2012
Modeling Transport Phenomena in Anisotropic Fibrous Media
H.V. Tafreshi1* and T.M. Bucher1
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Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University,
Richmond, Virginia 23284-3015.
*email: htafreshi@vcu.edu; phone: 804-828-9936; url: http://www.people.vcu.edu/~htafreshi/
ABSTRACT: We present a dual-scale methodology for modeling fluid imbibition and drainage in
fibrous porous media. Our approach is based on obtaining mathematical expressions for the
variation of a medium’s capillary pressure and permeability with respect to saturation via 3-D
numerical simulations conducted on the microscale (scales comparable to the dimensions of the
constituent fibers). This information is then used in a macroscale model (scales comparable to
the medium itself) to solve the Richards equation for two-phase flows in porous media,
predicting the rate of fluid absorption or drainage in a fibrous material as a function of time and
space. For the case of drainage from thin fibrous sheets, we also take into consideration the
affinity of the flat surface for the fluid in the fabric by way of a diffusive boundary condition
treatment in the Richards equation. This makes the model sensitive to the surface as well as the
fabric. A peculiar feature of the simulation method presented here is the possibility of isolating
different microstructure parameters in the medium (fiber diameter, fiber orientation…) and
studying their influence on the rate of fluid absorption and drainage.
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