How Honey Flows Through a Sponge: New Equations ⚡ экспресс
Governing equations have been derived for the flow of a polar liquid with pressure-dependent Newtonian viscosity through media with variable porosity. Using intrinsic volume averaging, macroscopic conservation equations were obtained. To account for fluid-porous matrix interaction, a resistance function was introduced. The model incorporates generalized Darcy and Forchheimer terms, capturing the contribution of pore microstructure in both granular and consolidated media. The developed equation system can be applied to calculate filtration of complex fluids in engineered and natural porous materials.
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.
🎯 The equations for porous media were first derived by an engineer building fountains in Dijon—he needed to prevent water from eroding the city.