Discrete Boltzmann equation for microfluidics

We propose a discrete Boltzmann model for microfluidics based on the Boltzmann equation with external forces using a single relaxation time collision model. Considering the electrostatic interactions in microfluidics systems, we introduce an equilibrium distribution function that differs from the Maxwell-Boltzmann distribution by an exponential factor to represent the action of an external force field. A statistical mechanical approach is applied to derive the equivalent external acceleration force exerting on the lattice particles based on a mean-field approximation, resulting from the electro-static potential energy and intermolecular potential energy between fluid-fluid and fluid-substrate interactions.