaling based on this hypothesis is shown
by the dashed line in Fig. 4E, which approximately follows $V\sim R^{-1/2}$
(see SI Scaling theory); the continuous line is a composite of the results for
small and large drops.

Previous studies reported that the photo-Marangoni effect occurs in isothermal
conditions (i.e., without localized heating). However, we note that heating
from light absorption is possible [50]. Here, we show that under the
experimental conditions investigated in our study, the photo-Marangoni effect
is the dominant factor despite the co-existence of a thermal-Marangoni effect.
For SP-DA-PEG, illumination causes the surface tension and interfacial tension
to increase, while increased temperature causes a decrease. The direction of
fluid motion observed in our experiments confirms that the contribution of
temperature change must be small compared to the photo-Marangoni stress. On
the other hand, for MCH-para solutions, since both heating and photo-switching
decrease the surface and interfacial tension, we measured the change of
surface tension caused purely by an increase in temperature from 20∘C to 60∘C
using a custom syringe heating system (SI Appendix, Fig. S8 A). Surface
tension decreases with temperature following the equation

$\centering\gamma\left[\mathrm{\frac{mN}{m}}\right]=-0.26\;T[^{\circ}C]+76.66\@add@centering$
(2)

To estimate the separate contributions from heating and from photoswitching on
the change of surface tension shown in Fig. 1H, we measured the temperature
rise of a water droplet (pH 3) containing MCH-para under the same illumination
condition (470 nm 31.8 mW/cm2) using an infrared camera (Telops, M3K, SI
Appendix, Fig. S9 A). We used the emissivity of pure water ($\epsilon$ = 1) to
approximate the emissivity of the MCH-para aqueous solution (see SI Appendix,
Fig. S8 C for details). As shown in SI Appendix, Fig. S9 C and D, the highest
temperature within the MCH-para droplet increased from 19.6∘C to 20.6∘C after
150 s of blue light illumination (31.8 mW/cm2). According to equation 2, this
temperature change only generates a 0.26 mN/m decrease in surface tension,
which is only 5.9% of the surface tension change in Fig. 1H. Furthermore, the
temperature increase is negligible within the timescale of the photoswitch
($<2$s). Therefore, under these optical intensities, even though both heating
and photo-switching contribute to a decrease in the surface tension, the
photoisomerization-induced Marangoni effect is the primary factor in driving
droplet motion. When applying a higher optical intensity, the surface tension
changes caused by heating and photoswitching both increase in their magnitude;
their relative contributions can be estimated by the method presented here.

### Liquid transport in microchannels

In addition to modulating droplet movement on LIS and liquid surfaces, here we
also demonstrate the direct movement of liquid on solid walls of microchannels
or capillary tubes using light-responsive surfactants. Fig. 4F shows time-
lapse side view images of a glass capillary tube (0.5 mm diameter) containing
toluene with 0.1 mM SP-DA-PEG surfactants (Movie S7). The glass tube was
intentionally tilted so that under the influence of gravity, the liquid
naturally slide toward the right (from 0 s to 6 s). Application of light
(351.1 nm and 363.8 nm, beam diameter of 1.3 mm, optical power of 101 mW) on
the right side of the liquid column caused the liquid to move toward the left
(12 s to 55 s). When the light was removed, the liquid resumed moving towards
the right due to gravity (65 s to 85 s). In our previous work, the surface
tension of toluene containing SP-DA-PEG was measured to decrease with UV
illumination [38]. Since the only fluid-fluid interface is the toluene-air
interface at the two ends of the liquid column, the mechanism driving fluid
motion is not the Marangoni effect, but rather, the unbalanced surface tension
forces on the liquid. Specifically, the surface tension on the left
unilluminated side remains the same whereas the surface tension on the right
illuminated side reduces, contributing to a net force driving the liquid to
move away towards the higher surface tension side. In addition, a change in
contact angle can also contribute to the horizontal component of the net
surface tension force (Fig. 1C). However, we did not observe a clear change in
the contact angle with and without illumination.

## Discussion

We demonstrated a novel approach for dynamic manipulation of droplet motions
on lubricant-infused surfaces (LIS), solid-wall microchannels, and on liquid
substrates using photo-responsive surfactants designed and synthesized by us.
The surfactants SP-DA-PEG and MCH-para selected in this study have different
reaction timescales (1 to 10 seconds) and cause surface tension and
interfacial tension to change in the opposite direction. MCH-para is
particularly stable in low-pH aqueous solutions. In addition, the photo-switch
is activated with UV or blue light with optical intensity 1-2 orders of
magnitude lower than what is typically used by thermal-capillary actuation. We
show for the first time that droplets are able to move and merge in linear
motions on LIS, and their moving directions can be changed dynamically by
light. The Marangoni-induced internal fluid flow was also visualized by
analyzing the trajectory and velocity of tracer particles, which confirmed our
proposed mechanism. In particular, the moving direction depends on if
surfactants increase or decrease the surface or interfacial tension.
Furthermore, we show fast motion (up to 5.8 mm) of droplets floating on
another liquid substrate, and that droplets are able to move in arbitrary
directions on a 2D surface to form complex patterns. We developed scaling
arguments to explain the observed droplet-size dependent velocity and a
simpliﬁed numerical model to qualitatively illustrate the internal ﬂow.

In addition to the photo-Marangoni effect, we also demonstrate the movement of
liquid inside solid-wall microchannels which is caused by unbalanced surface
tension along the moving direction. This can potentially be used as a non-
contact pumping mechanism for microfluidic applications.

The droplet manipulation platform presented in this work opens doors for
applications requiring non-contact, non-invasive, dynamically tunable and
programmable fluid motions with minimal external energy input. Compare with
digital microfluidics realized using electrowetting and surfactant-mediated
electro-dewetting, our approach does not require any fabrication of
microelectrodes and electrical connections. Light can also be focused down to
the diffraction-limit length, potentially enabling microfluidic manipulation
down to the 1-micron spatial resolution. This however requires further
development of photo-responsive surfactants with faster reaction kinetics. In
addition, photo-surfactants that can be soluble in the lubricant of LIS can
help with droplet removal in condensation processes, which can potentially
enhance condensation heat transfer significantly for power generation and
desalination applications. The approach presented here also serves as a
powerful method for multi-phase processes in microgravity, where droplet
motions cannot be achieved with gravity.

## Materials and Methods

### Sample preparations

The photoactive surfactant SP-DA-PEG used in this study is soluble in toluene
and water. The solutions with the desired concentration were prepared by
sonicating appropriate amount of SP-DA-PEG in solvents (35). The photoactive
surfactant MCH-para used in this study has a high solubility in aqueous
solutions. A concentrated stock solution was used to create a 1 mM MCH-para
solution. The stock solution of MCH-para (C = 2 mM) was prepared by adding 15
mg (Molecular Weight = 584.38 g/mol, 0.026 mmol) in 12.83 mL of deionized
water in a 20 ml vial, wrapped in aluminum foil and stored at 4 ∘C. Final
solutions were prepared in a 4 mL cuvette by adding 0.6 mL of DI water
followed by 0.4 mL of corresponding buffer solution (pH 1-4) and equilibrated
for 10 minutes. After which, 1 mL of MCH-para stock solution was added and
equilibrated for 15 minutes in the dark.

### Materials

Surfactants, SP-DA-PEG and MCH-para, were synthesized in the laboratory (SI
Appendix, Note S1). Buffer solutions were prepared in the laboratory by adding
NaOH or HCl to Na2HPO4 and NaH2PO4 solutions (reagents were obtained from
Sigma Aldrich, Oakwood Chemical, or Fisher Scientific). Solvents, deionized
water and toluene, were purchased from Sigma-Aldrich. Lubricant oil, Krytox
GPL 100, was supplied by Miller-Stephenson. PTFE thin films were obtained from
Sterlitech (PTFE unlaminated membrane filters, 0.2 micron, 90 mm; the typical
porosity of the PTFE is 90%). SiO2 microsepheric tracer particles were
obtained from Cospheric (sliver-coated hollow glass microsphere 25 - 65
$\mu$m, 0.9 g/cm3). All reagents were of analytical grade and used as
received.

