Answer Happy

Consider a closed and finite bulk environment with a volume of
V, which contains an adsorbate species of concentration Cb0. At
time t=0+, a single medium sized porous particle with a mass of m
and density of ρ, is exposed to this environment and the diffusion
and adsorption processes are started. The following assumptions are
made in the theoretical analysis.
(1) Particle is medium sized sphere which consists of many sphere
microparticles separated by network of macropores..
(2) Both pore and surface diffusions occur along the particle
coordinate.
(3) The adsorbed species is assumed to diffuse in two directions,
one is the direction along the particle coordinate (r, surface
diffusion), and the other is the direction along the microparticle
(rμ, micropore diffusion) which is in perpendicular to the particle
coordinate.
(4) The adsorbed species are in local equilibrium with those in the
gas phase inside the particle. (5) The physical properties of the
particle are constant. The macropore porosity is ε.
(6) The film mass transfer coefficient is km, pore diffusivity is
Dp, surface diffusivity is Ds abd nicropore diffusivity is
Dμ.
(7) The system is isothermal.
Use the mass balance to derive a mathematical model to cover all
the macropore, surface and micropore diffusion (MSMD) mechanisms,
with all boundary and initial conditions. A conceptual diagram of
the MSMD model is shown in following figure.
ADSORBENT PARTICLE Surface Diffusion Stagnant Film MICROPORE Micropore Diffusion Macropore Diffusion BULK PHASE