Figure 1. Separation of an individual
bubble from the heated surface
David R. Rector & Bruce J. Palmer
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. The lattice-Boltzmann approach 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.
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 con-necting it 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 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) that are free to move through the lattice grid. Using these interaction terms, liquid droplets have been simulated that 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.
Simulation of two-phase fluid systems had been limited to isothermal systems because the energy equation was originally designed for single-phase systems. The lattice Boltzmann energy model developed last year was expanded to include phase change terms, including latent heat. The lattice Boltzmann method is now capable of simulating evaporation and condensation behavior. Simulations have been performed for condensation in a micropore and bubble formation and evolution in pool boiling. The separation of an individual bubble from the heated surface is shown in Figure 1.
The separation of chemical species through adsorption, membrane separation, extraction, and distillation is enhanced at the microscale due to the reduced length scales for diffusion transport. The ability to model multiple species is essential to simulating fluid reactor and separation systems. The lattice-Boltzmann method has been expanded to include multiple chemical species with convection and diffusion transport. Each species is represented by a separate field, and the diffusion coefficients can be independently specified. The chemical species model has been verified by comparing simulation results with known analytical solutions. The usefulness of this method has been demonstrated by simulating the behavior of microscale liquid-liquid extraction devices.
The lattice Boltzmann method has been used to support the design and development activities of the PNNL microtechnology initiative. Simulations have been performed to predict the performance of absorber/desorber devices for use in microscale heat pump technology.
Rector DR and BJ Palmer. "Simulation of Chemical Separation Processes Using the Lattice-Boltzmann Method." Third IMRET conference, Frankfurt, Germany.
Palmer BJ and DR Rector. 1998. "Lattice Boltzmann Algorithm for Simulating Thermal Two-Phase Flow." Submitted to Phys. Rev. E.
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