Sherwood number in flow through parallel porous plates (Microchannel) due to pressure and electroosmotic flow

Vennela, Nallapusa; Mondal, Sourav; De, Sirshendu; Bhattacharjee, Subir

doi:10.1002/aic.12713

Cited by 36 publications

(27 citation statements)

References 34 publications

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“…can be solved with the similarity parameter, equals to

η = \frac{y^{*}}{δ^{*}} = y^{*} {((), \frac{A}{x^{*}})}^{1 / 3}

. In terms of the similarity parameter (η), the concentration profile can be expressed as :

\frac{c}{c_{0}} = \frac{1 - B \int_{0}^{η} prefixexp ((), - \frac{η^{3}}{9} - B η) d η}{1 - B \int_{0}^{\infty} prefixexp ((), - \frac{η^{3}}{9} - B η) d η},

where,

B = \frac{P e_{w}}{4} {((), \frac{x^{*}}{A})}^{1 / 3}

. The constant B can be calculated in terms of length averaged permeate flux

(\bar{P e_{w}})

, as

\bar{P e_{w}} = \int_{0}^{1} P e_{w} d x^{*} = 6 B A^{1 / 3}

.…”

Section: Theorymentioning

confidence: 99%

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Mass transport in a porous microchannel for non‐Newtonian fluid with electrokinetic effects

Mondal

2013

Electrophoresis

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Quantification of mass transfer in porous microchannel is of paramount importance in several applications. Transport of neutral solute in presence of convective-diffusive EOF having non-Newtonian rheology, in a porous microchannel was presented in this article. The governing mass transfer equation coupled with velocity field was solved along with associated boundary conditions using a similarity solution method. An analytical solution of mass transfer coefficient and hence, Sherwood number were derived from first principles. The corresponding effects of assisting and opposing pressure-driven flow and EOF were also analyzed. The influence of wall permeation, double-layer thickness, rheology, etc. on the mass transfer was also investigated. Permeation at the wall enhanced the mass transfer coefficient more than five times compared to impervious conduit in case of pressure-driven flow assisting the EOF at higher values of κh. Shear thinning fluid exhibited more enhancement of Sherwood number in presence of permeation compared to shear thickening one. The phenomenon of stagnation was observed at a particular κh (∼2.5) in case of EOF opposing the pressure-driven flow. This study provided a direct quantification of transport of a neutral solute in case of transdermal drug delivery, transport of drugs from blood to target region, etc.

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“…can be solved with the similarity parameter, equals to

η = \frac{y^{*}}{δ^{*}} = y^{*} {((), \frac{A}{x^{*}})}^{1 / 3}

. In terms of the similarity parameter (η), the concentration profile can be expressed as :

\frac{c}{c_{0}} = \frac{1 - B \int_{0}^{η} prefixexp ((), - \frac{η^{3}}{9} - B η) d η}{1 - B \int_{0}^{\infty} prefixexp ((), - \frac{η^{3}}{9} - B η) d η},

where,

B = \frac{P e_{w}}{4} {((), \frac{x^{*}}{A})}^{1 / 3}

. The constant B can be calculated in terms of length averaged permeate flux

(\bar{P e_{w}})

, as

\bar{P e_{w}} = \int_{0}^{1} P e_{w} d x^{*} = 6 B A^{1 / 3}

.…”

Section: Theorymentioning

confidence: 99%

“…The corresponding mass transfer problem in porous microchannel and microtubes was analyzed by Vennela et al for Newtonian fluids. They developed analytical solution of Sherwood number in such geometry for Newtonian rheology.…”

Section: Introductionmentioning

confidence: 99%

Mass transport in a porous microchannel for non‐Newtonian fluid with electrokinetic effects

