Faculty

Publications

Debashis Dutta, Arun Ramachandran and David T. Leighton Jr. Effect of channel geometry on solute dispersion in pressure-driven microfluidic systems. Microfluidics and Nanofluidics, 2:275-290, 2006. view abstract // link Pressure-driven transport of fluid and solute samples is often desirable in microfluidic devices, particularly where sufficient electroosmotic flow rates cannot be realized or the use of an electric field is restricted. Unfortunately, this mode of actuation also leads to hydrodynamic dispersion due to the inherent fluid shear in the system. While such dispersivity is known to scale with the square of the Peclet number based on the narrower dimension of the conduit (often the channel depth), the proportionality constant can vary significantly depending on its actual cross section. In this article, we review previous studies to understand the effect of commonly microfabricated channel cross sections on the Taylor–Aris dispersion of solute slugs in simple pressure-driven flow systems. We also analyze some recently proposed optimum designs which can reduce the contribution to this band broadening arising from the presence of the channel sidewalls. Finally, new simulation results have been presented in the last section of this paper which describe solutal spreading due to bowing of microchannels that can occur from stresses developed during their fabrication or operation under high-pressure conditions.

Debashis Dutta and David T. Leighton, Jr. A Low Dispersion Geometry for Microchip Separation Devices. Analytical Chemistry, 74:1007-1016, 2002. view abstract // link Curved channel geometries introduced on microchip separation devices to achieve greater separation distances often lead to large analyte dispersion, degrading the performance of these systems. While such electrokinetic dispersion may be minimized by reducing the channel width around the curved region, alternative strategies involving larger channel curvatures may be promising as well, depending on the application. For example, Culbertson et al. (Anal. Chem. 2000, 72, 5814-5819) recently demonstrated the effectiveness of gentle spiral geometries in carrying out separations of small molecules. For moderate and large Peclet number systems, however, larger spiral geometries are necessary to diminish electrokinetic dispersion of solute slugs which may not conform to the needs of the microchip format. In this work, we investigate a modified spiral geometry with a wavy wall along the inner track of the channel. Analysis shows that such width profiling may significantly improve the performance of the spiral geometry, making the design effective for larger Peclet number or smaller radii systems. Numerical simulations performed to optimize these modified spirals suggest equating transit times along the inner and the outer track of the channel as a useful design criterion for minimizing electrokinetic dispersion. An analytical model has been formulated to derive the optimal channel parameters based on this criteria which compares well with the simulation results.

Michael R. King and David T. Leighton, Jr. Title: Measurement of shear-induced dispersion in a dilute emulsion. Physics of Fluids, 13:397-406, 2001. view abstract // link The time-dependent drop distribution of a dilute, polydisperse emulsion is measured in a simple shear flow. The suspending fluid is much more viscous than the dispersed phase (1:1000). Drops are found to drift away from either bounding wall and accumulate near the center of the gap, due to the anisotropy of droplet–plane interactions. An expression for this drift velocity has been derived for single drops by Chan and Leal [J. Fluid Mech. 92, 131 (1979)] and was in agreement with isolated drop migration observed in our work. Eventually the inward drift is balanced by a shear-induced gradient diffusivity, and a steady-state concentration distribution is reached. When the drops are sufficiently far from either wall a self-similar, parabolic concentration profile is predicted at all times. Droplet diffusivities were determined for capillary numbers Ca = µ/ between 0.17 and 0.92, where is the shear rate, is the mean drop radius, µ is the viscosity of the suspending fluid, and the interfacial tension. The values obtained are an order of magnitude lower than theoretical predictions of Loewenberg made in the limit of small deformation. ©2001 American Institute of Physics.

Debashis Dutta and David T. Leighton, Jr. Dispersion reduction in pressure driven flow through microetched channels. Analytical Chemistry, 73:504-513, 2001. view abstract // link Fluid is often moved about microetched channels in lab-on-a-chip applications using electrokinetic flows (electrophoresis or electroosmosis) rather than pressure-driven flows because the latter result in large Taylor dispersion. However, small pressure gradients may arise unintentionally in such systems due to a mismatch in electroosmotic flow rates or hydrostatic pressure differentials along the microetched channel. Under laminar flow conditions, Doshi et al, (Chem. Eng, Sci, 1978, 33, 795-804) have shown that for a channel with rectangular cross-section of width W and depth d, longitudinal diffusivities can attain values as large as similar to8 K-0 for small values of the aspect ratio d/W, where K-0 is the value of the longitudinal diffusivity obtained by ignoring all variations across the channel, Microchannels in lab-on-a-chip geometries are often not rectangular in cross-section. Isotropic etching techniques, for example, lead to channels with quarter-circular ends. In this paper we examine the effect of this geometry on the magnitude of longitudinal dispersivity for pressure-driven flows and also investigate modifications to this design which may minimize such dispersion. Optimal channel profiles are shown to lead to dispersivities approaching K-0, the theoretical minimum, for small values of d/W.

