Linear response theory of front back-contraction during a single Haines jump

We study the linear response of a fluid–fluid interface in a porous medium subjected to a localised, transient perturbation. A single pore is driven out of mechanical equilibrium by a small displacement, initiating a back-contraction of the interface. Assuming negligible total flow, the interface relaxes with a time- and space-dependent profile h left parenthesis x comma t right parenthesis h ( x , t ) $h(x,t)$ , modelled for a flat geometry. This set-up reflects conditions achievable experimentally using a localised heterogeneity in pore-throat sizes. We determine the evolving interface shape during the relaxation process, together with the associated pressure and velocity fields, using both analytical calculations and pore-network simulations.