Effective slip due to Stokes flow through channels with patterned stick-slip walls

2011 ◽  
Author(s):  
Hong-man, Herman Mak
Keyword(s):  
Stokes Flow ◽  
Stick Slip ◽  
Effective Slip ◽  
Flow Through

Stokes Flow Through a Periodically Grooved Tube

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Chiu-On Ng ◽  
C. Y. Wang
Keyword(s):  
Stokes Flow ◽  
Slip Length ◽  
Geometrical Parameters ◽  
Slip Boundary ◽  
Effective Slip Length ◽  
Effective Slip ◽  
Flow Through ◽  
Transverse Grooves ◽  
Shear Area ◽  
Fluid Penetration

This is an analytical study on Stokes flow through a tube of which the wall is patterned with periodic transverse grooves filled with an inviscid gas. In one period of the pattern, the fluid flows through an annular groove and an annular rib subject to no-shear and no-slip boundary conditions, respectively. The fluid may penetrate the groove to a certain depth, so there is an abrupt change in the cross section of flow through the two regions. The problem is solved by the method of domain decomposition and eigenfunction expansions, where the coefficients of the expansion series are determined by matching velocities, stress, and pressure on the domain interface. The effective slip length and pressure distributions are examined as functions of the geometrical parameters (tube radius, depth of fluid penetration into grooves, and no-shear area fraction of the wall). Particular attention is paid to the limiting case of flow through annular fins on a no-shear wall. Results are generated for the streamlines, resistance, and pressure drop due to the fins. It is found that the wall condition, whether no-shear or no-slip, will be immaterial when the fin interval is smaller than a certain threshold depending on the orifice ratio.

Oscillatory Flow Through a Channel With Stick-Slip Walls: Complex Navier’s Slip Length

2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Chiu-On Ng ◽  
C. Y. Wang
Keyword(s):  
Oscillation Frequency ◽  
Oscillatory Flow ◽  
Slip Length ◽  
Complex Nature ◽  
Channel Height ◽  
Boundary Slip ◽  
Stick Slip ◽  
Effective Slip ◽  
Flow Through ◽  
Shear Area

Effective slip lengths for pressure-driven oscillatory flow through a parallel-plate channel with boundary slip are deduced using a semi-analytic method of eigenfunction expansions and point matching. The channel walls are each a superhydrophobic surface micropatterned with no-shear alternating with no-slip stripes, which are aligned either parallel or normal to the flow. The slip lengths are complex quantities that are functions of the oscillation frequency, the channel height, and the no-shear area fraction of the wall. The dependence of the complex nature of the slip length on the oscillation frequency is investigated in particular.

scholarly journals Stokes flow through a slit with periodic reabsorption: An application to renal tubule

2016 ◽  
Vol 55 (2) ◽  
pp. 1799-1810 ◽  
Author(s):  
T. Haroon ◽  
A.M. Siddiqui ◽  
A. Shahzad
Keyword(s):  
Stokes Flow ◽  
Renal Tubule ◽  
Flow Through

Stokes Flow Through a Row of Cylinders Between Parallel Walls: Model for the Glomerular Slit Diaphragm

1994 ◽  
Vol 116 (2) ◽  
pp. 184-189 ◽  
Author(s):  
M. Claudia Drumond ◽  
William M. Deen
Keyword(s):  
Stokes Flow ◽  
Stokes Equations ◽  
Slit Diaphragm ◽  
Hydraulic Permeability ◽  
Shear Stresses ◽  
Two Factors ◽  
Additional Resistance ◽  
Flow Through ◽  
Experimental Values ◽  
Glomerular Capillaries

As a model for flow through the slit diaphragms which connect the epithelial foot processes of renal glomerular capillaries, finite element solutions of Stokes equations were obtained for flow perpendicular to a row of cylinders confined between parallel walls. A dimensionless “additional resistance” (f), defined as the increment in resistance above the Poiseuille flow value, was computed for L/W≤4 and 0.1≤ R/L≤0.9, where L is half the distance between cylinder centers, W is half the distance between walls and R is the cylinder radius. Two factors contributed to f: the drag on the cylinders, and the incremental shear stresses on the walls of the channel. Of these two factors, the drag on the cylinders tended to be dominant. A more complex representation of the slit diaphragm, suggested in the literature, was also considered. The predicted hydraulic permeability of the slit diaphragm was compared with experimental values of the overall hydraulic permeability of the glomerular capillary wall.

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