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==Capillary pressure concepts==

==Capillary pressure concepts==

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.jpg|thumb|{{figure_number|1}}Effects of interaction of adhesive and cohesive forces on [[wettability]]. (a) If adhesive forces are greater than the cohesive forces, the fluid spreads out on the surface and is termed '''''wetting. '''''(b) If cohesive forces exceed adhesive forces, the liquid beads up and is termed nonwetting. The measure of relative [[wettability]] is the contact angle (θ), which is measured through the denser phase.]]

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.jpg|thumb|left|{{figure_number|1}}Effects of interaction of adhesive and cohesive forces on [[wettability]]. (a) If adhesive forces are greater than the cohesive forces, the fluid spreads out on the surface and is termed '''''wetting. '''''(b) If cohesive forces exceed adhesive forces, the liquid beads up and is termed nonwetting. The measure of relative [[wettability]] is the contact angle (θ), which is measured through the denser phase.]]

Capillary pressure results from interactions of forces acting within and between fluids and their bounding solids. These include both ''cohesive'' forces (surface and interfacial tension) and ''adhesive'' (liquid-solid) forces. When adhesive forces are greater than cohesive forces, the liquid is said to be ''wetting'' ([[:File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.jpg||Figure 1a]]). When cohesive forces exceed adhesive forces, the liquid is ''nonwetting'' ([[:File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.jpg|Figure 1b]]). The relative [[wettability]] of the fluids is described by the ''contact angle'' (θ), which is the angle between the solid and the fluid-fluid interface as measured through the denser fluid ([[:File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.jpg|Figure 1]]).

Capillary pressure results from interactions of forces acting within and between fluids and their bounding solids. These include both ''cohesive'' forces (surface and interfacial tension) and ''adhesive'' (liquid-solid) forces. When adhesive forces are greater than cohesive forces, the liquid is said to be ''wetting'' ([[:File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.jpg||Figure 1a]]). When cohesive forces exceed adhesive forces, the liquid is ''nonwetting'' ([[:File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.jpg|Figure 1b]]). The relative [[wettability]] of the fluids is described by the ''contact angle'' (θ), which is the angle between the solid and the fluid-fluid interface as measured through the denser fluid ([[:File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.jpg|Figure 1]]).

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_2.jpg|thumb|{{figure_number|2}}The wetting phase rises above the original or free surface in the capillary tube experiment until adhesive and gravitational forces balance. Capillary pressure (P_c) is the difference in pressure measured across the interface in the capillary (''P''_c = ''P''_nw - ''P''_w). This pressure results from the contrast in pressure gradients caused by the different densities of the nonwetting (''ρ''_nw) and wetting (''ρ''_w) phases (right).]]

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_2.jpg|thumb|{{figure_number|2}}The wetting phase rises above the original or free surface in the capillary tube experiment until adhesive and gravitational forces balance. Capillary pressure (P_c) is the difference in pressure measured across the interface in the capillary (''P''_c = ''P''_nw - ''P''_w). This pressure results from the contrast in pressure gradients caused by the different densities of the nonwetting (''ρ''_nw) and wetting (''ρ''_w) phases (right).]]

If the end of a narrow capillary tube is placed in a wetting fluid, net adhesive forces draw the fluid into the tube (Figure 2). The wetting phase rises in the capillary above the original interface or ''free surface'' until adhesive and gravitational forces are balanced. Because the wetting and nonwetting fluids have different densities, they also have different pressure gradients (Figure 2). ''Capillary pressure'' (''P''_c) is defined as the difference in pressure across the meniscus in the capillary tube. Put another way, capillary pressure is the amount of extra pressure required to force the nonwetting phase to displace the wetting phase in the capillary. Capillary pressure can be calculated as follows:

 

If the end of a narrow capillary tube is placed in a wetting fluid, net adhesive forces draw the fluid into the tube ([[:File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_2.jpg||Figure 2]]). The wetting phase rises in the capillary above the original interface or ''free surface'' until adhesive and gravitational forces are balanced. Because the wetting and nonwetting fluids have different densities, they also have different pressure gradients ([[:File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_2.jpg|Figure 2]]). ''Capillary pressure'' (''P''_c) is defined as the difference in pressure across the meniscus in the capillary tube. Put another way, capillary pressure is the amount of extra pressure required to force the nonwetting phase to displace the wetting phase in the capillary. Capillary pressure can be calculated as follows:

:<math>P_\mathrm{c} = (\rho_\mathrm{w} - \rho_\mathrm{nw}) g h</math>, or

:<math>P_\mathrm{c} = (\rho_\mathrm{w} - \rho_\mathrm{nw}) g h</math>, or