We will work with the displacement of phase (fluid) 2 by phase 1 in a uniform radius tube as shown below. Plx = L X = L X = Xf 1 X = 0 P|x = 0 There is a non-zero capillary pressure between fluids 1 and 2, and flow is laminar everywhere without entry/exit effects. The end-to-end pressure difference AP = P -P, is constant. %3D x=DL a. Derive an expression for the velocity of the interface %3D dt 2 TR b. Cast the equation from part a in terms of dimensionless groups: c. Plot the solution to equation F for various values of the parameters.