Total driving force

Boiling is to be inside /l -in. 16 BWG steel tubes, 8 ft long. Condensing steam at 25 psig is available for heating. An overall coefficient U = 300 Btu/ (hr) (fti) (°F) is expected. For the given duty and a total driving force of 20°F, the inside surfece required is 285 fti This is equivalent to 96 tubes. 

Total driving force Total (thermal resistance/area)... 

As an example, it may be supposed that in phase 1 there is a constant finite resistance to mass transfer which can in effect be represented as a resistance in a laminar film, and in phase 2 the penetration model is applicable. Immediately after surface renewal has taken place, the mass transfer resistance in phase 2 will be negligible and therefore the whole of the concentration driving force will lie across the film in phase 1. The interface compositions will therefore correspond to the bulk value in phase 2 (the penetration phase). As the time of exposure increases, the resistance to mass transfer in phase 2 will progressively increase and an increasing proportion of the total driving force will lie across this phase. Thus the interface composition, initially determined by the bulk composition in phase 2 (the penetration phase) will progressively approach the bulk composition in phase 1 as the time of exposure increases. 

Piping systems often involve interconnected segments in various combinations of series and/or parallel arrangements. The principles required to analyze such systems are the same as those have used for other systems, e.g., the conservation of mass (continuity) and energy (Bernoulli) equations. For each pipe junction or node in the network, continuity tells us that the sum of all the flow rates into the node must equal the sum of all the flow rates out of the node. Also, the total driving force (pressure drop plus gravity head loss, plus pump head) between any two nodes is related to the flow rate and friction loss by the Bernoulli equation applied between the two nodes. 

Also, the total driving force in a branch between any two nodes i and j is determined by Bernoulli s equation [Eq. (7-45)] as applied to this branch. If the driving force is expressed as the total head loss between nodes (where hi = i/pg), then... 

The process of mass transfer across a phase boundary is discussed in Volume 1, Chapter 10. A resistance to mass transfer exists within the fluid on each side of the interface, and the overall transfer rate of a component in a mixture depends on the sum of these resistances and the total driving force. 

If a reference datum plane (h = 0) is set at the bottom of each of the capillaries shown in the previous Fig. 5.5, the expression for the total driving force, that is the piezometric pressure difference along the penetration length h for a capillary with an upward (I pgh cos a) or a downward (—pgh cos a) orientation, can be represented by following equation (Bouchon and Pyle, 2005b),... 

Can the Chemical and Electrical Work Be Determined Separately In the case of transport processes, the total driving force for the flow of a particular species j, i.e., the gradient of electrochemical potential. 3pj./3bc, was considered split up into a chemical (diffusive) driving force dp/dx and an electrical driving force for conduction, ZjFdty/dx,... 

A Criterion of Thermodynamic Equilibrium between Two Phases Equality of Electrochemical Potentials. It has been stated that ihe total driving force responsible for Ihe flow or transport of a species j is the gradient d lj/dx of its electrochemical potential. However, when there is net flow or flux of any species, this means that the system is not at equilibrium. Conversely, for the system to be at equilibrium, it is essential that there be no drift of any species—hence, that there should be zero gradients for the electrochemical potentials of all the species. It follows, therefore, that, for an interface to be at equilibrium, the gradients of electrochemical potential of the various species must be zero across the phase boundary, i.e.,... 

The total driving force on a dislocation, /, is the sum of the forces previously considered and, therefore,... 

Downward Movement—In the case of downward movement, it is necessary to adjust the driving force in Eq (15-5) to take care of the capillary forces. Assume, following Green and Ampt, that this added driving force is taken as an extra head, hCi so that the total driving force is gp(h + hc) instead of ghp. Also, since the water occupies the pore-space of the soil, it follows that at any stage the velocity of the water front will be given by the equation... 

Some fundamentals of micelle formation and of the solubilization of water-insoluble substances by micelles are reviewed. The accelerating effect of micellization upon the rate of dissolution and of transport of solubilizate through bulk liquid is then considered. Membranes present an obstacle to transport. A larger fraction of the total driving force can be brought to bear upon this obstacle as other resistances are reduced by solubilization. Hence, transport across a membrane will, in general, be accelerated whether micelles are effective within the membrane or not. It is now possible to determine also this contribution of micelles to the transport within the membrane. In a specific case it was found to be negligible. 

