1070-4272/01/7405-0777$25.00C2001 MAIK [Nauka/Interperiodica]
Russian Journal of Applied Chemistry, Vol. 74, No. 5, 2001, pp. 777!783. Translated from Zhurnal Prikladnoi Khimii, Vol. 74, No. 5,
2001, pp. 754!761.
Original Russian Text Copyright + 2001 by Abiev.
PROCESSES AND EQUIPMENT
OF CHEMICAL INDUSTRY
Simulation of Extraction from a Capillary-Porous Particle
with Bidisperse Structure
R. Sh. Abiev
St. Petersburg State Technological Institute, St. Petersburg, Russia
Received October 30, 2000
Abstract-A mathematical model of extraction from a capillary-porous particle with bidisperse structure is
described. Results of numerical simulations are presented together with the criterial equation for calculating
the effective diffusion coefficient, obtained on processing these results. A criterion is established for selecting
the optimal oscillation frequency. The criterion is tested on a physical model, with the obtained numerical
results qualitatively confirmed.
Capillary-porous particles with bidisperse structure,
possessing capillaries of two, strongly different sizes,
frequently occur in nature and technology. Into this
category may be placed tissues of plant or animal
origin, and also many kinds of catalysts . Neglect-
ing the polydispersity of capillary sizes in capillary-
porous particles makes less accurate the obtained
results and gives no way of elucidating some physical
mechanisms of substance transfer inside the particles.
The bidisperse model of a capillary-porous particle is
the analytically simplest variety of the polydisperse
model, making it possible to reveal fundamental
aspects of mass transfer in real polydisperse particles.
The present study is concerned with the process of
extraction from a bidisperse model of a capillary-por-
In the simplest case the model of a bi-
disperse particle can be represented as fine capillaries,
which are the main channels for solutions of target
components, branching-off from coarse pores (blind or
through). As a rule, there is virtually no fluid motion
within the capillaries, with substance transfer occur-
ring by the molecular-diffusion mechanism. However,
at certain amplitudes, pulsation of the external pres-
sure in coarse pores may give rise to oscillatory
motion of fluid because of the compression of gas
trapped in capillaries [2, 3]. Thus, coarse pores play
the role of transport channels with convective sub-
stance transfer, with the resulting manyfold accelera-
tion of solute extraction from the particle as a whole.
In order to simplify the analysis, a planar model
[4, 5] of a capillary-porous particle with bidisperse
The mathematical model was developed with participation of
G.M. Ostrovskii (St. Petersburg State Technological Institute).
structure was adopted (Fig. 1). The ensemble of fine
capillaries was replaced by an anisotropic porous
structure with preset porosity e, a porous block whose
pores are filled at the initial instant of time with a
concentrated solution of the target component; the
anisotropy is manifested in that the diffusion occurs
only along the y-axis. A transport channel whose side
walls border on the porous block passes through the
particle. Molecular diffusion of the substance from
the porous block into the channel occurs (shown by
arrows in Fig. 1) through these boundaries. The diffu-
sion in the channel itself is convective.
The mathematical model of the extraction process
in the particle under consideration can be described by
the following system of equations [indices: (0) initial
state, (1) porous block, and (2) transport channel].
Diffusion equation for the porous block:
/§t = D(§
is the substance concentration in the porous
block (kg m
), t is time (s), and D is the molecular
diffusion coefficient (m s
Fig. 1. Planar model of a particle with bidisperse structure
and through transport pores: (1) porous block and (2) trans-