Pulsating Flow of a Viscous Fluid over a Cavity Containing a Compressible Gas Bubble

Abstract

A two-dimensional pulsating flow of a viscous fluid in a plane channel whose wall has rectangular microcavities partially or completely filled with a compressible gas is investigated. This problem formulation can clarify the friction reduction mechanism in a laminar sublayer of a turbulent viscous boundary layer flow over a textured stripped superhydrophobic surface containing periodically arranged rectangular micro-cavities filled with gas. It is assumed that the dimensions of the cavities are much smaller than the channel thickness. On the macroscale, the problem of one-dimensional unsteady viscous flow in a plane channel with no-slip conditions on the walls and a harmonic variation of the pressure difference is solved. The solution obtained in this way is used for formulating non-stationary in time and periodic in space boundary conditions for the flow on the scale of a chosen cavity (microscale), with the instantaneous volume of the gas bubble in the cavity depending on the instantaneous pressure over the cavity. The flow on the microscale near a cavity with a gas bubble occurs in the Stokes regime. The numerical solution is obtained using an original version of the boundary element method. A parametric numerical study of the flow field in a pulsating shear flow over a cavity with a compressible gas bubble is performed. The averaged parameters characterizing the effective ‘velocity slip’ of viscous fluid and the friction reduction in a pulsating flow over a stripped superhydrophobic surface are calculated.

Directional Transport of Underwater Bubbles on Solid Substrates: Principles and Applications

“…The driven force is still the component of buoyancy F driven = ρ l g V sin α. The resistance is mainly dominated by the viscous drag forces that F viscous ∼ μ l vR 2 /δ, where δ is the viscous boundary layer thickness around bubbles that δ ≈ μ l R / ρ l v . , When the driven force is balanced with the viscous drag force F driven = F viscous , the bubble moves at a constant speed: v ∼ ( ρ l g 2 ⁢ sin 2 ⁡ α ) 1 / 3 R μ l − 1 / 3 …”

“…The resistance is mainly dominated by the viscous drag forces that F viscous ∼ μ l vR 2 / δ, where δ is the viscous boundary layer thickness around bubbles that R v / l l . 83,84 When the driven force is balanced with the viscous drag force F driven = F viscous , the bubble moves at a constant speed:…”

Pulsating flow of stationary elastic-viscous fluids in flat-wall channel

“…Many scientific and practical studies have been devoted to the pulsating flows of Newtonian fluids in flat channels and cylindrical pipes by domestic and foreign scientists. In particular, in research studies [1][2][3][4][5][6][7], the stationary oscillation flows of pulsating viscous fluids in channels and pipes have been sufficiently studied. Scientific research on the pulsating flow of viscous fluids was applied to the circulatory system of biomechanics [8][9][10][11][12].…”