By eliminating the solid, solubilization actually may decrease the total driving force for the transport since an unsaturated solution necessarily has a lower activity than the undissolved material and the saturated boundary layer. In extreme cases, solubilization may thus slow down the rate of transport. This explains why so many germicides lose their effectiveness when incorporated into soap. They become so well solu-... 

The Total Driving Force for Ionic Transport The Gradient of the Electrochemical Potential... 

Expression (4.231) is known as the Nernst-Planckflux equation. It is an important equation for the description ofthe flux or flow of a species under the total driving force... 

The total driving force on an ionic species that is drifting independently of any other ionic species is the gradient of the electrochemical potential, dJI/dx. In terms of this total driving force, the expression for the total independent flux is given by the Nemst-Planck flux equation... 

The use of supports in asymmetric, supported membranes introduces a number of complications in the interpretation of permeation and separation data as well as in the optimalisation of membrane systems. If the flow resistance of the support is not negligible, there is a pressure drop across the support. This implies that the pressure and so the occupancy at the interface of separation layer and support is different from the (directly accessible) pressure at the support surface, usually the permeate side. Consequently, the driving force for permeation through the separation layer is different from the total driving force across the membrane system. In cases where one wants to calculate or compare transport properties of the separation layer material, it is necessary to correct for this effect (for illustration see below). 

In short, the total driving force is divided equally among each of the N effects. 

Considering total driving force coefficient of all LM transport system, K, WC obtain ... 

Equation (11) gives the relative values of the potential drop across the ITIES, which is one of two components of the total driving force for ET reaction. The driving force for interfacial ET is given by (26) ... 

Hie application of this equation to design requires information ou concentrations at the interface which is seldom known. As a result, absorption data frequently are correlated in terms of overall coefficients. These are based on the total driving force from the main body of the gas to the main body of the liquid. The overall cnefficients Kg and K,. are defined try the ftoBowing reJatioaship ... 

INDIVIDUAL AND OVERALL GROWTH COEFFICIENTS. In mass-transfer operations it is generally assumed that equilibrium exists at the interface between phases. If this were true in crystallization, the concentration of the solution at the face of the crystal would be the saturation value y, and the total driving force for mass transfer would be y — y, where y is the concentration at a distance from the crystal face. Because of the surface reaction, however, a driving force is needed for the interfacial step, and the concentration at the interface is therefore y, where y < y < y. Only y — / remains as the driving force for mass transfer. This is illustrated in Fig. 27.8. 

The driving forces for solute transport will depend on the overall charge and on the protons which are translocated, as well as on the solute gradient. The driving force is therefore composed of components of the proton-motive force and of the solute gradient, and translocation of solute will proceed until the total driving force is zero. At that stage a steady-state level of accumulation is reached. Fig. 9 shows... 

Formally, this limit is sufficient to define a reversible change, but in practice the dissipative components can be made to vanish only by simultaneously making the total driving force A vanish. To remind ourselves of this, we rewrite (1.3.4) in the form... 

Relating the Overpotential to a Difference in a Chemical or Electrochemical Potential If one wants to allocate to S (A(p) a relation to a total driving force, this is not trivial. A total driving force is associated with a gradient in the electrochemical potential of electrons, ions, or of the... 

In Coble s initial stage hot pressing model, the effective stress applied to the grain boundaries, p, is related to the externally applied stress, p, which is by Eq. (5.180). In that model, the total driving force (DF) is a linear combination of two effects (i) external applied stress and (ii) surface curvature, which determines the densification rate, and it is... 

The total driving force for grain boundary movement is the sum of the boundary drag force and the force FI for the movement of a grain boundary... 

According to the scheme above, the total driving force of the reaction will be given by the applied potential and also by the M(III)/M(II) formal potential of the catalyst, so the catalytic activity could be correlated with the formal potential of the catalyst. Many authors have discussed this issue and it is yet not clear what sort of correlation should be expected. Reduction should occur at the potential of reduction of the M(III)02 adduct and not at the potential of the M(III)/(II) couple. The latter should only be observed if the reaction were outer sphere. For the particular case of iron phthalocyanines and other iron macrocyclics, O2 reduction starts at potentials very close to the Fe(III)/(II) couple ". In contrast, for cobalt macrocyclics reduction of O2 begins at potentials much more negative than those corresponding to the Co(III)/(II) couple . Several authors have reported correlations between activity (measured as potential at constant current) and the M(III)/(II) formal potential and volcano-shaped curves have been obtained -see for... 

The sum of these two driving forces is the total driving force inducing the flow and since the flux must be the same, induced by both mechanisms, we write ... 

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