个人简介

Ph.D, Stanford University, 1985 M.S., Stanford University, 1981 B.S., Princeton University, 1980

研究领域

Professor Leighton's research interests are in the areas of fluid mechanics and separation processes. Of particular interest is the way in which mathematics may be applied to improve our understanding of physical processes that occur in these areas. Current research projects include the study of flow-induced microstructure in concentrated suspensions, shear-induced migration and segregation in bidisperse suspensions, dispersion in chip-based micro-laboratories, and zetafiltration, a novel electrophoretic separation process.

Suspension mechanics Separations

近期论文

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Debashis Dutta and David T. Leighton, Jr. A Low Dispersion Geometry for Microchip Separation Devices. Analytical Chemistry, 74:1007-1016, 2002. 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. 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. 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. 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. 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. Ramachandran A., Lowenberg, M., Leighton, D. T. A constitutive equation for droplet distribution in unidirectional flows of dilute emulsions for low capillary numbers. PHYSICS OF FLUIDS, 22:art:083301, 2010. The concentration distribution of droplets in the unidirectional flow of an emulsion for small capillary numbers (Ca) can be written as a balance between the drift flux arising from droplet deformation and the flux due to shear induced migration. The droplet drift flux is modeled using the O(Ca) theoretical results of Chan and Leal [J. Fluid Mech. 92, 131 (1979)], while the flux due to shear-induced migration is modeled using the suspension balance approach of Nott and Brady [J. Fluid Mech. 275, 157 (1994)], whereby particle migration is ascribed to normal stress gradients in the flowing dilute emulsion. In the limit of vanishingly small capillary numbers, the leading order contribution of the normal stresses in dilute emulsions arises from droplet-droplet interaction and thus scales as phi(2)tau, where phi is the droplet volume fraction and phi is the local shear stress. In our model, the normal stress calculations of Zinchenko [Prikl. Mat. Mekh. 47, 56 (1984)] are connected to our gradient diffusivity data computed from droplet trajectories [M. Loewenberg and E. J. Hinch, J. Fluid Mech. 338, 299 (1997)] via a reduced droplet mobility to derive the droplet flux due to shear-induced migration. As an example, the model is applied to the tube Poiseuille flow of a dilute emulsion at small Ca. It is demonstrated that the unsteady concentration distribution of droplets resulting from arbitrary time-dependent average velocity obeys a self-similar solution, provided the thickness of the droplet-depleted region near the walls is always nonzero. Ramachandran A. and Leighton, D. T. Particle migration in concentrated suspensions undergoing squeeze flow. JOURNAL OF RHEOLOGY, 54:563-589, 2010