Isidro E. Zarraga, Davide A. Hill, and David T. Leighton, Jr. The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. Journal of Rheology, 44:185-220, 2000. view abstract // link The total stress of a concentrated suspension of noncolloidal spheres in a Newtonian fluid was characterized by independent measurements in viscometric flows. Using a suspension balance formulation, the normal stress in the vorticity direction (33) for a suspension undergoing simple shear was extracted from Acrivos et al.'s [Int. J. Multiphase Flow 19, 797 (1993)] resuspension data in a Couette device. Employing a new correlation for the relative viscosity µr which obeys the Einstein relation in the dilute limit while diverging at random close packing, it was found that 33/ (where is the magnitude of the shear stress) was a strong function of the solid volume fraction , scaling as 3e2.34. The relative viscosity, measured in a parallel plate viscometer, was in good agreement with the proposed correlation, while the normal stress differences N1 and N2 for concentrated suspensions (= 0.30–0.55) were characterized using parallel plate and cone-and-plate geometries, as well as laser profilometry measurements of the suspension surface deflection in a rotating rod geometry. The normal stresses were proportional to the shear stress , and with N1/ and N2/, the parameter combinations resulting from the three experimental geometries, –, , and + , were all seen to increase with according to the derived scaling 3e2.34. Furthermore, the best-fit N1 and N2 values consistent with the set of experiments were both negative, with |N2| > |N1| at any given concentration and shear rate. Taken together, the results obtained allow a complete determination of the total stress of a sheared suspension and in particular enabled us to compute the shear-induced particle-phase pressure , as defined in Jeffrey et al. [Phys. Fluids A 5, 2317 (1993)]. ©2000 Society of Rheology.

Arun Ramachandran and David T. Leighton. The influence of secondary flows induced by normal stress differences on the shear-induced migration of particles in concentrated suspensions. Journal of Fluid Mechanics, 603:207-243, 2008. view abstract // link It was first demonstrated experimentally by H. Giesekus in 1965 that the second normal stress difference in polymers can induce a secondary flow within the cross-section of a non-axisymmetric conduit. In this paper, we show through simulations that the same may be true for suspensions of rigid non-colloidal particles that are known to exhibit a strong negative second normal stress difference. Typically, the magnitudes of the transverse velocity components are small compared to the average axial velocity of the suspension; but the ratio of this transverse convective velocity to the shear-induced migration velocity is characterized by the shear-induced migration Peclet number chi which scales as B-2/a(2), B being the characteristic length scale of the cross-section and a being the particle radius. Since this Peclet number is kept high in suspension experiments (typically 100 to 2500), the influence of the weak circulation currents on the concentration profile can be very strong, a result that has not been appreciated in previous work. The principal effect of secondary flows on the concentration distribution as determined from simulations using the suspension balance model of Nott & Brady (J. Fluid Mech. vol. 275, 1994, p. 157) and the constitutive equations of Zarraga et al. (J. Rheol. vol. 44, 2000, p. 185) is three-fold. First, the steady-state particle concentration distribution is no longer independent of particle size; rather, it depends on the aspect ratio B/a. Secondly, the direction of the secondary flow is such that particles are swept out of regions of high streamsurface curvature, e.g. particle concentrations in corners reach a minimum rather than the local maximum predicted in the absence of such flows. Finally, the second normal stress differences lead to instabilities even in such simple geometries as plane-Poiseuille flow.

Awards

John A. Kaneb Teaching Award

Given on April 11, 2000 by University of Notre Dame

Presidential Young Investigator Award

Given on December 31, 1986 by National Science Foundation

John A. Kaneb Teaching Award

Given on April 27, 2004 by University of Notre Dame

Courses

• CBE 30355 - Transport Phenomena I - Basic conservation principles of energy, mass, and momentum are used to derive the integral and differential forms of the transport equations. These equations are used to solve fluid flow problems ... more >
• CBE 60544 - Transport Phenomena I - Differential balance equations that govern transport processes are derived and used to solve problems that demonstrate the physical insight necessary to apply these equations to original situations... more >

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