(270a) Towards a Refined Theory for Liquid Transfer in Dense and Dilute Particle Beds

Radeke, C., Research Center Pharmaceutical Engineering (RCPE)
Khinast, J. G., Graz University of Technology

Existing research has focused on
forces connected to liquid bridges, yet there is much less theory concerned
with the process of liquid transfer upon particle-particle and particle-wall
collisions. Previous work on liquid transfer [1?3] used either a solution of the
Navier-Stokes equation in a simplified (i.e., axisymmetric) setup, or simpler
models that often neglect fluid inertia. These previous studies focused
exclusively on the rupture process. One of the missing links for a more general
model for liquid transfer seems to be a dynamical description of the process of
bridge formation.

Starting with the algorithm
documented by Shi and McCarthy [3], we calculate the driving pressure
difference that causes a drainage of free liquid from the wetted surfaces into a
liquid bridge. This process is coupled with the evolution of the film thickness
on wetted surfaces via a simple mass and force balance. This allows us to
calculate the instantaneous liquid bridge volume as a function of the amount of
liquid present on the surfaces in contact. A fit of the solution of Shi and
McCarthy model [3] for the liquid transfer ratio upon
rupture completes our liquid transfer model.

Finally, we study the effect of
various liquid transfer models on the liquid distribution for various test
cases using our in-house Discrete Element Method-based code. Interestingly, already
one of our simplest models predicts an imbibition front that progresses with l²~t,
i.e., yields Washburn's law.


[1]      P. Darabi, T. Li, K. Pougatch, M. Salcudean, and D. Grecov,
Modeling the evolution and rupture of stretching pendular liquid bridges. Chem.
Eng. Sci. 65 (2010) 4472-4483.

[2]      S. Dodds, M. Carvalho, and S.
Kumar, Stretching liquid bridges with moving contact lines: The role of
inertia. Phys. Fluids 23 (2011) 092101.

[3]      D. Shi and J.J. McCarthy,
Numerical simulation of liquid transfer between particles. Powder
Technol. 184 (2008) 64-75.

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