Fluid Mechanics Research Journal (FMRJ)

Research Article

Exact closed-form solutions for the two-fluid oscillatory flow and Navier’s partial slip boundary condition

C.Y. Wang^1,2 and J. Liu¹

¹Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA.

²Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA.

Submitted: April 16, 2020; Accepted: May 31, 2020

Abstract

Two-fluid flows occur when immiscible moving fluids of different properties are in contact. Exact closed- form solutions are presented for oscillatory two-fluid flows. Exact solutions are important not only due for its applicability to specific problems but also serve as accuracy standards for approximate solutions. These oscillatory solutions are governed by geometry, the viscosity ratios, and the normalized frequency s. The velocity profiles for large s are different from those of small s. As s → 0 the solutions may approach a steady-state. For non-zero s there is a phase difference between the two fluids. An important result is that Navier's partial slip condition fails for oscillatory flows.

Keywords

Two-fluid; Oscillatory; Viscous flow; Exact solution; Navier; Slip .

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