Laminar Flow in Porous Ducts

Chellam, Shankararaman; Wiesner, Mark R.; Dawson, Clint; Brown, George R.

doi:10.1515/revce.1995.11.1.53

Cited by 16 publications

(10 citation statements)

References 59 publications

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“…The classic Beavers-Joseph slip condition [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] was originally phrased in terms of the normal derivative of the tangential velocity (i.e., only the first term in square brackets, above), whereas we add the transposed gradient term to make the slip velocity proportional to the wall shear stress-as appears in [27] and [30]. The difference is negligible at macroscopic lengthscales, but becomes significant when the problem is scaled to resolve the (weakly singular) fine structure at the origin.…”

Section: Statement Of the Problemmentioning

confidence: 99%

Stokes flow singularity at a corner joining solid and porous walls at arbitrary angle

Nitsche

2017

J Eng Math

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Motivated by the internal flow geometry of spiral-wound membrane modules with ladder-type spacers, we consider the Stokes flow singularity at a corner that joins porous and solid walls at arbitrary wedge angle Θ. Seepage flux through the porous wall is coupled to the pressure field by Darcy's law; slip is described by a variant of the Beavers-Joseph boundary condition. On a macroscopic, outer length scale, the singularity appears like a jump discontinuity in the normal velocity, characterized by a non-integrable 1/r divergence of the pressure. For arbitrary Θ, we develop an algebraic criterion to determine the admissible radial exponent(s) in a leading, inner similarity solution-which represents a weaker, integrable singularity in the pressure. A complete map of exponent versus Θ is provided for 0 < Θ < 2π : this has an intricate structure with infinitely many solution branches clustering around Θ = π and Θ = 2π . By generalizing the similarity form with a (ln r ) term and iterating on the slip and seepage conditions, we can carry the outer and inner power series to arbitrarily high order. Nevertheless, a numerical splice is required in between. For this purpose, we apply an iterative, numerical-asymptotic patching scheme described by Nitsche and Parthasarathi (J Fluid Mech 713:183-215, 2012). Detailed velocity and pressure profiles are calculated for three wedge angles (Θ = 3π/4, π/2, π/4) and two dimensionless slip lengths (σ = 20, 40). The general trends for decreasing wedge angle are (i) weakening of the pressure singularity, (ii) increasing magnitude of the radial component of velocity, and (iii) movement of the inner-outer transition farther from the corner. Wedges with Θ < π are seen to differ fundamentally from the flat wedge (Θ = π ) previously considered by Nitsche and Parthasarathi (2012).Keywords Low-Reynolds-number flow · Porous walls · Generalized similarity solutions · Boundary integral method Electronic Supplementary material The online version of this article

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Section: Statement Of the Problemmentioning

confidence: 99%

Stokes flow singularity at a corner joining solid and porous walls at arbitrary angle

Nitsche

2017

J Eng Math

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“…First, absent phenomena presumed rare or inconsequential at the subcellular level such as porous boundaries (cf. Chellam, Wiesner & Dawson 1995) or slip boundary conditions (e.g. Allison 1999), the empirically observed nature of the liquid–solid interface dictates imposition of classical no‐slip boundary conditions: along a liquid–solid interface, the velocities of the two phases are equal (e.g.…”

Section: Convection: Mass Flow At Low Reynolds Numbermentioning

confidence: 99%

The role of cytoplasmic streaming in symplastic transport

Pickard

2003

Plant Cell & Environment

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The distributing of materials throughout a symplastic domain must involve at least two classes of transport steps: plasmodesmatal and cytoplasmic. To underpin the latter, the most obvious candidate mechanisms are cytoplasmic streaming and diffusion. The thesis will be here advanced that, although both candidates clearly do transport cytoplasmic entities, the cytoplasmic streaming per se is not of primary importance in symplastic transport but that its underlying molecular motor activity (of which the streaming is a readily visible consequence) is . Following brief tutorials on low Reynolds number flow, diffusion, and targeted intracytoplasmic transport, the hypothesis is broached that macromolecular and vesicular transport along actin trackways is both the cause of visible streaming and the essential metabolically driven cytoplasmic step in symplastic transport. The concluding discussion highlights four underdeveloped aspects of the active cytoplasmic step: (i) visualization of the real-time transport of messages and metabolites; (ii) enumeration of the entities trafficked; (iii) elucidation of the routing of the messages and metabolites within the cytoplasm; and (iv) transference of the trafficked entities from cytoplasm into plasmodesmata.

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“…17 and 19 for no-slip and in Ref. 35 for slip flows. Table II summarizes the initial guesses resulting in the entire set of similar solutions for axisymmetric flow in a channel with two porous walls as proved earlier in Sec.…”

Section: A Discussion Of Results For Flow In a Symmetric Channelmentioning

confidence: 91%

Effect of slip on existence, uniqueness, and behavior of similarity solutions for steady incompressible laminar flow in porous tubes and channels

Chellam

Liu

2006

Physics of Fluids

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The existence and multiplicity of similarity solutions for steady, fully developed, incompressible laminar flow in uniformly porous tubes and channels with one or two permeable walls is investigated from first principles. A fourth-order ordinary differential equation obtained by simplifying the Navier-Stokes equations by introducing Berman’s stream function [A. S. Berman, J. Appl. Phys. 24, 1232 (1953)] and Terrill’s transformation [R. M. Terrill, Aeronaut. Q. 15, 299 (1964)] is probed analytically. In this work that considers only symmetric flows for symmetric ducts; the no-slip boundary condition at porous walls is relaxed to account for momentum transfer within the porous walls. By employing the Saffman [P. G. Saffman, Stud. Appl. Math. 50, 93 (1971)] form of the slip boundary condition, the uniqueness of similarity solutions is investigated theoretically in terms of the signs of the guesses for the missing initial conditions. Solutions were obtained for all wall Reynolds numbers for channel flows whereas no solutions existed for intermediate values for tube flows. Introducing slip did not fundamentally change the number or the character of solutions corresponding to different sections. However, the range of wall Reynolds numbers for which similarity solutions are theoretically impossible in tube flows was found to be a weak function of the slip coefficient. Slip also weakly influenced the transition wall Reynolds number corresponding to flow in the direction of a favorable axial pressure gradient to one in the direction of an adverse pressure gradient. Momentum transfer from the longitudinal axis to the walls appears to occur more efficiently in porous channels compared to porous tubes even in the presence of slip.

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Laminar Flow in Porous Ducts

Cited by 16 publications

References 59 publications

Stokes flow singularity at a corner joining solid and porous walls at arbitrary angle

Stokes flow singularity at a corner joining solid and porous walls at arbitrary angle

The role of cytoplasmic streaming in symplastic transport

Effect of slip on existence, uniqueness, and behavior of similarity solutions for steady incompressible laminar flow in porous tubes and channels

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