Capillary forces measurement

O.D. Velev, N.D. Denkov, V.N. Paunov, P.A. Kralchevsky, and K. Nagayama, Direct measurement of lateral capillary forces, Lan mMir, 9,3702-3709 (1993). C.D. Dushkin, P.A. Kralchevsky, H. Yoshimura, and K. Nagayama, Lateral capillary forces measured by torsion microbalance, Phys. Rev. Lett., 75, 3454-3457 (1995). 

Streaming potentials, like other electrokinetic effects, are difficult to measure reproducibly. One means involves forcing a liquid under pressure through a porous plug or capillary and measuring E by means of electrodes in the solution on either side [6, 23, 71-73]. 

Protein adsorption has been studied with a variety of techniques such as ellipsome-try [107,108], ESCA [109], surface forces measurements [102], total internal reflection fluorescence (TIRE) [103,110], electron microscopy [111], and electrokinetic measurement of latex particles [112,113] and capillaries [114], The TIRE technique has recently been adapted to observe surface diffusion [106] and orientation [IIS] in adsorbed layers. These experiments point toward the significant influence of the protein-surface interaction on the adsorption characteristics [105,108,110]. A very important interaction is due to the hydrophobic interaction between parts of the protein and polymeric surfaces [18], although often electrostatic interactions are also influential [ 116]. Protein desorption can be affected by altering the pH [117] or by the introduction of a complexing agent [118]. 

Capillary Viscometers. Capillary flow measurement is a popular method for measuring viscosity (21,145,146) it is also the oldest. A Hquid drains or is forced through a fine-bore tube, and the viscosity is determined from the measured flow, appHed pressure, and tube dimensions. The basic equation is the Hagen-Poiseuike expression (eq. 17), where Tj is the viscosity, r the radius of the capillary, /S.p the pressure drop through the capillary, IV the volume of hquid that flows in time /, and U the length of the capillary. 

Surfactants aid dewatering of filter cakes after the cakes have formed and have very Httle observed effect on the rate of cake formation. Equations describing the effect of a surfactant show that dewatering is enhanced by lowering the capillary pressure of water in the cake rather than by a kinetic effect. The amount of residual water in a filter cake is related to the capillary forces hoi ding the Hquids in the cake. Laplace s equation relates the capillary pressure (P ) to surface tension (cj), contact angle of air and Hquid on the soHd (9) which is a measure of wettabiHty, and capillary radius (r ), or a similar measure appHcable to filter cakes. 

It can be shown, (Gibbs, Scientific Papers, I. J. J. Thomson, Applications of Dynamics to Physics and Chemistry), that a chemical equilibrium can be modified by the action of capillary forces. Thus, a state of equilibrium in solution may conceivably be modified if the latter is in the form of thin films, such as soap bubbles. Since, according to Freundlich (Kapillarchemie, 116), there is at present no direct evidence of the existence of such modification (which would no doubt be exceedingly, though possibly measurably, small) we shall not enter any further into the matter here. 

Here the phenomenon of capillary pore condensation comes into play. The adsorption on an infinitely extended, microporous material is described by the Type I isotherm of Fig. 5.20. Here the plateau measures the internal volume of the micropores. For mesoporous materials, one will first observe the filling of a monolayer at relatively low pressures, as in a Type II isotherm, followed by build up of multilayers until capillary condensation sets in and puts a limit to the amount of gas that can be accommodated in the material. Removal of the gas from the pores will show a hysteresis effect the gas leaves the pores at lower equilibrium pressures than at which it entered, because capillary forces have to be overcome. This Type IV isotherm. 

Another measure of wetting character in the field is the dimensionless capillary number N, which is the ratio of viscous to capillary forces. One expression for this number is (24)... 

The interplay between the attractive (e.g.. Van der Waals or capillary forces) and repulsive forces involved during the approach of the tip to different surfaces under different environments are presented in Fig. 5 and discussed here. When the cantilever approaches a hard and non-compressible surface (Fig. 5a), at first the forces are too small to produce any measurable deflection of the cantilever, and therefore the position of the cantilever remains unchanged. At a certain distance the attractive forces overcome the cantilever spring constant and the tip leaps into contact with the specimen surface (Fig. 5b). As the cantilever continues to press down while the tip rests on the surface, the separation between the base of the tip and the sample decreases further, which results in the deflection of the tip with a subsequent increase... 

