Capillary imbibition of a non-Newtonian fluid following a liquid slug in irregular capillaries

Capillary imbibition of a liquid displacing a pre-existing liquid slug arises in porous media and underlies sequential mixing in aluminium-anode manufacturing, where pitch first penetrates coke-particle pores before being displaced by a pitch–fine-coke binder matrix. We develop a lubrication-based analytical model for spontaneous imbibition of a non-Newtonian shear-thinning fluid following a generalized non-Newtonian liquid slug in an axially varying three-dimensional capillary. The model retains inertia, bulk viscous dissipation, geometric irregularity and contact-line resistance, the latter described using molecular kinetic theory to account for dynamic contact-angle effects. Volume-of-fluid simulations, together with prior experimental data, are used to validate the model and establish a predictive correlation for the molecular-kinetic fitting parameter. The model identifies three filling regimes: (i) an early inertia-dominated regime in which the penetration length grows quadratically in time, (ii) a late viscous-dissipation-dominated regime in which it follows the classical power-law imbibition scaling, and (iii) an intermediate linear penetration regime with nearly constant velocity. This linear regime may arise from short-lived interfacial dissipation or from longer-lived slug viscous dissipation; the latter is promoted by larger viscosity ratio, slug length and slug power-law index. A stress ratio separating these mechanisms is introduced, and correlations for the linear-regime capillary number and penetration velocity are proposed and validated. Application to anode manufacturing shows that pitch-first sequential mixing can substantially enhance open-pore saturation relative to conventional simultaneous mixing, although possible increases in interparticle voids require experimental assessment of the net effect on total anode porosity.