We introduce a lattice Boltzmann computational scheme capable of modeling ther-

The lattice Boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered. Although the equation is a derivative of lattice gas automata, it may be interpreted as a Lagrangian finite-difference method for the numerical simulation of the discrete-velocity Boltzmann equation that makes use of a BGK collision operator. As a result, it is not surprising that numerical instability of lattice Boltzmann methods have been frequently encountered by researchers. We present an analysis of the stability of perturbations of the particle populations linearized about equilibrium values corresponding to a constantdensity uniform mean flow. The linear stability depends on the following parameters: the distribution of the mass at a site between the different discrete speeds, the BGK relaxation time, the mean velocity, and the wavenumber of the perturbations. This parameter space is too large to compute the complete stability characteristics. We report some stability results for a subset of the parameter space for a 7-velocity hexagonal lattice, a 9-velocity square lattice and a 15-velocity cubic lattice. Results common to all three lattices are 1) the BGK relaxation time τ must be greater than 1 2 corresponding to positive shear viscosity, 2) there exists a maximum stable mean velocity for fixed values of the other parameters and 3) as τ is increased from 1 2 the maximum stable velocity increases monotonically until some fixed velocity is reached which does not change for larger τ .

Electrowetting refers to an electrostatically induced reduction in the contact angle of an electrically conductive liquid droplet on a surface. Most designs ground the droplet by either sandwiching the droplet with a grounding plate on top or by inserting a wire into the droplet. Washizu and others have developed systems capable of generating droplet motion without a top plate while allowing the droplet potential to float. In contrast to these designs, we demonstrate an electrowetting system in which the droplet can be electrically grounded from below using thin conductive lines on top of the dielectric layer. This alternative method of electrically grounding the droplet, which we refer to as groundingfrom-below, enables more robust droplet translation without requiring a top plate or wire. We present a concise electrical-energy analysis that accurately describes the distinction between grounded and nongrounded designs, the improvements in droplet motion, and the simplified control strategy associated with grounding-from-below designs. Electrowetting on a single planar surface offers flexibility for interfacing to liquidhandling instruments, utilizing droplet inertial dynamics to achieve enhanced mixing of two droplets upon coalescence, and increasing droplet translation speeds. In this paper, we present experimental results and a number of design issues associated with the grounding-frombelow approach.

A subgrid turbulence model for the lattice Boltzmann method is proposed for high Reynolds number fluid flow applications. The method, based on the standard Smagorinsky subgrid model and a single-time relaxation lattice Boltzmann method, incorporates the advantages of the lattice Boltzmann method for handling arbitrary boundaries and is easily implemented on parallel machines. The method is applied to a two-dimensional driven cavity flow for studying dynamics and the Reynolds number dependence of the flow structures. The substitution of other subgrid models, such as the dynamic subgrid model, in the framework of the LB method is discussed.