267419 Towards a Refined Theory for Liquid Transfer in Dense and Dilute Particle Beds
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 , 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  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.
 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.
 S. Dodds, M. Carvalho, and S. Kumar, Stretching liquid bridges with moving contact lines: The role of inertia. Phys. Fluids 23 (2011) 092101.
 D. Shi and J.J. McCarthy, Numerical simulation of liquid transfer between particles. Powder Technol. 184 (2008) 64-75.