Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session N01: Poster Session (3:20-4:05pm)
3:20 PM,
Monday, November 22, 2021
Abstract: N01.00127 : Mechanics of Saturated Colloidal Packings: A Comparison of Two Models*
Presenter:
ATIYA BADAR
(Indian Institute of Technology Bombay)
Authors:
ATIYA BADAR
(Indian Institute of Technology Bombay)
Mahesh S Tirumkudulu
(Indian Inst of Tech-Bombay)
critically on the use of appropriate constitutive relation for the material. The most commonly
used stress–strain relation that captures the behavior of poroelastic materials saturated
with a liquid is that proposed by Biot (J Appl Phys 12:155–164, 1941). It is a linear
theory akin to the generalized Hooke’s law containing material constants such as the effective
bulk and shear modulus of the porous material. However, the effective elastic coefficients
are not known a priori and need to be determined either via separate experiments or
by fitting predictions with measurements. The main cause for this drawback is that Biot’s
theory does not account for the microstructural details of the system. This limitation in
Biot’s model can be overcome by utilizing the constitutive relation proposed by Russel
et al. (Langmuir 5(24):1721–1730, 2008) for the case of colloidal packings. We show that
in the linear limit, the constitutive relation proposed by Russel and coworkers is equivalent
to that of Biot. The elastic coefficients obtained from such a linearization are related to the
micro-structural details of the packing such as the particle modulus, the packing concentration
and the nature of packing, thereby enabling a more effective utilization of Biot’s model
for problems in the linear limit. The derivation ignores surface forces between the particles,
which makes the results also applicable to particles whose sizes are beyond the colloidal
range. We compare the predictions of Biot’s model to those of the linearized model of Russel
and coworker’s for two different one-dimensional model problems: fluid outflow driven
by an applied mechanical load, also termed as the consolidation problem, and wave propagation
in a saturated colloidal packing.
*IIT Bombay for financial support. The project was funded in part byDepartment of Science and Technology, India.
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