In the non-contact mode (Fig. 6b), AFM acquires the topographic images from measurements of attractive forces in close proximity of the surface, as the tip does not touch the sample and the cantilever oscillates close to the sample surface [12]. This mode is difficult to work with in ambient conditions due to the interference of the capillary forces. Very stiff cantilevers are needed so that the attraction does not overcome the spring constant of the cantilever. However, the lack of contact with the sample means that this mode should be the least invasive and hence cause the least disruption. The disadvantage of this method is that the tip may jump into contact with the surface due to attractive forces. 

Further, it is known that real-world capillaries or pores are not always circular shaped. In fact, in oil reservoirs, the pores are more triangular shaped or square shaped than circular. In this case, the rise in capillaries of other shapes, such as rectangular or triangular (Birdi et al 1988 Birdi, 1997, 2002) can be measured. These studies have much significance in oil recovery or water treatment systems. In any system in which the fluid flows through porous material, it would be expected that capillary forces would be one of the most dominant factors. 

Ordinary foams from detergent solutions are initially thick (measured in micrometers), and, as the fluid hows away, due to gravity or capillary forces or surface evaporation, the him becomes thinner (by a few hundred angstroms). 

Interfacial tension may be measured by a number of techniques, including determining how far a solution rises in a capillary, by measuring the weight, volume or shape of a drop of solution formed at a capillary tip, measuring the force required to pull a flat plate or ring from the surface or the maximum pressure required to form a bubble at a nozzle immersed in the solution. Ring or plate techniques are most commonly used to determine y of milk. 

In SFM, the probe tip is mounted on a highly sensitive, cantilever-type spring. The force of interaction between the sample and the tip can be calculated from the spring constant and the measured deflection of the cantilever. The deflection is sensed using the STM principle (Vignette 1.8) or capacitance or optical methods. The SFM can be operated in the contact regime or like the SFA. In the latter mode, one can measure van der Waals forces (see Chapter 10), ion-ion repulsion forces (see Chapter 11), and capillary forces and frictional forces, among others. In contrast to STM, the SFM can be used for both conductors and... 

Capillary forces of attraction cause the hydrate-encrusted droplets to agglomerate. These capillary forces are a strong function of temperature at low temperatures the forces decrease between the particles, as measured by Taylor (2006). 

These long protruding chemical strands provide separation of the hydrate particles, so that agglomeration does not occur for the suspension in the oil phase. As measured by Yang et al. (2004) and by Taylor (2006), without such prevention the capillary forces between the hydrate particles are very strong, and can lead to large hydrate masses. 

In addition to the compression loading, uniaxial extension of entangled PDMS chains have been investigated by pulling a small portion of the material and measuring elastic response before the rupture happens [419]. The multiple ruptures observed in the force-distance curves (Fig. 43) have been interpreted as fractures of an entangled network of PDMS chains formed between the tip and the silica grafted surface. At small deformations, also the capillary forces were shown to contribute in the force. The elastic part of the curves was described us-... 

Magnetic resonance imaging permitted direct observation of the liquid hold-up in monolith channels in a noninvasive manner. As shown in Fig. 8.14, the film thickness - and therefore the wetting of the channel wall and the liquid hold-up -increase nonlinearly with the flow rate. This is in agreement with a hydrodynamic model, based on the Navier-Stokes equations for laminar flow and full-slip assumption at the gas-liquid interface. Even at superficial velocities of 4 cm s-1, the liquid occupies not more than 15 % of the free channel cross-sectional area. This relates to about 10 % of the total reactor volume. Van Baten, Ellenberger and Krishna [21] measured the liquid hold-up of katapak-S . Due to the capillary forces, the liquid almost completely fills the volume between the catalyst particles in the tea bags (about 20 % of the total reactor volume) even at liquid flow rates of 0.2 cm s-1 (Fig. 8.15). The formation of films and rivulets in the open channels of the structure cause the further slight increase of the hold-up. 

Figure 86. Haines Apparatus for Measuring Changes in Capillary Forces.

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