### Light sources

A custom multiline argon ion UV laser (351.1 & 363.8 nm) with a beam diameter
of 1.3 mm and maximum light intensity of 44 mW/mm2 was used for SP-DA-PEG
droplet movement experiments. The fiber-coupled 365 nm UV LED (M365FP1, 9.8 mW
Min Fiber-Coupled LED), 470 nm blue LEDs (M470F3, 17.2 mW Min Fiber-Coupled
LED and M470L3-C1, 350 mW Collimated LED), 530 nm green LED (M530F2, 6.8 mW
Min Fiber-Coupled LED) and white LED (MCWHF2, 21.5 mW Min Fiber-Coupled LED)
were directly bought from Thorlabs, Inc. The blue laser was built with
complete laser diode (LD) operation starter sets from Thorlabs, Inc, including
a laser diode controller (LDC 200C), a thermoelectric temperature controller
(TED 200C), and a 450 nm blue laser diode (L450P1600MM 1600 mW, 5.6 mm, G Pin
Code, MM). A high-intensity UV lamp (216 mm x 140 mm, UVP High Intensity Lamp,
Analytik Jena) coupled with an ND filter (Thorlabs NDL-10C-2) was used to
conduct experiments on driving SP-DA-PEG droplet motion.

### Instrument and Characterization

Surface tension, interfacial tension and contact angle were characterized
using a standard pendant drop method on commercial tensiometer, Biolin
Scientific, Theta Flex. Optical power was measured by using optical power
meter (Newport, 843-R) connected with a thermopile Sensor (Newport
919P-003-10, 3 W, 10 mm, 0.19-11 $\mu$m). Optical images and videos were taken
by a Canon EOS 80D camera. IR images were recorded by a high-performance
Telops M3K infrared camera. UV–Vis absorption spectra were recorded on an
Agilent 8453 UV–Vis spectrometer from 200 to 1200 nm wavelengths. 1H and 13C
NMR spectra were recorded on a Bruker 500 MHz NMR spectrometer. The pH of the
solutions was measured by using a Thermo Scientific Orion Star™ A111 Benchtop
pH Meter. The scanning electron microscope (SEM) image was obtained from a FEI
Sirion SEM.

### Fabrication of the lubricant-infused surface (LIS)

A porous thin film PTFE was obtained from Sterlitech. PTFE film is cut into
pieces and adhered to a flat surface, such as a silicon wafer or a microscopy
slide. Extra ethanol was applied to the PTFE and allowed to completely
infiltrate before evaporating at room temperature in the fume hood. To create
the lubricant-infused surface (LIS), inject Krytox GPL 100 lubricant oil into
the PTFE that was adhered to the solid, flat surface.

### Data Availability

The data described in this article are available in figshare at
10.6084/m9.figshare.22732736 and 10.6084/m9.figshare.21866181

## Acknowledgements

Research reported in this publication was supported by the Center for the
Advancement of Science in Space, the National Science Foundation, and
sponsored by the International Space Station National Laboratory under grant
number 2025655. The NMR results reported here benefited from the shared
analytical instrumentation of the Spectroscopy Facility at the UCSB Chemistry
and Biochemistry Department. We thank Vijay Kumar from UCSB for assistance in
the construction of the custom syringe heating system and IR temperature
measurements.

