Experimental and numerical investigations of the interface profile close to a moving contact line

Abstract

For the problem of one fluid displacing another on a solid surface, Dussan V. et al. (1991) proposed a one-parameter analytical solution (the DRG solution) to describe the dynamic interface shape in the overlap region of the intermediate and the outer regions, for small capillary numbers. In the present study we examined the validity of the DRG solution with both experimental and numerical approaches. Our experiments consisted of displacing air with paraffin oil in parallel (Hele–Shaw) glass cells. The slope of the air–oil interface was measured at distances from the contact line, ranging between 5 and 200 μm. The displacement speeds corresponded to capillary numbers ranging between 4.7×10−6 and 2.6×10−4. Excellent agreement was obtained among the DRG solution, the numerical, and the experimental results in the region >10 μm from the contact line, but systematic deviation was observed in the region close to the contact line. This deviation was confirmed by the numerical simulations that used the finite element method. The measured dynamic contact angle increases with the displacing speed and can be correlated with a power law in Ca, which is similar to Tanner’s law.