Stokes flow of micropolar fluid past a viscous fluid spheroid with non-zero boundary condition for microrotation

AbstractThe Stokes axisymmetric flow of an incompressible viscous fluid past a micropolar fluid spheroid whose shape deviates slightly from that of a sphere is studied analytically. The boundary conditions used are the vanishing of the normal velocities, the continuity of the tangential velocities, continuity of shear stresses and spin-vorticity relation at the surface of the spheroid. The hydrodynamic drag force acting on the fluid spheroid is calculated. An exact solution of the problem is obtained to the first order in the small parameter characterizing the deformation. It is observed that due to increase spin parameter value, the drag coefficient decreases. Well known results are deduced and comparisons are made with classical viscous fluid and micropolar fluid.

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Stokes Flow Past a Swarm of Deformed Porous Spheroidal Particles with Happel Boundary Condition

Journal of Porous Media ◽

10.1615/jpormedia.v12.i4.50 ◽

2009 ◽

Vol 12 (4) ◽

pp. 347-359 ◽

Cited By ~ 9

Author(s):

Satya Deo

Keyword(s):

Boundary Condition ◽

Stokes Flow ◽

Flow Past

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NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s021820250500039x ◽

2005 ◽

Vol 15 (03) ◽

pp. 343-374 ◽

Cited By ~ 12

Author(s):

GUY BAYADA ◽

NADIA BENHABOUCHA ◽

MICHÈLE CHAMBAT

Keyword(s):

Boundary Condition ◽

Friction Coefficient ◽

Boundary Conditions ◽

Existence And Uniqueness ◽

Micropolar Fluid ◽

Reynolds Equation ◽

Slip Boundary Condition ◽

Slip Boundary ◽

New Models ◽

Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

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Influence of wall roughness on the slip behaviour of viscous fluids

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210507000376 ◽

2008 ◽

Vol 138 (5) ◽

pp. 957-973 ◽

Cited By ~ 14

Author(s):

Dorin Bucur ◽

Eduard Feireisl ◽

Šárka Nečasová

Keyword(s):

Boundary Condition ◽

Viscous Fluid ◽

Boundary Conditions ◽

Limit Problem ◽

Viscous Fluids ◽

Wall Roughness ◽

Effective Boundary ◽

Specific Direction ◽

Friction Term ◽

Effective Boundary Conditions

We consider the stationary equations of a general viscous fluid in an infinite (periodic) slab supplemented with Navier's boundary condition with a friction term on the upper part of the boundary. In addition, we assume that the upper part of the boundary is described by a graph of a function φε, where φε oscillates in a specific direction with amplitude proportional to ε. We identify the limit problem when ε → 0, in particular, the effective boundary conditions.

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