Experimental and theoretical investigation of a low-Reynolds-number flow through deformable shallow microchannels with ultra-low height-to-width aspect ratios

AbstractWe consider convection–diffusion transport of a passive scalar within porous media having a piecewise-smooth and reflecting pore–grain interface. The corresponding short-time expansion of molecular displacement time-correlation functions is determined for the generalized steady convection field. By interpreting the generalized short-time expansion of dispersion dynamics in the context of low-Reynolds-number flow through macroscopically homogeneous porous media, we demonstrate the connection between hydrodynamic permeability and short-time dynamics. The analytical short-time expansion is compared with numerical simulation data for steady low-Reynolds-number flow through a random close-pack array of mono-disperse spheres. The quadratic short-time expansion term of the dispersion coefficient closely predicts the numerical data for a mean displacement of at least 10 % of the sphere diameter for a Péclet number of 54.49.

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Analysis of Low Reynolds Number Flow through a Pipe with an Annular Protrusion

Bulletin of JSME ◽

10.1299/jsme1958.23.1792 ◽

1980 ◽

Vol 23 (185) ◽

pp. 1792-1797

Author(s):

Kiyoshi TANIUCHI

Keyword(s):

Reynolds Number ◽

Low Reynolds Number ◽

Low Reynolds Number Flow ◽

Reynolds Number Flow ◽

Number Flow ◽

Flow Through ◽

Low Reynolds

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Low-Reynolds-number flow through two-dimensional shunts

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.99 ◽

2013 ◽

Vol 723 ◽

pp. 21-39 ◽

Cited By ~ 3

Author(s):

A. Setchi ◽

A. J. Mestel ◽

K. H. Parker ◽

J. H. Siggers

Keyword(s):

Reynolds Number ◽

Low Reynolds Number ◽

Industrial Applications ◽

Two Dimensional ◽

Low Reynolds Number Flow ◽

Reynolds Number Flow ◽

Flow Profiles ◽

Number Flow ◽

Flow Through ◽

Low Reynolds

AbstractMotivated by numerous biological and industrial applications relating to bypasses, mixing and leakage, we consider low-Reynolds-number flow through a shunt between two channels. An analytical solution for the streamfunction is found by matching biorthogonal expansions of Papkovich–Fadle eigenfunctions in rectangular subregions. The general solution can be adapted to model a variety of interesting problems of flow through two-dimensional shunts by imposing different inlet and outlet flux distributions. We present several such flow profiles but the majority of results relate to the particular problem of a side-to-side anastomosis in the small intestine. We consider different flux fractions through the shunt with particular emphasis on the pressure and recirculating regions, which are important factors in estimating health risks pertaining to this surgical procedure.

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Entrance Length of Low Reynolds Number Flow in Microchannel

Fluids Engineering ◽

10.1115/imece2004-61908 ◽

2004 ◽

Cited By ~ 1

Author(s):

Sang-Youp Lee ◽

Jaesung Jang ◽

Steve T. Wereley

Keyword(s):

Reynolds Number ◽

Low Reynolds Number ◽

Entrance Length ◽

Number Range ◽

Low Reynolds Number Flow ◽

Reynolds Number Flow ◽

Aspect Ratios ◽

Number Flow ◽

Low Reynolds ◽

Microfabrication Techniques

The entrance lengths in rectangular microchannels with planar reservoirs, geometries typically produced with microfabrication techniques, have been investigated in the low Reynolds number range, 1 < ReD < 100. Two microchannels having the complementary aspect ratios (H/W) of 2.75 and 0.37 are fabricated and tested. The hydraulic diameters of two microchannels are ~370 μm and ~56.4 μm. μPIV is used to measure the velocity profiles and the entrance lengths are found from the curve fitted centerline velocity growth. The entrance lengths in the channels with planar upstream reservoirs are found to be significantly different from those with infinite upstream reservoirs.

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