We will work with the displacement of phase (fluid) 2 by phase 1 in a uniform...

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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. 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.

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Notice that the gas phase is on the bottom where the pressure is low Solid is on the left where the ... View the full answer