## References

  * [1] Fengyue Wang, Ning Xu, Wei Zhao, Lin Zhou, Pengcheng Zhu, Xueyang Wang, Bin Zhu, and Jia Zhu.  A high-performing single-stage invert-structured solar water purifier through enhanced absorption and condensation.  Joule, 5(6):1602–1612, 2021.
  * [2] Hyeongyun Cha, Hamed Vahabi, Alex Wu, Shreyas Chavan, Moon-Kyung Kim, Soumyadip Sett, Stephen A Bosch, Wei Wang, Arun K Kota, and Nenad Miljkovic.  Dropwise condensation on solid hydrophilic surfaces.  Science advances, 6(2):eaax0746, 2020.
  * [3] Muhammad Jahidul Hoque, Soumyadip Sett, Xiao Yan, Derrick Liu, Kazi Fazle Rabbi, Haoyun Qiu, Mansoor Qureshi, George Barac, Leslie Bolton, and Nenad Miljkovic.  Life span of slippery lubricant infused surfaces.  ACS Applied Materials & Interfaces, 14(3):4598–4611, 2022.
  * [4] Kyoo-Chul Park, Philseok Kim, Alison Grinthal, Neil He, David Fox, James C Weaver, and Joanna Aizenberg.  Condensation on slippery asymmetric bumps.  Nature, 531(7592):78–82, 2016.
  * [5] Nenad Miljkovic, Ryan Enright, Youngsuk Nam, Ken Lopez, Nicholas Dou, Jean Sack, and Evelyn N Wang.  Jumping-droplet-enhanced condensation on scalable superhydrophobic nanostructured surfaces.  Nano letters, 13(1):179–187, 2013.
  * [6] Jia Li, Noel S Ha, Tingyi‘Leo’ Liu, R Michael van Dam, and Chang-Jin CJ’Kim.  Ionic-surfactant-mediated electro-dewetting for digital microfluidics.  Nature, 572(7770):507–510, 2019.
  * [7] Shingo Honda, Yoshihiro Minagawa, Hiroyuki Noji, and Kazuhito V Tabata.  Multidimensional digital bioassay platform based on an air-sealed femtoliter reactor array device.  Analytical Chemistry, 93(13):5494–5502, 2021.
  * [8] Inkyu Oh, Hyeongyun Cha, Jiehao Chen, Shreyas Chavan, Hyunjoon Kong, Nenad Miljkovic, and Yuhang Hu.  Enhanced condensation on liquid-infused nanoporous surfaces by vibration-assisted droplet sweeping.  ACS nano, 14(10):13367–13379, 2020.
  * [9] Huawei Chen, Pengfei Zhang, Liwen Zhang, Hongliang Liu, Ying Jiang, Deyuan Zhang, Zhiwu Han, and Lei Jiang.  Continuous directional water transport on the peristome surface of nepenthes alata.  Nature, 532(7597):85–89, 2016.
  * [10] Huawei Chen, Tong Ran, Yang Gan, Jiajia Zhou, Yi Zhang, Liwen Zhang, Deyuan Zhang, and Lei Jiang.  Ultrafast water harvesting and transport in hierarchical microchannels.  Nature materials, 17(10):935–942, 2018.
  * [11] Shile Feng, Joachim Delannoy, Antoine Malod, Huanxi Zheng, David Quéré, and Zuankai Wang.  Tip-induced flipping of droplets on janus pillars: From local reconfiguration to global transport.  Science advances, 6(28):eabb4540, 2020.
  * [12] Kai Zhuang, Yao Lu, Xiaolei Wang, and Xiaolong Yang.  Architecture-driven fast droplet transport without mass loss.  Langmuir, 37(43):12519–12528, 2021.
  * [13] Gaby Launay, Muhammad Subkhi Sadullah, Glen McHale, Rodrigo Ledesma-Aguilar, Halim Kusumaatmaja, and Gary G Wells.  Self-propelled droplet transport on shaped-liquid surfaces.  Scientific reports, 10(1):1–8, 2020.
  * [14] Shile Feng, Pingan Zhu, Huanxi Zheng, Haiyang Zhan, Chen Chen, Jiaqian Li, Liqiu Wang, Xi Yao, Yahua Liu, and Zuankai Wang.  Three-dimensional capillary ratchet-induced liquid directional steering.  Science, 373(6561):1344–1348, 2021.
  * [15] Cunjing Lv, Chao Chen, Yin-Chuan Chuang, Fan-Gang Tseng, Yajun Yin, Francois Grey, and Quanshui Zheng.  Substrate curvature gradient drives rapid droplet motion.  Physical review letters, 113(2):026101, 2014.
  * [16] Manoj K Chaudhury and George M Whitesides.  How to make water run uphill.  Science, 256(5063):1539–1541, 1992.
  * [17] Hao Bai, Lin Wang, Jie Ju, Ruize Sun, Yongmei Zheng, and Lei Jiang.  Efficient water collection on integrative bioinspired surfaces with star-shaped wettability patterns.  Advanced Materials, 26(29):5025–5030, 2014.
  * [18] Susan Daniel, Manoj K Chaudhury, and John C Chen.  Fast drop movements resulting from the phase change on a gradient surface.  Science, 291(5504):633–636, 2001.
  * [19] Zilong Deng, Chengbin Zhang, Chaoqun Shen, Jianguang Cao, and Yongping Chen.  Self-propelled dropwise condensation on a gradient surface.  International Journal of Heat and Mass Transfer, 114:419–429, 2017\.
  * [20] H Jeremy Cho, Jordan P Mizerak, and Evelyn N Wang.  Turning bubbles on and off during boiling using charged surfactants.  Nature communications, 6(1):1–7, 2015.
  * [21] S Ravi Annapragada, Susmita Dash, Suresh V Garimella, and Jayathi Y Murthy.  Dynamics of droplet motion under electrowetting actuation.  In International Electronic Packaging Technical Conference and Exhibition, volume 44618, pages 693–701, 2011.
  * [22] Cong Liu, Yihan Sun, Jinxia Huanng, Zhiguang Guo, and Weimin Liu.  External-field-induced directional droplet transport: A review.  Advances in Colloid and Interface Science, 295:102502, 2021.
  * [23] Yangying Zhu, Dion S Antao, Rong Xiao, and Evelyn N Wang.  Real-time manipulation with magnetically tunable structures.  Advanced Materials, 26(37):6442–6446, 2014.
  * [24] Wenwei Lei, Guanglei Hou, Mingjie Liu, Qinfeng Rong, Yichao Xu, Ye Tian, and Lei Jiang.  High-speed transport of liquid droplets in magnetic tubular microactuators.  Science advances, 4(12):eaau8767, 2018.
  * [25] An Li, Huizeng Li, Zheng Li, Zhipeng Zhao, Kaixuan Li, Mingzhu Li, and Yanlin Song.  Programmable droplet manipulation by a magnetic-actuated robot.  Science advances, 6(7):eaay5808, 2020.
  * [26] Karim S Khalil, Seyed Reza Mahmoudi, Numan Abu-Dheir, and Kripa K Varanasi.  Active surfaces: Ferrofluid-impregnated surfaces for active manipulation of droplets.  Applied physics letters, 105(4):041604, 2014.
  * [27] Zichao Yuan, Chenguang Lu, Cong Liu, Xiangge Bai, Lei Zhao, Shile Feng, and Yahua Liu.  Ultrasonic tweezer for multifunctional droplet manipulation.  Science Advances, 9(16):eadg2352, 2023.
  * [28] Lauren D Zarzar, Philseok Kim, and Joanna Aizenberg.  Bio-inspired design of submerged hydrogel-actuated polymer microstructures operating in response to ph.  Advanced materials, 23(12):1442–1446, 2011.
  * [29] Ximin He, Michael Aizenberg, Olga Kuksenok, Lauren D Zarzar, Ankita Shastri, Anna C Balazs, and Joanna Aizenberg.  Synthetic homeostatic materials with chemo-mechano-chemical self-regulation.  Nature, 487(7406):214–218, 2012.
  * [30] Ryo Yoshida, Katsumi Uchida, Yuzo Kaneko, Kiyotaka Sakai, Akihiko Kikuchi, Yasuhisa Sakurai, and Teruo Okano.  Comb-type grafted hydrogels with rapid deswelling response to temperature changes.  Nature, 374(6519):240–242, 1995.
  * [31] Nada Bjelobrk, Henri-Louis Girard, Srinivas Bengaluru Subramanyam, Hyuk-Min Kwon, David Quéré, and Kripa K Varanasi.  Thermocapillary motion on lubricant-impregnated surfaces.  Physical Review Fluids, 1(6):063902, 2016.
  * [32] Zhijie Yang, Jingjing Wei, Yaroslav I Sobolev, and Bartosz A Grzybowski.  Systems of mechanized and reactive droplets powered by multi-responsive surfactants.  Nature, 553(7688):313–318, 2018.
  * [33] Xichen Liang, Vijay Kumar, Farzad Ahmadi, and Yangying Zhu.  Manipulation of droplets and bubbles for thermal applications.  Droplet, 1(2):80–91, 2022.
  * [34] Damien Baigl.  Photo-actuation of liquids for light-driven microfluidics: state of the art and perspectives.  Lab on a Chip, 12(19):3637–3653, 2012.
  * [35] Rong Wang, Kazuhito Hashimoto, Akira Fujishima, Makota Chikuni, Eiichi Kojima, Atsushi Kitamura, Mitsuhide Shimohigoshi, and Toshiya Watanabe.  Light-induced amphiphilic surfaces.  Nature, 388(6641):431–432, 1997.
  * [36] Ren-De Sun, Akira Nakajima, Akira Fujishima, Toshiya Watanabe, and Kazuhito Hashimoto.  Photoinduced surface wettability conversion of zno and tio2 thin films.  The Journal of Physical Chemistry B, 105(10):1984–1990, 2001.
  * [37] Craig Hoffman and Ronald Driggers.  Encyclopedia of Optical and Photonic Engineering (Print)-Five Volume Set.  CRC Press, 2015.
  * [38] Lei Zhao, Serena Seshadri, Xichen Liang, Sophia J Bailey, Michael Haggmark, Michael Gordon, Matthew E Helgeson, Javier Read de Alaniz, Paolo Luzzatto-Fegiz, and Yangying Zhu.  Depinning of multiphase fluid using light and photo-responsive surfactants.  ACS central science, 8(2):235–245, 2022.
  * [39] Lauren D Zarzar, Vishnu Sresht, Ellen M Sletten, Julia A Kalow, Daniel Blankschtein, and Timothy M Swager.  Dynamically reconfigurable complex emulsions via tunable interfacial tensions.  Nature, 518(7540):520–524, 2015.
  * [40] Cunjing Lv, Subramanyan Namboodiri Varanakkottu, Tobias Baier, and Steffen Hardt.  Controlling the trajectories of nano/micro particles using light-actuated marangoni flow.  Nano Letters, 18(11):6924–6930, 2018.
  * [41] Yang Xiao, Sara Zarghami, Klaudia Wagner, Pawel Wagner, Keith C Gordon, Larisa Florea, Dermot Diamond, and David L Officer.  Moving droplets in 3d using light.  Advanced Materials, 30(35):1801821, 2018.
  * [42] Antoine Diguet, Reine-Marie Guillermic, Nobuyuki Magome, Arnaud Saint-Jalmes, Yong Chen, Kenichi Yoshikawa, and Damien Baigl.  Photomanipulation of a droplet by the chromocapillary effect.  Angewandte Chemie International Edition, 48(49):9281–9284, 2009\.
  * [43] Valentine K Johns, Zhuozhi Wang, Xinxue Li, and Yi Liao.  Physicochemical study of a metastable-state photoacid.  The Journal of Physical Chemistry A, 117(49):13101–13104, 2013\.
  * [44] Taku Satoh, Kimio Sumaru, Toshiyuki Takagi, Katsuki Takai, and Toshiyuki Kanamori.  Isomerization of spirobenzopyrans bearing electron-donating and electron-withdrawing groups in acidic aqueous solutions.  Physical Chemistry Chemical Physics, 13(16):7322–7329, 2011.
  * [45] Laura Wimberger, Shyamal KK Prasad, Martin D Peeks, Joakim Andréasson, Timothy W Schmidt, and Jonathon E Beves.  Large, tunable, and reversible ph changes by merocyanine photoacids.  Journal of the American Chemical Society, 143(49):20758–20768, 2021\.
  * [46] Martin Hammarson, Jesper R Nilsson, Shiming Li, Tamás Beke-Somfai, and Joakim Andréasson.  Characterization of the thermal and photoinduced reactions of photochromic spiropyrans in aqueous solution.  The Journal of Physical Chemistry B, 117(43):13561–13571, 2013\.
  * [47] Cesare Berton, Daniel Maria Busiello, Stefano Zamuner, Rosario Scopelliti, Farzaneh Fadaei-Tirani, Kay Severin, and Cristian Pezzato.  Light-switchable buffers.  Angewandte Chemie, 133(40):21905–21908, 2021.
  * [48] Qiushi Zhang, Yunsong Pang, Jarrod Schiffbauer, Aleksandar Jemcov, Hsueh-Chia Chang, Eungkyu Lee, and Tengfei Luo.  Light-guided surface plasmonic bubble movement via contact line de-pinning by in-situ deposited plasmonic nanoparticle heating.  ACS applied materials & interfaces, 11(51):48525–48532, 2019.
  * [49] Aiting Gao, Hans-Jörgen Butt, Werner Steffen, and Clarissa Schönecker.  Optical manipulation of liquids by thermal marangoni flow along the air–water interfaces of a superhydrophobic surface.  Langmuir, 37(29):8677–8686, 2021.
  * [50] Serena Seshadri, Luke F Gockowski, Jaejun Lee, Miranda Sroda, Matthew E Helgeson, Javier Read de Alaniz, and Megan T Valentine.  Self-regulating photochemical Rayleigh-Bénard convection using a highly-absorbing organic photoswitch.  Nat. Commun., 11(1):2599, May 2020.
  * [51] Serena Seshadri, Sophia J Bailey, Lei Zhao, Julia Fisher, Miranda Sroda, Michelle Chiu, Friedrich Stricker, Megan T Valentine, Javier Read de Alaniz, and Matthew E Helgeson.  Influence of polarity change and photophysical effects on photosurfactant-driven wetting.  Langmuir, 37(33):9939–9951, 2021.
  * [52] Nada Bjelobrk, Henri-Louis Girard, Srinivas Bengaluru Subramanyam, Hyuk-Min Kwon, David Quéré, and Kripa K Varanasi.  Thermocapillary motion on lubricant-impregnated surfaces.  Phys. Rev. Fluids, 1(6):063902, October 2016.

