Low Reynolds Number Transport Properties of Axisymmetric Particles Employing Stick and Slip Boundary Conditions

Existing analyses of the very low Reynolds number Stokes jet, e.g. Birkhoff & Zarantonello (1957) and Förste (1963), have been confined to a single-component fluid satisfying the usual zero-slip boundary conditions at a solid surface. In contrast, the low Reynolds number biological jets which emerge from the pores and channels at the secreting surfaces of numerous human, animal and insect organs entail the movement of water and solute subject to novel boundary conditions that arise from the local osmotic driving forces at the secreting surfaces. These boundary conditions introduce a nonlinear coupling between the fluid momentum and solute conservation equations. This paper first discusses the fundamental dimensionless groups and length scales that characterize these biological jet flows and then examines in detail, using the technique of matched inner and outer expansions, one flow situation important in epithelial membrane transport, namely, the two-dimensional mixing of an inhomogeneous jet with a quiescent outer bathing solution which is bounded by a semi-permeable mem brane in the plane of the exit. The paper concludes with a discussion of other physiologically relevant problems which arise from different orderings of the length scales, and different overall geometrical configurations and flow conditions.

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The Influence of Slip Boundary Conditions on Peristaltic Pumping in a Rectangular Channel

Journal of Fluids Engineering ◽

10.1115/1.3001107 ◽

2008 ◽

Vol 130 (12) ◽

Cited By ~ 4

Author(s):

X. Mandviwalla ◽

R. Archer

Keyword(s):

Reynolds Number ◽

Boundary Conditions ◽

Cross Section ◽

Rectangular Cross Section ◽

Rectangular Channel ◽

Slip Boundary Conditions ◽

Long Wavelength ◽

Slip Boundary ◽

Peristaltic Pumping ◽

Side Walls

The flow of an incompressible fluid is modeled in a channel of a rectangular cross section with two symmetric peristaltic waves propagating on the top and bottom. A low Reynolds number and a long wavelength are assumed. The effect on pumping of the inclusion of slip boundary conditions on the side walls is investigated.

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Investigation of DPD transport properties in modeling bioparticle motion under the effect of external forces: Low Reynolds number and high Schmidt scenarios

The Journal of Chemical Physics ◽

10.1063/1.5079835 ◽

2019 ◽

Vol 150 (5) ◽

pp. 054901 ◽

Cited By ~ 3

Author(s):

Waqas Waheed ◽

Anas Alazzam ◽

Ashraf N. Al-Khateeb ◽

Hyung Jin Sung ◽

Eiyad Abu-Nada

Keyword(s):

Reynolds Number ◽

Transport Properties ◽

Low Reynolds Number ◽

Low Reynolds ◽

External Forces

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Reevaluating the Roles of Eddies in Multiple Barotropic Wind-Driven Gyres

Journal of Physical Oceanography ◽

10.1175/jpo2743.1 ◽

2005 ◽

Vol 35 (7) ◽

pp. 1263-1278 ◽

Cited By ~ 12

Author(s):

Baylor Fox-Kemper

Keyword(s):

Reynolds Number ◽

Boundary Conditions ◽

Wind Forcing ◽

Slip Boundary Conditions ◽

Mean Flow ◽

Transport Efficiency ◽

Slip Boundary ◽

Eddy Transport ◽

Vorticity Flux ◽

Vorticity Transport

Abstract Multiple-gyre ocean models have a weaker mean subtropical circulation than single-gyre calculations with the same viscosity and subtropical forcing. Traditionally, this reduction in circulation is attributed to an intergyre eddy vorticity flux that cancels some of the wind input, part of which does not require a Lagrangian mass exchange (theory of dissipative meandering). Herein the intergyre eddy vorticity flux is shown to be a controlling factor in barotropic models at high Reynolds number only with exactly antisymmetric gyres and slip boundary conditions. Almost no intergyre flux occurs when no-slip boundary conditions are used, yet the subtropical gyre is still significantly weaker in multiple-gyre calculations. Sinuous modes of instability present only in multiple gyres are shown here to vastly increase the eddy vorticity transport efficiency. This increase in efficiency reduces the mean circulation necessary for equilibrium. With slip boundary conditions, the intergyre eddy transport is possibly much larger. However, with wind forcing relevant for the ocean—two unequal gyres—a mean flow flux of vorticity rather than an eddy flux between the regions of opposing wind forcing is increasingly important with increasing Reynolds number. A physical rationalization of the differing results is provided by diagnosis of the equilibrium vorticity budget and eddy transport efficiency. Calculations varying 1) boundary conditions, 2) sources and sinks of vorticity, 3) eddy transport efficiency, and 4) the degree of symmetry of the gyres are discussed.

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