average length of the polymer chains, which affects the resistance of the fluid to shear. [@Patterson1998]

  -------------- --------------- -------- ---------- ------- ---------- ------ -----
                                  $\eta$   $\rho_0$   $c_0$   $\sigma$   $K$    $M$
  Silicone Oil     Product No.      ()        ()       ()        ()       ()    ()
  0.5 St            PSF-50cSt                960      1004               0.97  
  10 St           PSF-1,000cSt               971      1004               0.98  
  300 St          PSF-30,000cSt              976      1004               0.98  
  -------------- --------------- -------- ---------- ------- ---------- ------ -----

A series of steady-state rheometry measurements were taken in order to verify the viscosity of the silicone oils presented in Tab. \[table1\] and determine their shear rate sensitivity. The measurements were taken using an Anton Paar MCR 502 rotational rheometer with a concentric cylinder arrangement, which was able to achieve shear rates of for the low and intermediate-viscosity oils and for the high-viscosity oil. Figure \[fig:steadystateviscositytest\] shows the measured dynamic viscosity of the silicone oils as a function of the shear rate. The zero-shear-rate viscosity of the fluids agreed with the manufacturer provided values presented in Tab. \[table1\]. All three oils had a constant viscosity at low shear rates, which was seen to transition to a shear thinning behavior at higher shear rates for the intermediate and high-viscosity oils. The measured zero-shear-rate viscosity ($\eta_0$) 