## Supporting Information

### Synthesis and Characterization of SP-DA-PEG and MCH-para

#### Materials and Instrumentation

All reagents were obtained from Sigma Aldrich, Oakwood Chemical, or Fisher
Scientific and were used as received without further purification unless
specified. Acetonitrile and dichloromethane were dispensed from a solvent
purification system immediately before use or stored over 3Å molecular sieves.
Ethanol and chloroform were stored over 3Å molecular sieves before use.
Analytical thin-layer chromatography (TLC) was performed with Merck silica gel
60 F254 pre-coated glass plates and visualized by UV light or stained with
p-anisaldehyde. 1H and 13C NMR spectra were recorded on a Bruker 500 MHz NMR
spectrometer. Chemical shifts are reported relative to residual solvent peaks
($\delta$ 7.26 ppm for CDCl3, 2.50 ppm for DMSO-_d 6_:) in 1H NMR, and
$\delta$ 77.20 ppm for CDCl3, 39.52 ppm for DMSO-_d 6_ in 13C NMR).

#### UV–Vis spectroscopy and UV–Vis kinetic measurements

UV–Vis absorption spectra were recorded on an Agilent 8453 UV–Vis spectrometer
from 200 to 1200 nm wavelengths. The photoinduced optical absorption kinetics
of SP-DA-PEG and MCH-para were measured on a custom pump-probe setup. The pump
beam was generated by a high-power LED (light-emitting diode) source
(Thorlabs) coupled into a multimode optical fiber terminated with an output
collimator. The UV pump source was generated by the fiber-coupled UV LED
(Thorlabs M365FP1, 365 nm, 9.8 mW Min Fiber-Coupled LED); the green pump
source was produced by green LED (Thorlabs M530F2, 530 nm 6.8 mW Min Fiber-
Coupled LED) and the blue pump source by blue LED (M470F3, 17.2 mW Min Fiber-
Coupled LED), which was positioned to illuminate the sample directly. The
probe beam was generated by a High-Power MINI Deuterium Tungsten Halogen
Source (Ocean Optics DH-MINI) w/shutter 200-2000 nm coupled into a multimode
optical fiber terminated with an output collimator. The probe light was
altered by a shutter (Uniblitz CS25) and controlled manually or through a
digital output port (National Instruments USB-6009) using the LabVIEW program.
A 10x10 mm2 rectangular spectrophotometer cell was placed in a sample holder.
The solution was continuously stirred by a miniature stirring plate inserted
into the sample holder (Starna Cells SCS 1.11). A system of lenses directed
the probe beam into the detector (Ocean Optics Flame-S1-XR spectrometer),
which acquired the spectra of the probe light. The detector was connected to a
PC via a USB port. The experiment was controlled by a National Instrument
LabVIEW program which collected the probe light spectra, determined sample
optical absorption spectra, and controlled pump and probe light sources.
Kinetics experiments with SP-DA-PEG were performed in 0.05 mM solutions (SI
Appendix, Fig. S1 A and B).

Figure S1: Pump probe kinetics measurements of SP-DA-PEG in (A) water with
alternative 365 nm and 530 nm lights and (B) toluene irradiated with 365 nm
light.

#### Solution preparation for the experiments and UV-Vis studies

Solution preparation procedures were modified from Wimberger et al [45].

##### 1\. Monobasic buffer preparation:

Buffer solutions ranging from pH 1-10 were prepared by adding NaOH (1 M) or
HCl (1 M) to Na2HPO4 and NaH2PO4 solutions (100 mM). DI water was used for all
solutions and buffers. The pH of the final solutions was measured by Thermo
Scientific Orion Star™ A111 Benchtop pH Meter. Prepared buffers were used for
both UV-Vis studies and experiments.

##### 2\. The following procedure was used for experiments:

The stock solution of MCH-para (C = 2 mM) was prepared by adding 15 mg
(Molecular Weight = 584.38 g/mol, 0.026 mmol) in 12.83 mL of DI water in 20 mL
vial, wrapped in aluminum foil and stored at 4 ∘C. Final solutions were
prepared in a 2 mL cuvette by adding 0.6 mL of DI water followed by 0.4 mL of
corresponding buffer solution (pH 1-4) and equilibrated for 10 minutes. After
which, 1 mL of MCH-para stock solution was added and equilibrated for 15
minutes in the dark.

##### 3\. UV-Vis samples were prepared as follows:

The stock solution of the MCH-para (C = 0.25 mM) was prepared by adding 14.6
mg (Molecular Weight = 584.38 g/mol, 0.025 mmol) in 100 mL of DI water into a
volumetric flask wrapped in aluminum foil and stored at 4 ∘C. Solutions for
UV-Vis analysis were prepared in a 1 cm cuvette by adding 0.57 mL of the
corresponding phosphate buffer (pH 1-10) followed by 2.052 mL of DI water,
placed in the spectrophotometer, and allowed to equilibrate thermally for 10
minutes. Then 0.228 mL of MCH-para stock solution was added to the final
concentration of C = 0.020 mM, with continuous stirring of the solution. Scans
were collected after 15 minutes of equilibration in the dark.

