How Honey Flows Through a Sponge: New Equations express
Drop honey onto a sponge. It lazily creeps, avoiding the voids. But if the honey becomes thinner under pressure, the flow gets trickier. Liquid with variable thickness in an uneven labyrinth of pores — a problem that had defied calculation. The authors of the new work averaged the chaos of microchannels into simple equations. The key trick is a braking function: it describes how the porous skeleton grabs the flow, like a sponge holding back the sweet stream.
These equations are now being applied to oil reservoirs. When oil seeps through rock, accurate prediction boosts recovery. The model explains why, in narrow pores, friction breaks orderly flow into disorder. This energy game was deciphered by Ludwig Boltzmann, building on Isaac Newton’s experiments with fluidity.
Original abstract
as written by the authors arXiv:2512.03240
Equations governing the flow of a polar fluid, with pressure-dependent Newtonian viscosity, through a variable-porosity medium are developed. Averaged equations are obtained using intrinsic volume averaging. A drag function is introduced to account for the interactions of the fluid with the porous matrix. Darcy and Forchheimer generalized terms are included in the model equations for both granular and consolidated media to account for the effects of the porous microstructure.
The equations for porous media were first derived by an engineer building fountains in Dijon: he needed to prevent water from eroding the city.