A Capillary Flow Model for Filtration
Lei Pan, Kaiwu Huang and Roe-Hoan Yoon*
Center for Advanced Separation Technologies
Virginia Tech, Blacksburg, VA 24061, United States
ABSTRACT
Darcy’s law has been used extensively to model cake filtration. It is a macroscopic model derived for fluid
flow through a bed of particles, with particle size being an important parameter. In the present work, we have derived
a capillary flow model to study the effect of microscopic parameters such as capillary radius, boundary layer slip, and
disjoining pressure that may be important for dewatering layer-structured minerals.
Our two-phase flow model assumes that a filter cake consists of multiple straight capillaries of a uniform
radius (r) as follows,
dV
AP

2
dt [8L / kr (1  b / 4r )  Rm ]
in which V is the volume of liquid with a viscosity  flowing through a filter of thickness L and a cross sectional area
A; k is the fraction of A due to capillaries; Rm is the medium resistance; P is the pressure drop across the filter cake
and a filter medium; and b is the slip length at the solid/liquid interface. These model parameters have been determined
iteratively using the experimental data obtained on kaolin clay with a 2 m top size.
As shown in Figure 1, the experimental data
obtained in pure water can be fitted with r = 49.5 nm and
other parameters shown in the figure. The data obtained in
the presence of dodecylaminiumhydrochloride (DAH) can
be fitted with r = 82 nm assuming that b = 0 and k = 0.63.
These results suggest that the improved dewatering
kinetics observed with DAH may be due to the increase in
capillary radius, which in turn can be attributed to the
hydrophobic coagulation associated with the increase in
water contact angle () of clay (Xu and Yoon, 1990). The
model is useful to study the effects of colloidal forces,
cake structure, and medium structure on dewatering
kinetics.
Reference:
Xu, Z. and Yoon, R.-H., 1990, A study of hydrophobic
coagulation, J Colloid Interf. Sci., 134, 427-434.
Fig. 1. Effect of DAH on the rate of filtration for
kaolinite clay at a driving pressure of 15 psi.
KEYWORDS
Modelling, Filtration, Mature fine tailing, Kaolinite, Dewatering aids, Hydrophobic