#### Synthesis

##### 1\. Synthesis of SP-DA-PEG:

SP-DA-PEG and its precursors SP-NBD and Mal-PEG were synthesized as previously
reported by Seshadri et al. [51]. and kept under a nitrogen atmosphere at 0
°C. Spectral data matches those reported in the literature [51, 38].
1H NMR (500 MHz, CDCl3) $\delta$ 8.02–8.00 (m, 2H), 7.20 (t, 1H), 7.08 (d,
1H), 6.93 (dd, 1H), 6.89 (t, 1H), 6.75 (d, 1H), 6.67(d, 1H), 5.89 (d, 1H),
4.68 (dd, 1H), 4.30 (dd, 1H) 4.27–4.19 (m, 4H), 3.64 (m, 47H), 3.55–3.53 (m,
2H), 3.38 (s, 3H), 2.63–2.54 (m, 4H), 2.48–2.45 (m, 2H), 2.19–2.14 (m, 1H),
1.82–1.77 (m, 1H), 1.71 (d, 1H), 1.50–1.47 (m, 2H) 1.37–1.18 (m, 9H), 1.17 (s,
3H), 0.87 (t, 3H) ppm. Mn(NMR) = 1390 g/mol.

##### 2\. Synthesis of merocyanine MCH-para:

###### 5-Methoxy-2,3,3-trimethyl-3H-indole

Synthesis of 5-Methoxy-2,3,3-trimethyl-3H-indole was adapted from Wimberger et
al [45]. To a solution of 3-methyl-2-butanone (2.48 mL, 2.0 g, 23.2 mmol, 2.00
eq.) in 50 mL of glacial acetic acid was added 4-methoxyphenylhydrazine
hydrochloride (2.0 g, 11.6 mmol, 1.00 eq.). The mixture was heated to 140 ∘C
for 20 min to dissolve 4-methoxyphenylhydrazine hydrochloride completely. The
purple solution was stirred at room temperature overnight, after which
potassium hydroxide pellets were added slowly to neutralize the mixture. The
solution was extracted with diethyl ether (3 × 50 mL), and the combined
organic phases were washed with brine (35 mL), dried over magnesium sulfate,
and concentrated under reduced pressure. The final product can be purified by
column chromatography (hex/EtOAc = 7/3 → 1/1) if necessary. 1.76 g (80%
yield). Due to possible decomposition at room temperature, the product was
kept in the fridge.
1H NMR (500 MHz, CDCl3) $\delta$ 7.43 (dd, _J_ = 8.2, 0.7 Hz, 1H), 6.87 – 6.78
(m, 2H), 3.83 (s, 3H), 2.24 (s, 3H), 1.28 (s, 6H) ppm.
Spectral data matches the reported literature [45].

Figure S2: 1H NMR spectrum of 5-Methoxy-2,3,3-trimethyl-3H-indole.

###### 5-Methoxy-2,3,3-trimethyl-1-(3-(trimethylammonio)propyl)-3H-indol-1-ium
dibromide

Synthesis of
5-Methoxy-2,3,3-trimethyl-1-(3-(trimethylammonio)propyl)-3H-indol-1-ium
dibromide was adapted from Wimberger et al [45]. To an oven-dry round bottom
flask equipped with a magnetic stir bar, a condenser was added
(3-bromopropyl)trimethyl-ammonium dibromide (1.5 g, 5.75 mmol, 1.10 eq)
followed by a 5-methoxy-2,3,3-trimethyl-3H-indole (0.99 g, 5.22 mmol, 1.00
eq.) in deoxygenated absolute acetonitrile (25 mL). The reaction mixture was
heated to 100 ∘C and refluxed under a nitrogen atmosphere for three days.
After cooling down to room temperature, acetonitrile was removed under reduced
pressure. The resulting purple solid was dissolved in 70 ml of water and
washed with diethyl ether (3 × 40 mL) to remove impurities. The aqueous phase
was evaporated in a vacuum, and the product was dissolved in a minimum amount
of methanol and precipitated in cold diethyl ether, filtered, and dried in a
vacuum oven overnight. The final product contains a small amount of
(3-bromopropyl)trimethyl-ammonium dibromide, which due to similar solubility,
was impossible to remove. Therefore, it was used without further purification.
1.69 g (72% yield).
1H NMR (500 MHz, DMSO-_d 6_:) $\delta$ 7.99 (d, _J_ = 8.9 Hz, 1H), 7.51 (d,
_J_ = 2.5 Hz, 1H), 7.17 (dd, _J_ = 8.9, 2.5 Hz, 1H), 4.46 (t, _J_ = 8.0 Hz,
2H), 3.87 (s, 3H), 3.60 – 3.57 (m, 2H), 3.11 (s, 9H), 2.85 (s, 3H), 2.32 (qt,
_J_ = 7.9, 4.9 Hz, 2H), 1.54 (s, 6H) ppm.

Figure S3: 1H NMR spectrum of
5-Methoxy-2,3,3-trimethyl-1-(3-(trimethylammonio)propyl)-3H-indol-1-ium
dibromide.

######
(E)-2-(2-hydroxy-4-methoxystyryl)-5-methoxy-3,3-dimethyl-1-(3-(trimethylammonio)propyl)-3H-indol-1-ium
dibromide) (MCH-para)

To an oven-dry three-neck round-bottom flask equipped with a magnetic stir bar
and condenser was added 2-hydroxy-4-methoxybenzaldehyde (0.30 g, 1.96 mmol,
1.4 eq.) to a solution of
5-methoxy-2,3,3-trimethyl-1-(3-(trimethylammonio)propyl)-3H-indol-1-ium
dibromide (0.7 g, 90 wt%, 1.40 mmol, 1.00 eq.), in 10 mL of anhydrous ethanol
under nitrogen atmosphere. The reaction mixture was heated to 100 ∘C and
refluxed under an inert atmosphere for 26 hours. After letting the solution
cool down to room temperature, it was precipitated in cold diethyl ether and
washed with a considerable amount of cold dichloromethane or acetone to remove
the excess amount of 2-hydroxy-4-methoxybenzaldehyde. 0.52 g (68% yield).

###### Merocyanine form:

1H NMR (500 MHz, DMSO-_d 6_:) $\delta$ 11.25 (s, 1H), 8.49 (d, _J_ = 16.0 Hz,
1H), 8.20 (d, _J_ = 8.9 Hz, 1H), 7.87 (d, _J_ = 8.9 Hz, 1H), 7.53 (d, _J_ =
2.5 Hz, 1H), 7.47 (d, _J_ = 16.1 Hz, 1H), 7.16 (dd, _J_ = 8.8, 2.5 Hz, 1H),
6.64 (dd, _J_ = 8.9, 2.5 Hz, 1H), 6.60 (d, _J_ = 2.4 Hz, 1H), 4.57 (t, _J_ =
7.8 Hz, 2H), 3.89 (s, 3H), 3.85 (s, 3H), 3.64 – 3.58 (m, 2H), 3.11 (s, 9H),
2.28 (td, _J_ = 10.1, 6.0 Hz, 2H), 1.76 (s, 6H) ppm.
13C NMR (126 MHz, DMSO-_d 6_:) $\delta$ 179.63, 165.90, 161.45, 160.31,
147.71, 145.10, 134.07, 132.04, 115.65, 115.17, 114.65, 108.94, 108.23,
108.13, 100.67, 62.06, 56.20, 55.76, 52.55, 51.56, 43.11, 26.83, 21.73 ppm.

Figure S4:1H NMR spectrum of
5-Methoxy-2,3,3-trimethyl-1-(3-(trimethylammonio)propyl)-3H-indol-1-ium
dibromide.

Figure S5: 1H NMR spectrum of
5-Methoxy-2,3,3-trimethyl-1-(3-(trimethylammonio)propyl)-3H-indol-1-ium
dibromide.

### Stability of SP-DA-PEG and MCH-para in water solutions

The stability of SP-DA-PEG and MCH-para is estimated by recording UV–Vis
absorption spectra with an Agilent 8453 UV–Vis spectrometer and measuring
surface tension with a commercial tensiometer (Theta Flex, Biolin Scientific).
The 0.05 mM SP-DA-PEG solution was prepared as outlined in the methods and
stored in a cool, dark environment. Weekly measurements of its UV–Vis spectra
are depicted in SI Appendix, Figure S6 A. After eight weeks, the SP peak
shifts and decreases, indicating hydrolysis-induced degradation. Additionally,
using the standard pendant drop method, the change in surface tension of a
fresh SP-DA-PEG aqueous solution was measured in an inert gas, nitrogen. As
shown in Figure S6 B, the peak decreases as the exposure time increases,
indicating that excessive exposure can hasten degradation.

