Capillary force balance

The mobile phase is transported from the trough to the sorbent layer by surface tension and capillary forces and will continue to travel through the sorbent layer by capillary action. When a plate is developed from both edges simultaneously, the chamber must be kept in a perfectly horizontal position to allow the two solvent fronts the same rate of migration and to meet precisely in the middle. At this point, the capillary forces balance out and the chromatographic development ceases. 

Also, we have recently used the capillary force balance in conjunction with reflected-light microinterferometry to study stratification (i.e., micelles ordered in layers) phe-... 

The third chapter, by Wasan and Nikolov, discusses fundamental processes in emulsions, i.e., ereaming/sed-imentation, flocculation, coalescence, and final phase separation. A number of novel experimental facilities for characterization of emulsions and the above-mentioned processes are presented. This chapter highlights recent techniques such as film rheometry for dynamic film properties, capillary force balance in eonjunetion with differential microinterferometry for drainage of curved emulsion films, Kossel diffraction, imaging of interdroplet interactions, and piezo imaging spectroscopy for drop-homophase coalescence rate processes. 

A combination of adhesion and surface tension gives rise (pardon the pun) to capillary action. By its adhesion to the solid surface of the soil particles, the water wants to cover as much solid surface as possible. However, by the effect of surface tension, the water molecules adhering to the solid surface are connected with a surface him in which the stresses cannot exceed the surface tension. As water is attracted to the soil particles by adhesion, it will rise upward until attractive forces balance the pull of gravity (Figure 3.28). Smaller-diameter tubes force the air-water surface into a smaller radius, with a lower solid-surface-to-volume ratio, which results in a greater capillary force. Typical heights of capillary rise for several soil types are presented in Table 3.9. The practical relationship between normal subsurface water and capillary rise is presented in the following equation. 

Steady skirt lengths increase with Re (B3, H5, W2). Wairegi (W2) and Bhaga (B3) also reported skirt lengths which increased with time. The length of steady skirts is controlled by a balance of viscous and capillary forces at the rim of the skirt (B3), whereas the length of wavy skirts appears to be determined by growth of Helmholtz instability waves (H5). 

To explain this spreading rate behavior, Nikolov et al. [35] postulated that the excess driving force (assuming that capillary and hydrostatic forces balance each other) is a radial surface tension gradient, which can be approximated as... 

The situation shown in Figure 6.2b is one in which surface tension and contact angle considerations pull a liquid upward in opposition to gravity. A mass of liquid is drawn up as if it were suspended by the surface from the supporting walls. At equilibrium the upward pull of the surface and the downward pull of gravity on the elevated mass must balance. This elementary statement of force balance applies to two techniques by which 7 can be measured if 6 is known the Wilhelmy plate and capillary rise. 

When an electric field is applied across the working capillary, the double-layer ions begin to migrate and soon reach the steady-state velocity. In the steady state, electrical and viscous forces balance one another. The forces exerted on the ions by the medium are equal and opposite to the forces exerted on the medium by the ions consequently, the liquid also attains a stationary-state velocity. The tangential displacement of the fluid relative to the wall defines a surface of shear at which the potential equals f. 

Figure 16.2 Force-balance diagram for a body with capillary forces and applied load...

Figure D3.6.8 illustrates the different phases of drop development and detachment during the measurement. As shown in Figure D3.6.8, the drop does not detach at the exact tip of the capillary. Instead a neck is formed at which the liquid meniscus will eventually be disrupted. The radius of the neck is smaller than the radius of the capillary, rcap. A force balance on the drop yields ...

So far a number of important conclusions can be summarised. The SFM signal (deflection of the cantilever) results from a combination of surface and deformation forces. The total surface force between a SFM tip and a polymer surface includes adhesion and capillary forces, Fs=Fadh+Fcap. For polymer surface, it can be estimated to Fs 15 nN. Lower values might be expected for nonwettable and lower energy surfaces. The surface force is balanced by forces from the surface deformation, Fd, and from the deflection of the cantilever, Fc. In order to monitor a signal in contact SFM, the deformation forces must exceed the total surface forces, Fc=Fd - Fs. E.g., a net repulsive force of 0.4 nN will be monitored by 1 nm deflection of a Si cantilever with the following parameters E=50 GPa, 1= 100 pm,b=30 pm, h=4 pm, k=0.4 N/m. 

The efficiency of a TASA process is dependent upon the balanced interplay of a number of forces. As illustrated in Figure 8.4A, there are three major forces exerted on each colloidal particle as the liquid dewetts across the cell the capillary force (Fc) associated with the meniscus of the liquid slug the gravitational force (Fg) due to the difference in density between the particle and the dispersion medium and the electrostatic force (Fe) caused by charges resting on the surface of the particle and the bottom substrate. When colloidal... 

Clarke and co-workers developed a model to calculate the thickness of the amorphous film observed in polycrystalline ceramics.37,38 The model is based on a force balance between an attractive van der Waals dispersion force that acts across the grain boundaries, any capillary forces present, and repulsive disjoining forces (such as steric forces and electrical double-layer forces) in the amorphous film.37,38 The repulsive steric force is based on the... 

The capillary rise method is a classical method for determining surface tension that has important applications. For capillary rise in a narrow capillary (Figure 3.7) a force balance yields ... 

Flow in a capillary can be maintained by a steady pressure difference Ap applied between inlet and outlet ends. We assume gravitational (and other external) forces to be negligible (true for a horizontal tube or for any tube with a large Ap). With the application of Ap, the fluid in the tube accelerates to a flowrate at which the viscous drag forces balance the applied pressure forces. For thin tubes the Newtonian acceleration forces are significant for only a brief moment before steady flow is achieved. 

Flow in a thin rectangular channel (Figure 4.2), such as that used in field-flow fractionation, can be treated in a manner similar to that used for cylindrical capillary tubes. If the drag at the edges of the channel is neglected (infinite parallel plate model), then the force balance expression (corresponding to Eq. 4.5 for capillary tubes) becomes... 

Figure 4.7. Vertical capillary forces acting on the hydrophobic faces pull the hexagons into the PFD/H20 interface. The dashed line indicates the level of the interface far from the objects, (a) Hexagons with an unbalanced distribution of vertical capillary forces float with a tilt relative to the plane of the PFD/H20 interface. The surface tension, yLL, can be separated into vertical, y L, and horizontal, components, (b, c) Hexagons with a balanced distribution of vertical capillary forces float parallel to the plane of the interface. Thick and thin lines indicate hydrophobic and hydrophilic...

The above equations describe a simple mechanical model of the film, its adjacent transition zone and the bulk meniscus. According to this model the force quantities, lAytosd and 2Ayf, are applied only on the basic surface of tension. The disjoining pressure and the capillary pressure act always and everywhere normally to the phase surfaces, identified as surfaces of tension. There are other two A) in0 force components related to the two phase surfaces. These components counterbalance each other at any point of the basic surface of tension. Eq. (3.33) coincides formally with the force balance condition of de Feijter and Vrij [22] if one would write... 

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