UC Riverside

This thesis summarizes my Ph.D. research on the interactions of virus like particles in equilibrium and non-equilibrium biological systems.

In the equilibrium system, we studied the fluctuation-induced forces between inclusions in a fluid membrane. We developed an exact method to calculate thermal Casimir forces between inclusions of arbitrary shapes and separation, embedded in a fluid membrane whose fluctuations are governed by the combined action of surface tension, bending modulus, and Gaussian rigidity. Each object's shape and mechanical properties enter only through a characteristic matrix, a static analog of the scattering matrix. We calculate the Casimir interaction between two elastic disks embedded in a membrane. In particular, we find that at short separations the interaction is strong and independent of surface tension.

In the non-equilibrium system, we studied the transport and deposition dynamics of colloids in saturated porous media under un-favorable filtering conditions. As an alternative to traditional convection-diffusion or more detailed numerical models, we consider a mean-field description in which the attachment and detachment processes are characterized by an entire spectrum of rate constants, ranging from shallow traps which mostly account for hydrodynamic dispersivity, all the way to the permanent traps associated with physical straining. The model has an analytical solution which allows analysis of its properties including the long time asymptotic behavior and the profile of the deposition curves. Furthermore, the model gives rise to a filtering front whose structure, stability and propagation velocity are examined. Based on these results, we propose an experimental protocol to determine the parameters of the model.