Figure S6: (A) UV-vis absorbance of SP-DA-PEG in water at 0.05 mM over eight
weeks. (B) Surface tension of a solution of 0.2 mM SP-DA-PEG under repeatedly
pulsed UV light.

MCH-para is stable in acidic aqueous media at room temperature for more than
one month. Spectra of UV–Vis absorbance for 1 mM solutions are recorded. In
Figure S7 A, UV-Vis absorbance spectra with a 1–10 pH range indicate that both
MC and MCH states can exist in a solution depending on its acidity. The
equilibrium shifts to the MCH state at pH values between 1 and 4 (Fig. S7 B).
MCH is stable at pH ranges between 1 and 3, as shown in SI Appendix, Figure S7
C, where peak decreases are all less than 10% after six weeks. Since pH 3 has
the greatest surface tension change, for experiments involving the driving
droplet motions, we utilized pH 3 solutions and evaluated the stability of the
corresponding solution weekly (SI Appendix, Figure S7 D).

Figure S7: (A) UV-Vis absorbance spectra of equilibrated coexisting states of
MCH-para aqueous solution over the pH range of 1 to 10. MCH form is the
predominant form in low pH solutions, whereas MC is the predominant form in
high pH solutions. (B) Switching mechanism of MCH-para in aqueous solution (pH
1). (C) UV-Vis spectra of trans-MCH para in low pHs. Red line and blue line
overlap. (D) UV-Vis spectra of MCH-para in aqueous solution at pH 3 from week
1 to week 6.

### Temperature rise of droplet due to heating from light illumination

It is possible for the thermal Marangoni effect induced by irradiating the
substances with light to partially contributes to the droplet motion. Surface
tension of an aqueous solution containing the photo-responsive surfactants as
a function of temperature was measured using the standard pendant drop method
on a commercial tensiometer. The increase in temperature caused by
illumination of light with specific intensity was estimated using an infrared
(IR) camera (Telops M3K). To decouple the photo Marangoni effect from heating
effect under illumination, we first heated the solution to varying
temperatures using a custom syringe heating system and then measured the
surface tension. Several film heater plates were attached to the exterior of
the syringe to heat the solution, and a thermocouple was attached to the
needle to measure the temperature of the injected droplet (SI Appendix, Figure
S8 A). As a result, the relationship between surface tension and temperature
is linear, ranging from 20 ∘C to 60 ∘C (SI Appendix, Figure S8 B). As
temperature increases, surface tension decreases:

$\gamma\left[\frac{\text{mN}}{\text{m}}\right]=-0.26\;T\,[^{\circ}\text{C}]+76.66$
(3)

To further assess the thermal effect, a series of temperature measurement
experiments have been conducted. The emissivity of an aqueous solution
containing 1 mM MCH-para was calibrated with reference to the emissivity of
deionized water. Images of the two droplets show comparable temperature
profiles and heat distributions when two identically sized droplets of
deionized water and MCH-para solution are subjected to the same room
temperature and light conditions (SI Appendix, Figure S8 C). As a result, the
emissivity of water, $\epsilon$ = 1, can be used to estimate the emissivity of
MCH-para. The temperature rise in MCH-para droplet due to blue LED
illumination with an intensity of 31.8 mW/cm2 is small. The collimated 470 nm
LED used to illuminate the droplet is the same one utilized for measuring
surface tension (SI Appendix, Figure S9 A). As comparison, the LED was first
used to heat a water droplet of equal size, resulting in a temperature change
of less than 1 ∘C (SI Appendix, Figure S9 B). Then, the MCH-para droplet was
stabilized at room temperature. After 150 s of heating, the maximum
temperature within the droplet rises from 19.6 ∘C to 20.6 ∘C (SI Appendix,
Figure S9 C and D), resulting in a 0.26 mN/m decrease in surface tension. This
decrease is negligible compared to the total change of 4.4 mN/m in surface
tension (pH = 3) depicted in Figure 1H. The thermal effect caused by
irradiation only accounts for 5.9% of the total change in surface tension. For
blue light with similar intensities, the photo Marangoni effect is the primary
factor that induces shear flow and causes droplet motions.

## Simulations of drops over liquid-infused surfaces

In order to help understand the flow patterns arising within drops on LIS, we
performed simulations using COMSOL Multiphysics. The simulations solved the
Navier-Stokes equations for the transport of mass and momentum in the fluid.
For simplicity, the aqueous drop shape is approximated as a hemisphere, and is
placed on an oil layer of uniform thickness. The flow is assumed steady in a
reference frame moving at a velocity $V$ with drop. Therefore, at the oil-
water interface we enforce no normal flow, and we enforce uniform flow, equal
to $-V$, in the oil layer sufficiently far away from the drop. The bottom of
the oil layer has a no-slip boundary condition in the fixed reference frame,
and therefore has a velocity equal to $-V$ when observed in the frame of
reference moving with the drop. We enforce continuity of tangential velocity
at the drop-oil interface. The effect of the Marangoni stress is captured by
applying a meridional stress along the bottom and top boundaries of the drop.
A refined mesh at the interface and near the endpoints is used to ensure
numerical accuracy.

The pure photo-switch is

$\frac{\partial{C_{\text{A}}}}{\partial{t}}=-a_{\text{BA}}C_{\text{A}}+a_{\text{AB}}{C_{\text{B}}}=-\frac{\partial{C_{\text{B}}}}{\partial{t}}$
(4)

where

$\displaystyle a_{\text{BA}}$
$\displaystyle=\frac{\text{d}a_{\text{BA}}}{\text{d}I_{\text{BA}}}\,I_{\text{BA}}$
(5) $\displaystyle a_{\text{AB}}$ $\displaystyle=\frac{\partial
a_{\text{AB}}}{\partial
I_{\text{AB}}}\,I_{\text{AB}}+a_{\text{AB}}^{\text{dark}}$ (6)

Bulk:

$\displaystyle\vec{\nabla}\cdot\vec{u}$ $\displaystyle=0,$ (7)
$\displaystyle\frac{\partial{\vec{u}}}{\partial{t}}+\vec{\nabla}\cdot(\vec{u}\,\vec{u})$
$\displaystyle=\nu\nabla^{2}\vec{u}-\rho^{-1}\vec{\nabla}p,$ (8)
$\displaystyle\frac{\partial{C_{\text{A}}}}{\partial{t}}+\vec{\nabla}\cdot(\vec{u}\,C_{\text{A}})$
$\displaystyle=D\nabla^{2}C_{\text{A}}-a_{\text{AB}}{C_{\text{A}}}+a_{\text{BA}}{C_{\text{B}}},$
(9)
$\displaystyle\frac{\partial{C_{\text{B}}}}{\partial{t}}+\vec{\nabla}\cdot(\vec{u}\,C_{\text{B}})$
$\displaystyle=D\nabla^{2}C_{\text{B}}+a_{\text{AB}}{C_{\text{A}}}-a_{\text{BA}}{C_{\text{B}}}.$
(10)

On interface:

