Simulation of Microfluid Systems

David Rector and Bruce Palmer

Project Description

Lattice-Boltzmann simulation has the potential to model complex fluid dynamics problems in a size range that is currently not amenable to conventional simulation methods and which is critically important to the development of compact energy and chemical systems. Therefore, we are developing a lattice-Boltzmann simulation code which takes into account microscale surface interactions that can strongly affect physical and chemical properties of the fluid, and which therefore substantially influence heat, mass and momentum transport in microfluidic systems. This code is based on the lattice-Boltzmann approach, which has the virtue of being applicable to a wide range of flow fields, including the representation of phase interfaces (e.g., solid-liquid, solid-gas, liquid-liquid, and liquid-gas interfaces). We will apply this simulation code to model a series of microfluid systems. The results will be used to characterize the importance of such parameters as wall surface effects, wettability, and phase interfaces on the fluid flow behavior of these systems. Molecular dynamics simulations will also be performed to support the development of the lattice-Boltzmann method, especially in the development of boundary conditions.

Technical Accomplishments

In the lattice-Boltzmann method, space is divided into a regular lattice. Each lattice point has an assigned set of velocity vectors with specified magnitudes and directions connecting the lattice point to neighboring lattice points. The total velocity and fluid density is defined by specifying the amount of fluid associated with each of the velocity vectors. The fluid distribution function evolves at each time step through a two step procedure. The first step is to advance the fluid particles to the next lattice site along their directions of motion. The second step is to simulate particle collisions by relaxing the distribution toward an equilibrium distribution using a linear relaxation parameter. Interaction rules are designed to satisfy mass and momentum conservation, resulting in a second-order solution of the Navier-Stokes equations.

One major advantage of the lattice-Boltzmann method is the ability to incorporate interaction potential terms into the equations of motion. A lattice-Boltzmann program with both fluid-fluid and fluid-solid interaction potentials has been developed. A fluid-fluid interparticle potential is used to incorporate a non-ideal equation of state that represents both liquid and vapor phases. This allows a first-order phase transition to occur, forming individual bubbles or droplets (represented by hundreds of lattice points) which are free to move through the lattice grid. Using these interaction terms, liquid droplets have been simulated which are in equilibrium with the surrounding vapor. The interfacial region, where the fluid density transitions from liquid to vapor values, is usually only a couple of lattice sites in thickness and has an associated surface tension. A similar approach has also been demonstrated for simulating immiscible fluids. A fluid-solid interparticle potential is used to incorporate an external chemical potential that is a function of the material properties of the solid boundary. These terms are used to represent the wettability or non-wettability of a solid surface.

Most of the applications that has been performed in the past with lattice-Boltzmann methods have been for isothermal systems, due to the lack of a general purpose energy model. To address this problem, PNNL researchers this year have developed a unique lattice-Boltzmann energy model which simulates both conduction and convection energy transport, as well as thermodynamic effects such as compressive heating/expansive cooling and viscous dissipation (Palmer and Rector 1998; Rector et al. 1998). With this model, the lattice-Boltzmann method is now capable of doing detailed simulations of heat transfer in microdevices, including phase change.

Molecular dynamics simulations using state of the art techniques have been performed to help guide the development of lattice-Boltzmann simulations appropriate for modeling fluids in the microscale regime. Work focused on the development of simplified molecular models for use in studying fluid behavior in micro-channels and the effects of different coating materials on fluid thermodynamic and transport behavior in the channel. Because of the large dimension of the micro-channel, the primary focus of these investigations is on the structure and dynamical properties of fluids near the fluid-solid interface. The effect of wettability on wall slip has been explored using this approach (Palmer 1998). These simulations are coupled to the lattice-Boltzmann simulation effort and are used to develop appropriate boundary conditions and constitutive relations for performing simulations on a micron scale.

Publications and Presentations

Palmer, B.J. and D.R. Rector. 1998. "lattice-Boltzmann Algorithm for Simulating Thermal Flow in Compressible Fluids", presented at the 7th International Conference on the Discrete Simulation of Fluids, Oxford.

Rector, D.R., J.M. Cuta and B.J. Palmer, "Lattice-Boltzmann Simulation Code Development for Micro-Fluidic Systems", presented at the 1998 Spring AIChE Meeting, New Orleans.

B.J. Palmer. 1998. "Direct Simulation of Hydrodynamic Relaxation in Microchannels", Journal of Chemical Physics, 109:196.

B.J. Palmer and D.R. Rector. 1998. "Lattice-Boltzmann Algorithm for Simulating Thermal Flow in Compressible Fluids", submitted.