Sherwood number in porous microtube due to combined pressure and electroosmotically driven flow

EOF of non-Newtonian power-law fluids in a cylindrical microchannel is analyzed theoretically. Specially, exact solutions of electroosmotic velocity corresponding to two special fluid behavior indices (n = 0.5 and 1.0) are found, while approximate solutions are derived for arbitrary values of fluid behavior index. It is found that because of the approximation for the first-order modified Bessel function of the first kind, the approximate solutions introduce largest errors for predicting electroosmotic velocity when the thickness of electric double layer is comparable to channel radius, but can accurately predict the electroosmotic velocity when the thickness of electric double layer is much smaller or larger than the channel radius. Importantly, the analysis reveals that the Helmholtz-Smoluchowski velocity of power-law fluids in cylindrical microchannels becomes dependent on geometric dimensions (radius of channel), standing in stark contrast to the Helmholtz-Smoluchowski velocity over planar surfaces or in parallel-plate microchannels. Such interesting and counterintuitive effects can be attributed to the nonlinear coupling among the electrostatics, channel geometry, and non-Newtonian hydrodynamics. Furthermore, a method for enhancement of EOFs of power-law fluids is proposed under a combined DC and AC electric field.

“…The solution of EDL potential can be found as :

ψ (r) = ζ \frac{I_{0} (κ r)}{I_{0} (κ R)}

where

I_{0} (x)

is the zeroth‐order modified Bessel function of the first kind, and κ is the Debye Hückel parameter given by:

κ = \sqrt{\frac{2 n_{\infty} {(e z)}^{2}}{ɛ k_{B} T}}

…”

Section: Theorymentioning

confidence: 99%

Electroosmotic flows of non‐Newtonian power‐law fluids in a cylindrical microchannel

Zhao

Yang

2013

“…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

Self Cite

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.

“…Analysis of the mass transport phenomena under the influence of external field for various solution rheology and channel geometry has already been studied . However, an interesting implication is observed in the situation of induced streaming potential.…”

Section: Introductionmentioning

confidence: 99%

Mass transfer of a neutral solute in porous microchannel under streaming potential

Mondal

2013

Self Cite

The mass transport of a neutral solute in a porous wall, under the influence of streaming field, has been analyzed in this study. The effect of the induced streaming field on the electroviscous effect of the fluid for different flow geometries has been suitably quantified. The overall electroosmotic velocity profile and expression for streaming field have been obtained analytically using the Debye-Huckel approximation, and subsequently used in the analysis for the mass transport. The analysis shows that as the solution Debye length increases, the strength of the streaming field and, consequently, the electroviscous effect diminishes. The species transport equation has been coupled with Darcy's law for quantification of the permeation rate across the porous wall. The concentration profile inside the mass transfer boundary layer has been solved using the similarity transformation, and the Sherwood number has been calculated from the definition. In this study, the variation of the permeation rate and solute permeate concentration has been with the surface potential, wall retention factor and osmotic pressure coefficient has been demonstrated for both the circular as well as rectangular channel cross-section.