Surface retreat rate

Example 6.5. Surface retreat rate for dissolving forsterite... 

For a dissolving flat surface, the linear rate of surface retreat (dzidt, m/sec) is the dissolution flux (/, mol/m sec) multiplied by the molar volume of the solid V , mVmol). 

The factors which decrease evaporation rate with time are (1) retreat of an initially continuous deposit into discrete small areas as it gets too thin to be coherent, (2) influence of adsorption or solution in the porous, oily, or wet surface, (3) retreat of a deposit, initially lying on the outer surface, into deeper capillary spaces. 

In this method, the solid surface is also aligned vertically and brought into contact with the liquid. Instead of the capillary pull as in the Wilhelmy method, the capillary rise h at the vertical surface is measured (see Fig. 3). This method has been found particularly effective for measuring contact angles as a function of the rate of advance and retreat and for determining the temperature coefficient of 0. 

Toei et al. (T5, T6) believe that when the moisture content on the surface becomes less than the critical moisture content, the first falling-rate period starts and the evaporation occurs at the interior of the solid. The second falling-rate period starts when the moisture content at the surface reaches the equilibrium value. The evaporating plane retreats into the solid and dried-up zone begins to grow from the surface into the solid. The dried zone retains the equilibrium moisture content. 

Drying is necessary to crystallize the salt on the pore surface. If not performed properly, this step can result in irregular and uneven concentra lion distributions. For example. Fig. 6.19 demonstrates how the rate of drying affeas pore and particle profiles. If the rate is too slow, evaporation occurs at the miniscus. which retreats down the pore. Some salt deposition occurs but most of the solute merely concentrates deeper in the pore. When finally crystallized, the salt is located at the bottom of a pore... 

The enormous weight of an overlying ice sheet causes the Earth s crust beneath it to sag. Once the ice sheet disappears, the land slowly rises to recover its former position and, thereby, restores isostatic equilibrium. Consequently, the areas of northern Europe and North America presently affected by isostatic uplift more or less correspond with those areas that were formerly covered with ice. At present, the rate of isostatic recovery, for example, in the centre of Scandinavia, is approximately one metre per century. Isostatic uplift is neither regular nor continuous. Consequently, the rise in the land surface so affected has been overtaken at times by a rise in sea level. The latter was caused by melt water from the retreating ice sheets. 

Fig. 5a gives a schematic representation of the processes that occur near a retreating meniscus of surfactant solution resulting in formation of a dynamic surface tension y. In the steady state, the flux of surfactant molecules from the meniscus onto the wetting film interface is compensated by the dilfusion flux of surfactant molecules to the meniscus surface from the solution inside the capillary. The flux is assumed to be proportional to the flow rate v and the surface concentration of surfactant molecules Ff on the wetting film interface ... 

FIG. 6 Dependencies of dynamic surface tension of the retreating meniscus (curve 1) and corresponding concentration of EOjo surfactant solution near to the meniscus Cm (curve 2) on flow rate v in a quartz capillary, r = 5 pm. By dotted line (curve 3) the results of calculation of the ratio Cm/Co using Eq. (8) are shown. 

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