Gravitational draining

Such evaporation singularities can be very easily observed because the thickness profile of a thin liquid film locally reflects the rate of solvent removal. For very thin films, especially near the drying line, back flow due to gravitational draining can be neglected. The mass flux h(x+dx)uo carried into a fluid element dx, as shown in Figure 1, is balanced by the flux carried out by the substrate h(x)m and the mass lost through evaporation E(x)dx this observation leads to the continuity equation... 

Gravitational draining creates hydrodynamic shear throughout the entrained film. Unlike particle... 

Figure 24-5. Schematic of the dip-coating process. As the substrate is withdrawn from solution, bulk solution adheres to the substrate. Initially the solution is very dilute in surfactant, but due to solvent evaporation and gravitational draining the solution becomes more concentrated causing micelles to form. As the film thickness decreases and surfactant concentration increases the micelles become elongated, and pack parallel to the substrate. Several studies suggest that these micelles break up prior to formation of the final mesostructure and that the ordering transition occurs after the film has reached its final thickness.

Thickness profile for steady-state gravitational draining with constant evaporation and no curvature effects according to Eq. 5. From Hurd and Drinker [10]. 

Thickness profile of drying titanate film determined by imaging ellipsomelry. The displacement along the film was measured from a fiducial point near the drying front. The dashed line represents a constant evaporation profile with no surface tension. The dotted line is the profile for gravitational draining with a non-conslaiU evaporating rale. 

Usually, excess sluny is removed either by air blowing [2,4,24,28,32] or centrifuging [29,36]. In general, by gravitational draining or by applying some form of pressure or... 

Gravitational force favors the separation of gas from liquid in a disperse system, causing the bubbles to rise to the hquid surface and the liquid contained in the bubble walls to drain downward to the main body of the liquid. Interfacial tension favors the coalescence and ultimate disappearance of bubbles indeed, it is the cause of bubble destruction upon the rupture of the laminae. 

Step 1. Load a disposable mini-chromatography col-umn with Sephadex G-50 (fine) dextran that was previously permitted to equilibrate with 5 volumes of the desired new buffer. Allow all the liquid to drain under the earth s gravitation to leave a 1 mL bed volume. Transfer this spin-column to an appropriately sized centrifuge tube and spin at 100 X g (calculated for the radial distance to the tip of the column itself, and not the bottom of the centrifuge tube) for 2 min in a swinging bucket rotor". The volume of the now semi-dry gel bed will be reduced by 25-40%, and the media will appear as a gel mass that may even break away from the walls of the chromatography tube. (This is normal and will not affect performance.)... 

Another process which leads to HIPE instability is gravitational syneresis, or creaming, where the continuous phase drains from the thin films as a result of density differences between the phases. This produces a separated layer of bulk continuous phase and a more concentrated emulsion phase. The separated liquid can be located either above or below the emulsion, depending on whether the continuous phase is more or less dense, respectively, than the dispersed phase. This process has been studied by Princen [111] who suggests that it can be reduced by a number of parameters, including a high internal phase volume, small droplet sizes, a high interfacial tension and a small density difference between phases. 

King s experiments, described above, showed a complicating feature which makes it difficult to determine the borderline between gravitational and capillary moisture. After the columns drained for two and one-half years, King determined the moisture-content of each column at 3 in. sections. These results are shown in Table 54. The table illus-... 

When a column of particulate matter is flooded with water and then allowed to drain, several important points must be considered. The water in excess of the amount the particles are able to retain is called gravitation water. The water retained is called capillary water. The amount of water retained depends upon the effect of gravitational forces and the surface tension. Briggs (1897) has given what is probably the best description of gravitation and capillary waters, and the following is quoted from his investigation of the subject ... 

The rate of condensation on a vertical surface is controlled by the force of gravity acting on the condensed liquid film. A consideration of Eq. (11.20) shows for example that for a vertical plate the mean heat transfer rate from the plate with laminar flow in the film is proportional to gw. Attempts have therefore been made to increase condensation rates by using centrifugal forces instead of the gravitational force to drain the condensed liquid film from the cold surface [55], The simplest example of this would be condensation on the upper surface of a cooled circular plate rotating in a horizontal plane. This situation is shown in Fig. 11.23. A Nusselt-type analysis of this situation will be considered in the present section. 

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