Number capillary

Fig. 10. Reverse-roU, metered film thickness on the appHcator roU divided by gap, tjG, as a function of the ratio of the metering roU speed, U, to apphcator roU speed, U, for various capillary numbers. (—) represents theoretical values ( ) experimental ones and (------) is the lubrication model (11).

S. E. Kistier and L. E. Scriven, "Finite Element Analysis of Dynamic Wetting for Curtain Coating at High Capillary Numbers," presented at... 

For other packings and for the case in which static holdup is changed by gas flowing through the bed, the method of Dombrowsld and Brownell [Jnd. Eng. Chem., 46, 1207 (1954)], which correlates static holdup with a dimensionless capillary number, should be used. 

We next determine the residual saturation, m , by first calculating the dimensionless capillary number ... 

To understand how the dispersed phase is deformed and how morphology is developed in a two-phase system, it is necessary to refer to studies performed specifically on the behavior of a dispersed phase in a liquid medium (the size of the dispersed phase, deformation rate, the viscosities of the matrix and dispersed phase, and their ratio). Many studies have been performed on both Newtonian and non-Newtonian droplet/medium systems [17-20]. These studies have shown that deformation and breakup of the droplet are functions of the viscosity ratio between the dispersity phase and the liquid medium, and the capillary number, which is defined as the ratio of the viscous stress in the fluid, tending to deform the droplet, to the interfacial stress between the phases, tending to prevent deformation ... 

There is a number of theoretical and experimental relations determining the dependence of the dynamic contact angle on flow velocity (Dussan 1979 Ngan and Dussan 1982 Cox 1986 Blake 1994 Kistler 1993). Hoffman (1975) expressed the dynamic contact angle as a function solely of dimensionless parameters capillary number Ca... 

Species concentration Capillary number Concentration of species a Computer aided design Concentration of species b Charge-coupled device Eluid specific heat Computational fluid dynamics Constrained-geometry catalyst Concentration at node i Concentration of species i Elux limiter Specific heat... 

Relative permeability and capillary pressure functions, collectively called multiphase flow functions, are required to describe the flow of two or more fluid phases through permeable media. These functions primarily depend on fluid saturation, although they also depend on the direction of saturation change, and in the case of relative permeabilities, the capillary number (or ratio of capillary forces to viscous forces). Dynamic experiments are used to determine these properties [32]. 

Conventionally, the sample is initially saturated with one fluid phase, perhaps including the other phase at the irreducible saturation. The second fluid phase is injected at a constant flow rate. The pressure drop and cumulative production are measured. A relatively high flow velocity is used to try to negate capillary pressure effects, so as to simplify the associated estimation problem. However, as relative permeability functions depend on capillary number, these functions should be determined under the conditions characteristic of reservoir or aquifer conditions [33]. Under these conditions, capillary pressure effects are important, and should be included within the mathematical model of the experiment used to obtain property estimates. 

The ratio of deforming viscous forces to resisting interfacial tension forces in the case of droplets is the capillary number, Ca. Similarly, the ratio of viscous to cohesive forces in agglomerates is the fragmentation number, Fa. 

The tensor L defines the character of the flow. The capillary number for the drop deformation and breakup problem is... 

The degree of deformation and whether or not a drop breaks is completely determined by Ca, p, the flow type, and the initial drop shape and orientation. If Ca is less than a critical value, Cacri the initially spherical drop is deformed into a stable ellipsoid. If Ca is greater than Cacrit, a stable drop shape does not exist, so the drop will be continually stretched until it breaks. For linear, steady flows, the critical capillary number, Cacrit, is a function of the flow type and p. Figure 14 shows the dependence of CaCTi, on p for flows between elongational flow and simple shear flow. Bentley and Leal (1986) have shown that for flows with vorticity between simple shear flow and planar elongational flow, Caen, lies between the two curves in Fig. 14. The important points to be noted from Fig. 14 are these ... 

Fig. 14. Critical capillary number (Cac ) as a function of the viscosity ratio (p) for two-dimensional linear flows with varying vorticity (Bentley and Leal, 1986).

Figure 9 teaches that large pore-body to pore-throat radii ratios lead to a more unstable foam. The effect is more dramatic for higher capillary numbers. 

Pc for capillary numbers relevant to reservoir displacement rates. 

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