Droplet-based microfluidics with nonaqueous solvents and solutions

In droplet-based ("digital") microfluidics, liquid droplets in contact with dielectric surfaces are created, moved, merged and mixed by applying AC or DC potentials across electrodes patterned beneath the dielectric. We show for the first time that it is possible to manipulate droplets of organic solvents, ionic liquids, and aqueous surfactant solutions in air by these mechanisms using only modest voltages (<100 V) and frequencies (<10 kHz). The feasibility of moving any liquid can be predicted empirically from its frequency-dependent complex permittivity, epsilon*. The threshold for droplet actuation in air with our two-plate device configuration is /epsilon*/>8x10(-11). The mechanistic implications of these results are discussed, along with the greatly expanded range of applications for digital microfluidics that these results suggest are now feasible.     

Unstable Willmore surfaces of revolution subject to natural boundary conditions

In the class of surfaces with fixed boundary, critical points of the Willmore functional are naturally found to be those solutions of the Euler-Lagrange equation where the mean curvature on the boundary vanishes. We consider the case of symmetric surfaces of revolution in the setting where there are two families of stable solutions given by the catenoids. In this paper we demonstrate the existence of a third family of solutions which are unstable critical points of the Willmore functional, and which spatially lie between the upper and lower families of catenoids. Our method does not require any kind of smallness assumption, and allows us to derive some additional interesting qualitative properties of the solutions.     

ON QUOTIENTS OF BRAID GROUPS

ABSTRACT.

Let G be the group ?[t, t ^?1] x ?. By studying the action of the braid group B_n on the set Gⁿ , we obtain representations of B_n into a wreath product of the symmetric group and the general linear group over ?[t, t ^?1]. This in particular recovers the Burau representation of the braid group. Furthermore, some quotients of the braid group are obtained by using the representations found.     

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Ohne Zusammenfassung     

Numerical discretization of a Darcy–Forchheimer model

We solve a steady Darcy–Forchheimer flow in a bounded region by means of piecewise constant velocities and nonconforming piecewise pressures. For the computation, we solve the nonlinearity by an alternating-directions algorithm and we decouple the computation of the velocity from that of the pressure by a gradient algorithm. We prove a priori error estimates of the scheme and convergence of the alternating-directions algorithm. The first author was supported by the J. Tinsley Oden Faculty Fellowship, ICES, The University of Texas at Austin.     

Digital microfluidics for cell-based assays

We introduce a new method for implementing cell-based assays. The method is based on digital microfluidics (DMF) which is used to actuate nanolitre droplets of reagents and cells on a planar array of electrodes. We demonstrate that this method is advantageous for cell-based assays because of automated manipulation of multiple reagents in addition to reduced reagent use and analysis time. No adverse effects of actuation by DMF were observed in assays for cell viability, proliferation, and biochemistry. A cytotoxicity assay using Jurkat T-cells was performed using the new method, which had approximately 20 times higher sensitivity than a conventional well plate assay. These results suggest that DMF has great potential as a simple yet versatile analytical tool for implementing cell-based assays on the microscale.