$\displaystyle\gamma$
$\displaystyle=\gamma_{o}+nRT\Gamma_{\text{m}}\ln\left(1-\frac{\Gamma_{\text{A}}+\Gamma_{\text{B}}}{\Gamma_{\text{m}}}\right)$
(11)
$\displaystyle\frac{\partial{\Gamma_{\text{A}}}}{\partial{t}}+\vec{\nabla}_{\text{I}}\cdot(\vec{u}_{\text{I}}\Gamma_{\text{A}})$
$\displaystyle=D\nabla_{\text{I}}^{2}\Gamma_{\text{A}}+S_{\text{A}}-a_{\text{AB}}{C_{\text{A}}}+a_{\text{BA}}{C_{\text{B}}}$
(12)
$\displaystyle\frac{\partial{\Gamma_{\text{B}}}}{\partial{t}}+\vec{\nabla}_{\text{I}}\cdot(\vec{u}_{\text{I}}\Gamma_{\text{B}})$
$\displaystyle=D\nabla_{\text{I}}^{2}\Gamma_{\text{B}}+S_{\text{B}}+a_{\text{AB}}{C_{\text{A}}}-a_{\text{BA}}{C_{\text{B}}}$
(13) $\displaystyle S_{\text{A}}$
$\displaystyle=\kappa_{\text{ads}}^{\text{A}}\,\left.C_{\text{A}}\right|_{\text{I}}[\Gamma_{\text{m}}-(\Gamma_{\text{A}}+\Gamma_{\text{B}})]-\kappa_{\text{des}}^{\text{A}}\,\Gamma_{\text{A}}$
(14) $\displaystyle S_{\text{B}}$
$\displaystyle=\kappa_{\text{ads}}^{\text{B}}\,\left.C_{\text{B}}\right|_{\text{I}}[\Gamma_{\text{m}}-(\Gamma_{\text{A}}+\Gamma_{\text{B}})]-\kappa_{\text{des}}^{\text{B}}\,\Gamma_{\text{B}}$
(15)
$\displaystyle-D\left.\frac{\partial{C_{\text{A}}}}{\partial{n}}\right|_{\text{I}}$
$\displaystyle=S_{\text{A}}$ (16)
$\displaystyle-D\left.\frac{\partial{C_{\text{B}}}}{\partial{n}}\right|_{\text{I}}$
$\displaystyle=S_{\text{B}}$ (17) $\displaystyle\vec{\nabla}_{\text{I}}\gamma$
$\displaystyle=\mu\left[\left.\frac{\partial\vec{u}}{\partial{n}}\right|_{\text{I}+}-\left.\frac{\partial\vec{u}}{\partial{n}}\right|_{\text{I}-}\right]$
(18)

## Scaling theory for drops in liquid

The Marangoni stress across the drop is of order
$(\gamma_{\text{hi}}-\gamma_{\text{lo}})/R$, where $\gamma_{\text{hi}}$ and
$\gamma_{\text{lo}}$ are the interfacial tension values at the front and rear
of the drop, whereas $R$ is the drop radius. The drop surface area is of order
$R^{2}$; therefore

$F_{\text{Ma}}\sim(\gamma_{\text{hi}}-\gamma_{\text{lo}})R.$ (19)

At low Reynolds numbers $Re=\rho V2R/\mu$ (where $\rho,\mu$ are the Krytox
density and viscosity), the fluid resistance associated with a self-propelled
drop in a fluid whose viscosity is much greater than the drop’s is of order
$F_{\text{drag}}\sim\mu VR$ [52]. Therefore the balance $F_{\text{drag}}\sim
F_{\text{Ma}}$ yields

$V\sim\frac{\gamma_{\text{hi}}-\gamma_{\text{lo}}}{\mu}\quad\text{if}\quad\mu\gg\mu_{\text{drop}},Re\ll
1.$ (20)

We must determine how the difference $\gamma_{\text{hi}}-\gamma_{\text{lo}}$
depends on other parameters, such as drop radius. Let us label
$\gamma_{\text{A}}$ the tension in the rest (dark) state, whereas
$\gamma_{\text{B}}$ is the steady-state value eventually reached under
illumination. Empirically, based on our surface tension measurements, we
approximate the forward switch dynamics (starting in the dark and illuminating
at $t=0$)

$\gamma(t)=\gamma_{\text{B}}+(\gamma_{\text{A}}-\gamma_{\text{B}})\,\text{e}^{-t/\tau_{\text{fwd}}},$
(21)

where $\tau_{\text{fwd}}$ is the timescale for the forward switch. Similarly,
when illumination is stopped from the initial steady state
$\gamma=\gamma_{\text{B}}$, the interfacial tension follows approximately

$\gamma(t)=\gamma_{\text{A}}+(\gamma_{\text{B}}-\gamma_{\text{A}})\,\text{e}^{-t/\tau_{\text{rev}}}$
(22)

where $\tau_{\text{rev}}$ is the timescale for the reverse switch. Here,
$\gamma_{\text{A}},\gamma_{\text{B}},\tau_{\text{rev}}$ and
$\tau_{\text{fwd}}$ are found empirically from surface-tension measurements,
such as those in Fig. Stability of SP-DA-PEG and MCH-para in water solutionsB.

To find expressions for $\gamma_{\text{hi}}$ and $\gamma_{\text{lo}}$, we
derive a set of equations relating the interfacial tensions at key locations
on the drop. We label the solution the leaves the illuminated region of the
drop as $\gamma_{\text{hi}}$. This liquid takes a time
$t_{\text{d}}\sim(2R-d)/V_{\text{I}}$ to reach the rear end of the drop, where
$V_{\text{I}}$ is the fluid velocity scale at the interface and in the
interior of the drop. Therefore, noting that the initial condition is
$\gamma=\gamma_{\text{hi}}$, Eq. 22 becomes:

$\gamma_{\text{lo}}\sim\gamma_{\text{A}}+(\gamma_{\text{hi}}-\gamma_{\text{A}})\,\text{e}^{-t_{\text{d}}/\tau_{\text{rev}}}$
(23)

where $d$ is the light beam diameter. As the liquid recirculates inside the
drop, the photo-surfactant continues its reverse reaction. Even though this
liquid is not at an interface, we can model the value of the interfacial
tension that would arise if this fluid element were placed at an interface
(for brevity, we label this a ‘virtual tension’). Since the liquid has
traveled over a time of order $2t_{\text{d}}$ since it was last illuminated,
when it is about to enter the illuminated region again it will have a virtual
tension, labeled here $\gamma_{\text{1}}$,

$\gamma_{\text{1}}\sim\gamma_{\text{A}}+(\gamma_{\text{hi}}-\gamma_{\text{A}})\,\text{e}^{-2t_{\text{d}}/\tau_{\text{rev}}}$
(24)

The highest surface tension is reached by illumination of this fluid as it
travels a length of order $2d$, over a time $t_{\text{i}}\sim
2d/(VI\tau_{\text{rev}})$,

$\gamma_{\text{hi}}\sim\gamma_{\text{B}}+(\gamma_{\text{1}}-\gamma_{\text{B}})\,\text{e}^{-t_{\text{i}}/\tau_{\text{rev}}}$
(25)

We use Eqs. (23), (24) and (25) in Eq. (20) and eliminate
$\gamma_{\text{1}},\gamma_{\text{hi}}$, and $\gamma_{\text{lo}}$, obtaining:

$V_{Re\ll
1}\sim\frac{\gamma_{\text{hi}}-\gamma_{\text{lo}}}{\mu}\sim\frac{\gamma_{\text{B}}-\gamma_{\text{A}}}{\mu}\,\dfrac{(1-\text{e}^{-t_{\text{d}}/\tau_{\text{rev}}})(1-\text{e}^{-t_{\text{i}}/\tau_{\text{fwd}}})}{1-\text{e}^{-(2{t_{\text{d}}}/{\tau_{\text{rev}}}+{t_{\text{i}}}/{\tau_{\text{fwd}}})}}.$
(26)

If $Re\ll 1$, we can assume $V_{I}\sim V$. Introducing scaling constants
$c_{1}$ and $c_{2}$, we obtain an implicit equation for $V$:

$V_{Re\ll
1}=c_{1}\frac{\gamma_{\text{B}}-\gamma_{\text{A}}}{\mu}\,\dfrac{(1-\text{e}^{-c_{2}t_{\text{d}}/\tau_{\text{rev}}})(1-\text{e}^{-c_{2}t_{\text{i}}/\tau_{\text{fwd}}})}{1-\text{e}^{-c_{2}(2{t_{\text{d}}}/{\tau_{\text{rev}}}+{t_{\text{i}}}/{\tau_{\text{fwd}}})}}.$
(27)

Eq. (27) above is solved by iteration and is used to plot the dotted line in
Fig. 4E. We use $\gamma_{\text{B}}-\gamma_{\text{A}}=0.73$ mN/m, as this is
the value observed after repeated illumination cycles (as exemplified in Fig.
Stability of SP-DA-PEG and MCH-para in water solutionsB), and
$\tau_{\text{fwd}}=0.437\,\text{s},\tau_{\text{rev}}=2.19\,\text{s},\mu=1.24\cdot
10^{-2}$/ kg/(m s), $d=1.3$ mm and $R=(\frac{4}{3\pi}\mathcal{V})^{1/3}$,
where $\mathcal{V}$ is the drop volume. The constants we use are $c_{1}=0.2$
and $c_{2}=0.15$; we note these are of order-one, as should be expected for a
physically plausible scaling theory.

