Exploring Brownian Phenomena using Hydrodynamic Memory Kernels

Licentiate thesis, 2025

Accurate modelling of Brownian phenomena at low particle-fluid density ratios can improve the design of many microfluidic devices. Two novel simulation
methods are presented that rely on the generalised Langevin equation (GLE) and its associated memory kernel to accurately model Brownian motion in
complex flow scenarios. The methods are capable of capturing the drag, added mass and history effects that are relevant at low particle-fluid density ratio (ρ_p/ρ_f close to 1). The first method is a pure Direct Numerical Simulation (DNS) method that relies on numerically solving the Navier-Stokes equations to measure the total hydrodynamic force on the particle. The memory kernel required for the GLE based model is obtained via optimisation procedures that rely on the hydrodynamic force and the velocity history of the particle. The random colored Brownian force required for the GLE is then generated using the memory kernel. Finally, the particle is moved under the influence of the hydrodynamic force and the Brownian force. Unhindered and wall-adjacent Brownian motion are accurately simulated using the method.
The second method is a multiscale Lagrangian particle tracking (LPT) method, which is demonstrated to accurately capture hydrodynamic forces and Brownian motion by relying on solely the memory kernel associated with a particle’s position. The method is used to study the migration of a Brownian particle towards a wall under the influence of a constant attractive force. A memory kernel library mapping the hydrodynamic forces (including nonlocal history and added mass effects) is generated using short DNS that utilise the optimisation routine developed as part of the previous pure DNS approach. The effects of the distance to the wall and the strength of the pulling force on the impact region of the particle on the wall are analysed and presented. The multiscale method is seen to be computationally more efficient than the pure DNS method while being capable of capturing detailed flow physics. The capabilities of the memory kernel to capture the effects associated with different fluid, particle and domain properties open up the possibility to extend these methods to more complex flow cases relevant to various microfluidic applications.