Fluid flow through porous media

In fluid mechanics, fluid flow through porous media is the manner in which fluids behave when flowing through a porous medium, for example sponge or wood, or when filtering water using sand or another porous material. As commonly observed, some fluid flows through the media while some mass of the fluid is stored in the pores present in the media. In fluid mechanics, fluid flow through porous media is the manner in which fluids behave when flowing through a porous medium, for example sponge or wood, or when filtering water using sand or another porous material. As commonly observed, some fluid flows through the media while some mass of the fluid is stored in the pores present in the media. The basic law governing the flow of fluids through porous media is Darcy's Law, which was formulated by the French civil engineer Henry Darcy in 1856 on the basis of his experiments on vertical water filtration through sand beds. For transient processes in which the flux varies from point to-point, the following differential form of Darcy’s law is used. Darcy's law is valid for situation where the porous material is already saturated with the fluid. For the calculation of capillary imbibition speed of a liquid to an initially dry medium, Washburn's or Bosanquet's equations are used. Mass conservation of fluid across the porous medium involves the basic principle that mass flux in minus mass flux out equals the increase in amount stored by a medium. This means that total mass of the fluid is always conserved. In mathematical form, considering a time period from t {displaystyle t} to Δ t {displaystyle Delta t} , length of porous medium from x {displaystyle x} to Δ x {displaystyle Delta x} and m {displaystyle m} being the mass stored by the medium, we have Furthermore, we have that m = ρ V p {displaystyle m= ho V_{p}} , where V p {displaystyle V_{p}} is the pore volume of the medium between x {displaystyle x} and x + Δ x {displaystyle x+Delta x} and ρ {displaystyle ho } is the density. So m = ρ V p = ρ ϕ V = ρ ϕ A Δ x , {displaystyle m= ho V_{p}= ho phi V= ho phi ADelta x,} where ϕ {displaystyle phi } is the porosity. Dividing both sides by A Δ x {displaystyle ADelta x} , while Δ x → 0 {displaystyle Delta x ightarrow 0} , we have for 1 dimensional linear flow in a porous medium the relation