multiplying $\vec{F}_{\tau A}$ with mesh size, i.e. $\Delta A_{w} / \Delta V$: $$\vec{F}_{\tau V}
=
  \vec{F}_{\tau A} \frac{\Delta A_{w}}{\Delta V}
=
  \sigma \cos{\theta_{0}} \frac{\nabla_{2D} \tilde{c}
  {\left( \vec{x} \right)}}{{\left[ c \right]}} \frac{\Delta A_{w}}{\Delta V}
\label{eqn:volumeForce}$$ where $\Delta A_{w}$ is the surface area of the wall in volume $\Delta V$.

While the above equation has the correct limiting behavior, it was found that, due to the diffuse nature of the interface, at too low resolution the interface gets pulled apart. To counter this phenomenon, a modification is proposed to localize the contact line force more to the interface: $$g {\left( \tilde{c} \right)}
=
  H {\left( \pi/2-\theta_{0} \right)} \frac{5}{4} H {\left( \tilde{c}-\frac{1}{5} \right)}
+ H {\left( \theta_{0}-\pi/2 \right)} \frac{5}{4} H {\left( \frac{4}{5}-\tilde{c} \right)}$$ Where $H(x)$ is the Heaviside step function. Depending on the value of the Young’s angle, this function truncates the contact line force. For $\theta_{0} <
\pi/2$ this means that the contact line does not get pulled apart, while for $\theta_{0} > \pi/2$ this prevents the gas phase from being pulled into the droplet at the contact line. The value $5/4$ is to normalize the function. The new function for the contact line restoring force at low resolution thus becomes: $$\vec{F}_{\tau 