## Lattice Boltzmann Model

Let's ignore for a moment any complications of locomotion. Flows over surfaces within the hemocoel are complex enough.

A Lattice-Boltzmann simulation may reveal interactions on the microscale, and a simulation would allow modeling the microflu-idic dynamics. Wettability of the surfaces, phase interfaces, and chemical properties interact to determine transport of momentum, heat and mass through the hemolymph.

Using a Lattice-Boltzmann model, we divide the hemocoel into a regular lattice and assign a set of velocity vectors to each lattice point. To connect each lattice point to its neighbors, we assign specified magnitudes and directions to our vectors. To define the total velocity and density of fluid, we specify how much fluid moves with each vector in each interval. By using time increments, we evolve a fluid distribution function that moves our particles progressively stepwise through the hemocoel. We simulate how particles collide by relaxing our distribution towards an equilibrium distribution having a linear relaxation parameter. We must specify rules for these interactions, so they satisfy laws for the conservation of mass and momentum to give a second order solution of the Navier-Stokes equations. Similarly constructed Lattice-Boltzmann models simulate heat transfer and phase changes in solid-liquid interfaces along micro-channels of micro-fluidic devices. Some include the effects of wetability on wall slip (Ref: Lattice-Bolzmann Models).

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