Analytical solutions for species transport in a T‐sensor at low peclet numbers

Abstract

A 3D analytical solution is presented for the problem of mass transport in a T-sensor by taking the axial diffusion effects into account. The solution methodology is based on an eigenfunction expansion of the solute concentration and enjoys the variational calculus for the solution of the associated eigenvalue problem. The method is capable of handling a mixed electroosmotic and pressure-driven velocity profile and is executed assuming a rectangular channel crosssection although it can be easily extended to more complex geometries. Two simplified models, one based on a uniform velocity profile, valid for the channel half height to Debye length ratios of above 100, and the other based on a depthwise averaging of the species concentration to be used for cases in which the channel width to height ratio is above 5 are also presented. As a part of the latter, expressions are derived for the Taylor dispersion coefficient of the mixed flow in a slit microconduit. The most interesting finding of this study is that, when the diffusion mechanism significantly contributes to the axial movement of the species, the well-known heterogeneous mass transport evolves into a nearly uniform pattern in the depthwise direction and the mixing length noticeably increases.The predictions of the thin EDL solution are also presented to be compared with those of C50.

High-throughput, non-equilibrium studies of single biomolecules using glass-made nanofluidic devices

“…diffusion of a species Pe < 10 from one inlet upstream into the other inlet) has been predicted for this geometry but had never been experimentally observed. 29,30 The presence of axial diffusion is confirmed in our experiments.…”

Unsteady convective–diffusive transport in semicircular microchannels with irreversible wall reaction

“…The hydrodynamic dispersion phenomenon has significant importance in various areas in science and engineering processes such as homogenization (Matsunaga, Lee & Nishino 2013;Cheng et al 2015;Sadeghi 2016), separation (Garcia et al 2005) and DNA amplification (Tripathi, Bozkurt & Chauhan 2005). It has also attracted the attention of researchers working on drug delivery systems (Siepmann & Siepmann 2013;Thomas et al 2019) since the dependence of a drug release profile on the thickness of the hydrodynamic diffusion layer has been proven (Patel et al 2011).…”

Unsteady solute dispersion by electrokinetic flow in a polyelectrolyte layer-grafted rectangular microchannel with wall absorption

“…The efficiency of solute transport inside microchannels is an important issue in microfluidics (Datta & Ghosal 2009) because of its vast applications in different areas such as microfluidic mixing (Wu & Nguyen 2005;Matsunaga, Lee & Nishino 2013;Sadeghi 2016), capillary electrophoresis (Wu, Qin & Lin 2008), capillary electrochromatography and capillary liquid chromatography (Feltkamp 1966), DNA amplification (Tripathi, Bozkurt & Chauhan 2005) and molecular separation (Garcia et al 2005). Solute transport occurs via advection, diffusion and hydrodynamic dispersion mechanisms.…”