10th International Aerosol Conference September 2 - September 7, 2018 America's Center Convention Complex St. Louis, Missouri, USA
Abstract View
Time-dependent Robin Boundary Condition for Convective Diffusion Equations
Panagiotis Neofytou, Marika Pilou, Christos Housiadas, YANNIS DROSSINOS, European Commission, Joint Research Centre
Abstract Number: 674 Working Group: Aerosol Physics
Abstract Convective diffusion of nanoparticles in bounded flows is an important transport mechanism in many industrial processes. Particle deposition via convective diffusion is of importance to, among others, scrubbers and filters, and aerosol measurement systems. An essential element in the calculation of nanoparticle deposition is the choice of the wall boundary condition. Under steady-state conditions, the wall boundary condition is usually taken to be totally absorbing, namely the particle concentration vanishes at the wall.
Microscopic considerations based on a generalized Fokker-Planck equation for the motion of a particle in a fluid suggest that a properly defined wall boundary condition relates the particle concentration at the wall to its derivative (at the wall). This boundary condition is known as the Robin boundary condition or radiation boundary condition. The associated constants (in the absence of external forces) depend on the particle diffusion coefficient, the particle thermal velocity, and the probability of particle adhesion to the wall (the momentum accommodation coefficient or the sticking fraction). As such, for most aerosol applications at atmospheric pressures and for high particle sticking probabilities the calculated deposition profile or total deposited mass do not depend on whether the Robin or the absorbing boundary is used. In fact, under these conditions the Robin boundary condition reduces to the absorbing boundary condition (i.e., a Dirichlet boundary condition).
The Robin boundary condition is common in systems where a heterogeneous reaction occurs at the wall because it connects the diffusive flux towards the wall to the particle flux that adheres to the wall. The proportionality constant is related to the heterogeneous reaction rate at the wall. Such relevant cases are encountered in, for example, biomedical uses of inhaled particles designed for targeted drug delivery at specific sites of the respiratory system. We extended the Robin boundary condition to transient situations. Under non steady-state conditions an additional, first order derivative term appears in the time-dependent boundary condition. We investigated the conditions under which this additional time-dependent term influences deposition patterns of nanoparticles in various flows of interest in aerosol and biomedical applications (e.g., in laminar pipe flow).