College - Author 1

College of Science and Mathematics

Department - Author 1

Physics Department

Degree Name - Author 1

BS in Physics



Primary Advisor

Tatiana Kuriabova, College of Science and Mathematics, Physics Department


Diffusion is a transport process common in several biological systems. In this process particles of different species mix together through random (stochastic) motion at molecular length scales. Diffusion in fluids is unique as the coupling of the flow and fluid have been found to produce giant concentration fluctuations. The molecular length scale of these concentration fluctuations are magnitudes larger than the movement of the particles themselves, earning them the title “giant”. The diffusion of particles in bio-membranes displays a combination of 2D and 3D hydrodynamic properties; the movements of the particles are restricted to the plane of the membrane and the membrane itself is embedded in a bulk fluid; we describe this crossover as a Quasi-2d fluid. In this project we theoretically examine the effects of these giant fluctuations on the aggregation rate of diffusing particles within this model of a Quasi 2D fluid. This project involves a mathematical model for these fluctuations and the construction of a simulation in which we have applied analytic calculations, the immersed boundary approach, and stochastic hydrodynamics while introducing conditions for aggregation, periodic boundary conditions, and mapping methods to track our aggregates and individual particles. This work contributes to an improved understanding of diffusion in bio-membranes and the impact of giant fluctuations.