I performed an experiment which basically pour 10 ml of crude oil on the water surface in a basin (0.76 m * 0.32 m * 0.18 m), leave the oil spread till reach equilibrium. Then, applying some chemical which cause contraction of the oil slick. This method used in oil spill accidents. See images at t=0 s before applying chemical and at t=13.33s after chemical is applied.
Here is my dimensional analysis
I did initially perform a dimensional analysis for the case with no obstacles, where the oil slick thickness was the dependent variable and the oil surface tension (i.e. spreading coefficient), density, viscosity, gravity, and initial thickness were the independent variables. We found that the final thickness normalized by the initial thickness was a function of a Capillary number and a Weber number, as shown above.
Experiment image t=0 s
Experiment image t= 13.33 s
However, since we only tested a single oil (and thus did not vary the oil surface tension, density, or viscosity), we found this dimensional analysis to be of limited use and thus did not include it in the manuscript. Regarding the reviewer’s specific point, changing oil temperature or weathering state would likely affect the oil viscosity the most. Again, however, the predictive value of this dimensional analysis is limited since the variables we examined in the manuscript related more to the obstacle size and shape.
ρ(oil)= 0.860 g/cm^3
µ(oil)= 11.66 mPa.s = 0.1166 g/cm.s
ρ(water)= 0.997 g/cm^3
µ(water)= 1.002 mPa.s = 0.01002 g/cm.s.
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