Unsteady dean flow of dusty fluids between two oscillating cylinders

Abstract

This study investigates the unsteady Dean flow of dusty, viscous, incompressible fluids confined between two oscillating concentric horizontal cylinders under a semi-analytical framework based on Laplace transformation, which is preferred over fully numerical methods due to its ability to provide analytical expressions that enhance understanding of the system dynamics, reduce discretization errors, and efficiently handle complex boundary conditions. The Laplace-domain solutions are numerically inverted using the Riemann-sum approximation (RSA). The problem is modelled using the momentum and continuity equations for fluid and particulate phases, incorporating the effects of azimuthal pressure gradients and oscillatory boundary conditions. The semi-analytical framework is employed to derive the velocity profiles, skin frictions, and vorticity in the Laplace domain, which are then inverted to obtain time-dependent solutions. Steady-state solutions for the velocity, skin frictions, and vorticity (for the case of oscillation with different frequencies, non-oscillating cases, and oscillating with the same frequency) are obtained in closed forms to validate the method employed at large time values. Key dimensionless parameters such as the mass concentration of dust particles, relaxation time, dimensionless time, and angular velocities are explored to assess their impact on the flow dynamics. Results reveal that increasing relaxation time parameters delay the velocity profile and helps fluid velocity in achieving equilibrium flow states. The findings provide a benchmark for studies on industrial mixing, chemical reactors, and biomedical flows involving particle-laden fluids under oscillatory conditions.