It is instructive to seek an approximation of Eq. (27) for small drops. We
assume that, as $R$ approaches zero, $V$ decreases more slowly that $R$, such
that the ratio $R/(VI\,\tau_{\text{rev}})$ also approaches zero. Since in
practice the beam diameter $d$ is essentially constant, we assume that the
ratio $d/(VI\,\tau_{\text{fwd}})\sim t_{\text{i}}/\tau_{\text{rev}}\gg 1$,
such that, in Eq (27), we neglect the second exponential in the numerator, as
well as the exponential in the denominator:

$V_{Re\ll 1}\approx
c_{1}\frac{\gamma_{\text{B}}-\gamma_{\text{A}}}{\mu}\,(1-\text{e}^{-c_{2}t_{\text{d}}/\tau_{\text{rev}}}).$
(28)

Introducing a Taylor expansion in $t_{\text{d}}/\tau_{\text{rev}}$, neglecting
second-order terms, and solving for $V$, we obtain the explicit expression

$V_{Re\ll
1}\approx\sqrt{c_{1}c_{2}\frac{\gamma_{\text{B}}-\gamma_{\text{A}}}{\mu}\,\dfrac{2R-d}{\tau_{\text{rev}}}},$
(29)

suggesting that for small drops the velocity is highly sensitive to volume, as
$V\sim R^{1/2}\sim\mathcal{V}^{1/6}$.

At large drop volumes, we observe empirically that the velocity decreases
slightly. There are several potential explanations for this observation. We
tentatively consider here the effect of finite Reynolds number, as the larger
drops have $Re=\rho V2R/\mu\sim 4$. For a self-propelled object, the
propulsive thrust $T$ scales as $T\sim\dot{m}\Delta V$, where $\dot{m}$ is the
mass flow rate that is accelerated by a velocity increment $\Delta V$. Here
$\dot{m}\sim\rho(V+\Delta V)\delta^{2}$, where $\delta$ is the half-width of
the faster-moving fluid region behind the drop. Equating the thrust with the
Marangoni force $\sim(\gamma_{\text{hi}}-\gamma_{\text{lo}})R$ we find

$(\gamma_{\text{hi}}-\gamma_{\text{lo}})R\sim\rho(V+\Delta V)\Delta
V\delta^{2}.$ (30)

For large $Re\gg 1$, we use the canonical laminar flow scaling $\delta^{2}\sim
R^{2}\,Re_{\Delta V}^{-1}\sim R\nu\Delta V$. Assuming $\Delta V\sim V$, the
scaling simplifies to

$(\gamma_{\text{hi}}-\gamma_{\text{lo}})\sim\mu\Delta V.$ (31)

To relate $V$ and $\Delta V$, we assume that at $Re\gg 1$ the fluid resistance
scales as $\rho V^{2}R^{2}$. Balancing this fluid resistance with $T$,

$\rho(V+\Delta V)\Delta V\delta^{2}\sim\rho V^{2}R.$ (32)

Using again the assumption $\Delta V\sim V$, Eq. (32) reduces to

$\Delta V\sim V^{2}\frac{R}{\nu}.$ (33)

Substituting (33) into (31), solving for $V$, and introducing scaling
constants $C_{1},C_{2},C_{3}$

$\displaystyle V_{Re\gg 1}$
$\displaystyle=C_{1}\sqrt{\dfrac{\gamma_{\text{hi}}-\gamma_{\text{lo}}}{R\rho}},$
(34) $\displaystyle\gamma_{\text{hi}}-\gamma_{\text{lo}}$
$\displaystyle=(\gamma_{\text{B}}-\gamma_{\text{A}})\,\dfrac{\left[1-\exp\left(-C_{2}\dfrac{2R-d}{V_{\text{I}}\,\tau_{\text{rev}}}\right)\right]\left[1-\exp\left(-C_{2}\dfrac{2d}{V_{\text{I}}\,\tau_{\text{fwd}}}\right)\right]}{1-\exp\left[-C_{2}\left(2\dfrac{2R-d}{V_{\text{I}}\,\tau_{\text{rev}}}+\dfrac{2d}{V_{\text{I}}\,\tau_{\text{fwd}}}\right)\right]},$
(35) $\displaystyle V_{I}$ $\displaystyle=V_{Re\gg 1}+C_{3}\,V_{Re\gg
1}^{2}\dfrac{R}{\nu}.$ (36)

The expression (34) is used to plot the dashed line in Fig. 4E, with
$C_{1}=1.2,C_{2}=3.9,C_{3}=0.1$. For large drops, $V_{Re\gg 1}\sim
R^{-1/2}\sim\mathcal{V}^{-1/6}$. A composite relation of the two Reynolds
number regimes is shown by the continuous line in Fig. 4E, and is obtained
using

$V_{\text{composite}}=\left[(V_{Re\ll 1})^{-m}+(V_{Re\gg
1})^{-m}\right]^{-1/m}$ (37)

where we set $m$=12.

Figure S8: (A) Experimental setup for measuring surface tension at various
temperatures. (B) The response of MCH-para surface tension to temperature. (C)
IR images of the deionized water (right) and the MCH-para aqueous solution
droplet (left; pH = 3) at room temperatrue. Ranges on the legend bar represent
temperatures in ∘C.

Figure S9: (A) Schematic of single droplet IR image capture under collimated
LED illumination (31.8 mW/cm2). (B) IR images of blue light-heated deionized
water droplets. (C) IR images of 1 mM MCH-para water droplet heated by blue
light illuminations. (D) Maximum temperature occurs within the MCH-para
droplet over six minutes.

## Supplementary Figures

Figure S10: The changes in the color of SP-DA-PEG in toluene under UV
illumination. (A) 0.1 mM SP toluene solution transforms from transparent (SP)
to dark blue (MC) under 365 nm UV illumination. (B) After achieving
equilibrium, the MC-rich solution under white light illumination changes color
from dark blue to transparent.

Figure S11: (A) Experimental setup for measuring surface tension under
repeated exposure to corresponding light. (B) Surface tension response of 0.2
mM SP-DA-PEG in water under UV (365 nm) illumination with optical intensities
in the range of 7.7 to 37.1 mW/cm2.

Figure S12: Schematic of a liquid droplet on LIS under UV illumination.
Scanning Electron Microscopy (SEM) image of a porous PTFE substrate.

Figure S13: Surface of a bare 0.2 mM SP-DA-PEG water droplet placed on the
PTFE film.

Figure S14: Contact angle measurements of 1 mM MCH-para in water at pH 3. The
contact angle of MCH-para water droplet on LIS reduced from 117° to 113° upon
blue light (470 nm, 31.8 mW/cm2) irradiation.

Figure S15: Optical images (side view) of a stationary pure DI water droplet
illuminated by UV light with an intensity gradient after passing through an ND
filter. The intensity of the light is greater on the left and weaker on the
right.