Mondal

2013

Electrophoresis

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“…The mass transport analysis for Newtonian fluid rheology in porous microchannel and microtubes has been analyzed by Vennela et al 38,39 They have developed an analytical solution of Sherwood number in such geometry for Newtonian rheology, considering the combined effects of pressure and electroosmotic gradients. Mass transfer in a microchannel bioreactor partially filled with porous medium has been studied numerically by Chen et al 40,41 However, they have dealt with Newtonian fluid and pressure driven flow only.…”

Section: Introductionmentioning

confidence: 99%

Effects of non-Newtonian power law rheology on mass transport of a neutral solute for electro-osmotic flow in a porous microtube

Mondal

2013

Biomicrofluidics

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Mass transport of a neutral solute for a power law fluid in a porous microtube under electro-osmotic flow regime is characterized in this study. Combined electroosmotic and pressure driven flow is conducted herein. An analytical solution of concentration profile within mass transfer boundary layer is derived from the first principle. The solute transport through the porous wall is also coupled with the electro-osmotic flow to predict the solute concentration in the permeate stream. The effects of non-Newtonian rheology and the operating conditions on the permeation rate and permeate solute concentration are analyzed in detail. Both cases of assisting (electro-osmotic and poiseulle flow are in same direction) and opposing flow (the individual flows are in opposite direction) cases are taken care of. Enhancement of Sherwood due to electro-osmotic flow for a non-porous conduit is also quantified. Effects if non-Newtonian rheology on Sherwood number enhancement are observed. V C 2013 AIP Publishing LLC. [http://dx

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“…This ultimately makes all terms on the right hand side of the Eq. (1b) insignifi cant indicating that pressure at a particular section of the permeating tube can be assumed to be constant (i.e., ∂p/∂r≈0) which supports the simplifying assumption used in many cases of weak permeation 14 . These indicate that for fl uid dynamic studies inside a tubular channel with weak permeation, only the axial component of the momentum equation and the equation of continuity is suffi cient.…”

Section: Modeling Flow Through Tubular Hollow--fibersmentioning

confidence: 74%

“…In reality, such viscosity variations are caused by the variation in concentration or temperature which can be predicted by introducing more terms in model equation representing heat and mass transfer. However, to avoid further complexity, and to see the effect of change in viscosity on the fl ow characteristics, the viscosity of fl uid as a function of radial position is defi ned directly by assuming following hypothetical equation: (14) A steep increase in viscosity near the tube wall is obtained by substituting β = 20 and n = 32 in equation (14), whereas the moderate increase or decrease in viscosity is predicted by putting β = 5 and -0.7, and n = 7 and 4, respectively (Fig. 3a).…”

Section: Resultsmentioning

confidence: 99%

Flow behavior in weakly permeable micro-tube with varying viscosity near the wall

Gupta

Kumar

Chand

2017

Polish Journal of Chemical Technology

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Weakly permeable micro-tubes are employed in many applications involving heat and/or mass transfer. During these processes, either solute concentration builds up (mass transfer) or steep change in temperature (heat transfer) takes place near the permeable wall causing a change in the viscosity of the fl uid. Results of the present work suggest that such change in viscosity leads to a considerable alteration in the fl ow behavior, and the commonly assumed parabolic velocity profi le no longer exists. To solve the problem numerically, the equation of motion was simplifi ed to represent permeation of incompressible, Newtonian fl uid with changing viscosity through a micro-tube. Even after considerable simplifi cation, the accuracy of the results was the same as that obtained by previously reported results for some specifi c cases using rigorous formulation. The algorithm developed in the present work is found to be numerically robust and simple so that it can be easily integrated with other simulations.

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Sherwood number in flow through parallel porous plates (Microchannel) due to pressure and electroosmotic flow

Cited by 36 publications

References 34 publications

Mass transport in a porous microchannel for non‐Newtonian fluid with electrokinetic effects

Mass transport in a porous microchannel for non‐Newtonian fluid with electrokinetic effects

Effects of non-Newtonian power law rheology on mass transport of a neutral solute for electro-osmotic flow in a porous microtube

Flow behavior in weakly permeable micro-tube with varying viscosity near the wall

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