Brownian Particle Adsorption in Unsteady-State Viscous Flows in Pores

In this study, an idealized pore model is used to examine the salient features of Brownian particle adsorption onto the inner pore walls in unsteady-state flow. An important example is the expansion/contraction of the alveolar region of the lung that gives rise to the unsteady-state gas flow and can have a significant effect on the transport and adsorption of submicron particles. An idealized pore model with an oscillating outer wall is developed to systematically study fluid and Brownian particle motion as well as adsorption. The unsteady-state gas flow is derived in a general way using a Fourier series representation of the oscillating outer wall in order to simulate various patient specific breathing patterns. The Smoluchowski-Chandrasekhar equation is used to describe the convective-diffusion of a solution of non-interacting Brownian particles. A perturbation method is adopted to obtain analytical solutions for the Brownian particle concentration and flux behavior. The leading order solution describes pure unsteady-state diffusion, while the first-order solution takes into account the effects of fluid convection. As expected, the adsorption of Brownian particles is enhanced during inhalation cycles and is reduced during exhalation cycles. An interesting feature of the first-order solution is the appearance of local particle concentration maximum ("hot spots") between the wall and centerline of the pore due to large zero-order concentration gradients in those regions. These solutions can be used to maximize or minimize deposition by controlling the various parameters such as breathing pattern, flow rate, and particle concentration. We also summarize the general domains of the problem of Brownian particle motion for unsteady-state flows in pores.