Colloidal hydrodynamics using a quasi-steady algorithm in lattice Boltzmann method

Hydrodynamics can play an important role in determining the behaviour of colloidal particles in many soft matter systems. Analytical solutions for fluid dynamics are limited and incorporating the particle dynamics in numerical methods is challenging, since grid points belonging to fluid and solid phases are exchanged during the simulations. As a solution, here, we introduce a quasi-steady method to simulate dynamics of particles within the frame work of lattice Boltzmann method. This method not only carries the advantages of lattice Boltzmann, namely the simple and straight forward algorithm of programming and the simplicity in imposing the boundary conditions, but it also avoids the complications associated with exchange of particle and fluid nodes. Exploiting the smallness of Reynold’s number associated with colloidal hydrodynamics, the proposed algorithm works in an instantaneous frame of reference and particle velocities are then calculated by imposing additional constraints of force and torque acting on the particle. We illustrate the method using the classic examples of settling particles and a system of recent interest-dynamics of active particles, both in the presence of a wall. Therefore, we expect the proposed method to be suitable and useful in variety of soft and active matter systems.