Force driving

The equilibrium state corresponds to the state when the exchange of heat and mass between the starting material and the product becomes zero at the 

In the growth of crystals from the vapor phase, the degree of the driving force is expressed by the ratio S, i.e. the ratio between the equilibrium vapor pressure and the pressure p at growth  

In the case of solution growth, the driving force corresponds to the difference between the concentration C at the equilibrium temperature T of the saturated solution and the concentration C at the growth temperature T and it is expressed as follows  

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Figure 6.6 illustrates what happens to the cost of the system as the relative position of the composite curves is changed over a range of values of AT ir,. When the curves just touch, there is no driving force for heat transfer at one point in the process, which would require an... 

Once the distillation is integrated, then driving forces between the composite curves become smaller. This in turn means the capital/energy tradeofiF for the heat exchanger network should be adjusted accordingly. 

Unfortunately, the overall design problem is even more complex in practice. Spare driving forces in the process could be exploited equally well to allow the use of moderate utilities or the integration of heat engines, heat pumps, etc. in preference to distillation integration. 

Figure 16.9 Even though threshold problems have large driving forces, there are still often essential matches to be made, especially at the no-utility end.

The driving force is generally the insolubility of one of the products in the reaction medium or the volatility of one of the products. 

Development planning and production are usually based on the expected production profile which depends strongly on the mechanism providing the driving force in the reservoir. The production profile will determine the facilities required and the number and phasing of wells to be drilled. The production profile shown in Figure 1.1 is characterised by three phases ... 

Solution gas drive occurs in a reservoir which contains no initial gas cap or underlying active aquifer to support the pressure and therefore oil is produced by the driving force due to the expansion of oil and connate water, plus any compaction drive.. The contribution to drive energy from compaction and connate water is small, so the oil compressibility initially dominates the drive energy. Because the oil compressibility itself is low, pressure drops rapidly as production takes place, until the pressure reaches the bubble point. 

The resistance to nucleation is associated with the surface energy of forming small clusters. Once beyond a critical size, the growth proceeds with the considerable driving force due to the supersaturation or subcooling. It is the definition of this critical nucleus size that has consumed much theoretical and experimental research. We present a brief description of the classic nucleation theory along with some examples of crystal nucleation and growth studies. 

For some types of wetting more than just the contact angle is involved in the basic mechanism of the action. This is true in the laying of dust and the wetting of a fabric since in these situations the liquid is required to penetrate between dust particles or between the fibers of the fabric. TTie phenomenon is related to that of capillary rise, where the driving force is the pressure difference across the curved surface of the meniscus. The relevant equation is then Eq. X-36,... 

The Washburn equation has most recently been confirmed for water and cyclohexane in glass capillaries ranging from 0.3 to 400 fim in radii [46]. The contact angle formed by a moving meniscus may differ, however, from the static one [46, 47]. Good and Lin [48] found a difference in penetration rate between an outgassed capillary and one with a vapor adsorbed film, and they propose that the driving force be modified by a film pressure term. 

It is quite clear, first of all, that since emulsions present a large interfacial area, any reduction in interfacial tension must reduce the driving force toward coalescence and should promote stability. We have here, then, a simple thermodynamic basis for the role of emulsifying agents. Harkins [17] mentions, as an example, the case of the system paraffin oil-water. With pure liquids, the inter-facial tension was 41 dyn/cm, and this was reduced to 31 dyn/cm on making the aqueous phase 0.00 IM in oleic acid, under which conditions a reasonably stable emulsion could be formed. On neutralization by 0.001 M sodium hydroxide, the interfacial tension fell to 7.2 dyn/cm, and if also made O.OOIM in sodium chloride, it became less than 0.01 dyn/cm. With olive oil in place of the paraffin oil, the final interfacial tension was 0.002 dyn/cm. These last systems emulsified spontaneously—that is, on combining the oil and water phases, no agitation was needed for emulsification to occur. 

Here p is the chemical potential just as the pressure is a mechanical potential and the temperature Jis a thennal potential. A difference in chemical potential Ap is a driving force that results in the transfer of molecules tlnough a penneable wall, just as a pressure difference Ap results in a change in position of a movable wall and a temperaPire difference AT produces a transfer of energy in the fonn of heat across a diathennic wall. Similarly equilibrium between two systems separated by a penneable wall must require equality of tire chemical potential on the two sides. For a multicomponent system, the obvious extension of equation (A2.1.22) can be written... 

The driving force for migration is established by the different electrochemical potentials (AU) that exist at the two interfaces of the oxide. In other words, the electrochemical potential at the outer interface is controlled by the dominant redox species present in the electrolyte (e.g. O2). 

The situation in figure C2.8.5(b) is different in that, in addition to the mechanism in figure C2.8.5(a), reduction of the redox species can occur at the counter-electrode. Thus, electron transfer tlirough the layer may not be needed, as film growth can occur with OH species present in the electrolyte involving a (field-aided) deprotonation of the film. The driving force is provided by the applied voltage, AU. 

During pressure sintering, interiDarticle compressive stress, approximated by the externally applied stress and nonnalized by the relative density of the compact p, supplements the surface tension driving force for pore shrinkage ... 

Electron transfer reaction rates can depend strongly on tire polarity or dielectric properties of tire solvent. This is because (a) a polar solvent serves to stabilize botli tire initial and final states, tluis altering tire driving force of tire ET reaction, and (b) in a reaction coordinate system where the distance between reactants and products (DA and... 

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