Capillary Pressure Gradients

Capillary pressure gradients and Marongoni flow induce flow in porous media comprising glass beads or sand particles [40-42], Wetting and spreading processes are an important consideration in the development of inkjet inks and paper or transparency media [43] see the article by Marmur [44] for analysis of capillary penetration in this context. 

The asymmetry in the capillary pressure gradients distribution around a bubble-cap adjacent to an empty cavity is supposed to be the main... 

Eq. (10), when compared to Poiseuille s law, is characterized by an enhancement factor ((r-t) /r )ft RT/MPm, which is physically attributed to capillary pressure gradients [15] Indeed, an additional driving force occurs due to the difference in the curvatures of the menisci that are formed... 

Hydrostatic secondary hydrocarbon migration systems, in which the dominant forces influencing hydrocarbon migration are the buoyancy forces and the capillary pressure gradients (Section 4.3.3). 

Under the assumption that the capillary pressure gradient across the carrier rock-barrier rock interface is the only significant resistant force affecting hydrocarbon accumulation in a conventional hydrostatic trap, i.e. the influence of the hydrodynamic condition in the barrier rock on its sealing capacity can be considered to be negligible, the maximum height of the hydrocarbon column below the barrier rock can be given by Equation 4.22... 

Magnitude and direction of the capillary pressure gradient (grad p )... 

Snap-Off A mechanism for foam lamella generation in porous media. When gas enters and passes through a constriction in a pore, a capillary pressure gradient is created and causes liquid to flow toward the region of the constriction, where it accumulates and may cause the gas to pinch-off or snap-off to create a new gas bubble separated from the original gas by a liquid lamella. See also Lamella Division, Lamella Leave-Behind. 

Figure 12.36 illustrates the relationship between the static liquid and static vapor pressures in an operating heat pipe. As shown, the capillary pressure gradient across a liquid-vapor interface is equal to the pressure difference between the liquid and vapor phases at any given axial position. For a heat pipe to function properly, the net capillary pressure difference between the wet and dry points, identified in Fig. 12.36, must be greater than the summation of all the pressure losses occurring throughout the liquid and vapor flow paths. This relationship, referred to as the capillary limitation, can be expressed mathematically as... 

Finally, the fluxes of liquid and gas are represented in Figure 7. From these fluxes it can be observed that the dried zone is not static. Liquid water continuously flows towards the dry zone due to capillary pressure gradients. This flux is compensated by water evaporation and gas flow in the opposite direction. The downward regional flux is diverted by the dried zone. This indicates that dissolved substances would tend to be confined in the dried zone because, although water is flowing, the flow in the outward direction is gas flow and does not transport solutes while the flow in the inward direction is liquid flow. So, solutes would tend to precipitate in the dry zone. 

Condensation occurs throughout the anodic GDL due to hydrogen depletion. Similar to the cathode side, the liquid water can only leave the GDL through the build-up of a capillary pressure gradient to overcome the viscous drag, because at steady state operation, all the condensed water has to leave the cell. 

Knowing the surface tension y of the material, the primary particles of diameter d, the sinter bridge diameter x and the radius of meniscus curvature s, the capillary pressure gradient can be calculated through Eq. 7.10 ... 

---