Unsteady-state laminar flow of viscoelastic gel and air in a channel: Application to mucus transport in a cough machine simulating trachea

Unsteady laminar flow of two immiscible fluids in a channel due to time-dependent pressure gradient has been considered. One of the fluids is a viscoelastic gel represented by the Maxwell model and the other one is air, which is taken as a Newtonian fluid of low viscosity. An approximate solution valid for small time is obtained by the Laplace transform method. Further, to fully analyze the problem a robust finite-difference scheme, which efficiently handles the sensitive interfacial boundary conditions of the model, has been developed. The analytical and numerical solution qualitative behavior compares favorably with the experimental observations of mucus gel transport in a cough machine.