(298i) Effective Mass Transfer Rates to Heterogeneous Porous or Reactive Interfaces Under Strong Shear

Authors: 
Shaqfeh, E. S. G., Stanford University
Shah, P., Stanford University

Problems involving mass transport to surfaces with heterogeneous reaction are common in the field of reaction engineering, heterogeneous catalysis and even in thermal contact analysis. Transport to porous surfaces such as leaky tumor vasculatures or others occurring naturally in biological systems may also be understood by modeling the mass transfer resistance at pores via a lumped reaction rate. To this end, we first solve the point particle problem where a species with uniform bulk concentration adsorbs to an otherwise inert surface containing micro-scale surface reactive patches of arbitrary shape and unbound shear flow over it. The micro-scale reaction rate is characterized by a Damkohler number (k), while the Peclet number (P) is a dimensionless ratio of the bulk shear rate to the inverse diffusion time scale. Using a scaling analysis and boundary element simulations, we calculate the yield of reaction, aka the Sherwood number (S), and demonstrate the limits of using the traditional ansatz of reaction-limited micro-scale transport in modeling effective surface properties. We obtain the effective surface reaction rate that depends on porosity, micro-scale reaction rate and the shear rate. In modeling at the macro-scale, one can use this as a boundary condition to replace the micro-scale details, as long as one is beyond a surface-normal effective slip distance that is also determined from our analysis and found to scale with the size of reactive patches. Our results are valid for the entire range from reaction-limited (k<<1) to the diffusion-limited (k>>1) regime of the Damkohler number, and a wide range of Peclet numbers. The transport in the dilute limit of porosity is governed by large-scale interactions between reactive patches. In the inverse case where we study the dilute limit of inert irregularities on an otherwise homogeneous reactive surface, it is observed that the transport problem is geometric in nature, and that a concentration boundary layer that scales with (1/k) surrounds each inert region. To allow for hydrodynamic and steric effects due to interaction of finite sized particles with the flow and domain geometry, we perform Brownian dynamics simulations of the advection-diffusion of spheroidal particles through a porous membrane. A greater flux is observed for particles with skewed aspect ratios, which is explained based on simple geometric arguments.