An Approximate Analytical Solution of Flow Fields at the Front of Poiseuille Flows

Abstract

Poiseuille's law predicts the stationary flows of fluids between two solid surfaces. Here we use an approximate treatment to predict the velocity fields at the flow front when a fluid is introduced to the space between solid surfaces. Our theory predicts that the velocity of fluids in the flowing direction decreases, while the velocity in the perpendicular direction increases, as one moves from the bulk to the free surface. This theory predicts an analytical expression of the traveling time, destination, and trajectory of fluid particles that flow through the flow front region and these may be accessible by quantitative measurements. Our theory may be useful to treat the dynamics of soft matters that fill the space between solid surfaces.