Capillary flow contact angle

Because ceramic powders usually have macropores, mercury porosimetry is more suitable than gas adsorption. The principle of the technique is the phenomenon of capillary rise, as shown schematically in Fig. 4.4 [19]. When a liquid wets the walls of a narrow capillary, with contact angle, 9 < 90°, it will climb up the walls of the capillary. If the liquid does not wet the walls of a capillary, with contact angle, 9 > 90°, it will be depressed. When a nonwetting liquid is used, it is necessary to force the liquid to flow up the capillary to the level of the reservoir by applying a pressure. For a capillary with principal radii of curvature rj and r2 in two orthogonal directions, the pressure can be obtained by using the Young and Laplace equation ... 

The Washburn model is consistent with recent studies by Rye and co-workers of liquid flow in V-shaped grooves [49] however, the experiments are unable to distinguish between this and more sophisticated models. Equation XIII-8 is also used in studies of wicking. Wicking is the measurement of the rate of capillary rise in a porous medium to determine the average pore radius [50], surface area [51] or contact angle [52]. 

Barajas AM, Panton RL (1993) The effect of contact angle on two-phase flow in capillary tubes. Int J Multiphase Flow 19 337-346... 

First we restricted ourselves to considering a particular case of flow in a capillary tube with q j = const. ((/ = 0). We also neglected the change of the capillary pressure through the changes of the contact angle, due to the motion of the meniscus. Accordingly we assume that / = 0 in condition (11.25). 

In this section the influence of the pressure in the capillary and the heat flux fluctuations on the stability of laminar flow in a heated capillary tube is analyzed. All the estimations performed in the framework of the general approach and developed in the previous section are kept also in the present cases. Below we will assume that the single cause for capillary pressure oscillations is fluctuations of the contact angle due to motion of the meniscus, whereas heat flux oscillations are the result of fluid temperature fluctuations only. 

Assuming that the dynamic contact angle 9d is a sum of its basic value corresponding to stationary flow 0st and small perturbation 9 we arrive at the following relation for the fluctuation of capillary pressure... 

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... 

Equation (52) allows us to estimate the impact of viscoelastic braking on the capillary flow rate. As an example, we will consider that the liquid is tricresyl phosphate (TCP, 7 = 50 mN-m t = 0.07 Pa-s). The viscoelastic material is assumed to have elastic and viscoelastic properties similar to RTV 615 (General Electric, silicone rubber), i.e., a shear modulus of 0.7 MPa (E = 2.1 MPa), a cutoff length of 20 nm, and a characteristic speed, Uo, of 0.8 mm-s [30]. TCP has a contact angle at equilibrium of 47° on this rubber. 

Finally, we consider the case of a sohd particle attached to a hquid-fluid interface. This configuration is depicted in Figure 5.17e note that the position of the particle along the normal to the interface is determined by the value of the three-phase contact angle. Stoos and Leal investigated the case when such an attached particle is subjected to a flow directed normally to the interface. These authors determined the critical capillary number, beyond which the captured particle is removed from the interface by the flow. 

Capillarity may be defined as the phenomena resulting from the fact that a free liquid surface has a finite or zero contact angle with a solid wall and will attain this angle when placed in contact with the wall. It is commonly thought of as the rise (or fall) of liquids in small tubes or finely porous media. More generally, capillary motion can be said to be any flow that is governed in some measure by the forces associated with surface tension. Ordinary capillarity is observed in a fine tube open at both ends that is placed vertically in a pool of liquid exposed to the atmosphere, with the liquid seen to attain a level in the tube above the level of the pool. The actual rise velocity of the free surface of the liquid in the tube from the level of the pool is one simple example of capillary motion. ... 

An alternative approach to forced flow is to seal the layer with a flexible membrane or an optically flat, rigid surface under hydraulic pressure, and to deliver the mobile phase to the layer by a pump [9,41,43-46]. Adjusting the solvent volume delivered to the layer optimizes the mobile phase velocity. In the linear development mode, the mobile phase velocity (uf) will be constant and the position of the solvent front (Zf) at any time (t) after the start of development is described by Zf = Uft. The mobile phase velocity no longer depends on the contact angle and solvent selection is unrestricted for reversed-phase layers in forced flow, unlike capillary flow systems. 

Resistance to Flow in Capillary Systems of Positive Contact Angle... 

The rationalization of their data at intermediate velocities in terms of interfacial effects is a valient attempt at understanding dynamic contact angles in terms of surface interactions. However, the dynamic angle was measured by optical methods which, as in the case of flow in capillary tubes, gives 0 values considerably away fi-om the line of intersection and it is problematical whether they are governed by hydrodynamic forces or by surface forces. 

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