Taylor dispersion in an oscillatory squeeze flow of an Oldroyd-B fluid between hydrophobic disks

We investigate the Taylor-Aris dispersion resulting from oscillatory squeeze flow (OSF) of an Oldroyd-B viscoelastic fluid in the gap between two hydrophobic disks. The slippage between the fluid and the surfaces of both disks is modeled using a dynamic slip boundary condition, which accounts for periodic motion and the fluid's rheological properties. The fluid motion is induced by the periodic vertical movement of one of the disks. Using the lubrication approximation, we simplify and solve the governing equations to determine the flow field. We then derive key variables, including the velocity field, pressure distribution, and the force and power associated with OSF. To analyze mass transport, we used the convection-diffusion equation, which we solved using the multiple-timescale homogenization method. This study highlights the influence of various dimensionless parameters that govern hydrodynamics and Taylor dispersion, specifically the Womersley number, two Deborah numbers related to the fluid's relaxation and retardation times, and a slip parameter. Our research focuses on how the slip boundary condition and the fluid's rheology affect the dispersion process and other related variables. A key aspect of our work is to identify conditions that maximize the effective dispersion coefficient under the given assumptions. Our findings indicate that the slip condition generally reduces the dispersion coefficient in an OSF. Furthermore, when comparing the effect on the effective dispersion coefficient using the Oldroyd-B and Maxwell models, we observe that the Maxwell model tends to overestimate the effective dispersion coefficient.