Net flux

The rate of storage of chemical potential (in other words, the power P carried by the chemical reaction) isypg, where j = d/j/dt = the net flux per unit volume (here, as elsewhere, lower case letters denote concentrations,... 

Wlren the door is open, the optimal net flux into the store isgiven by equation (C2.14.7). It may be that the stochastically gated diffusion treated by Szabo et aJ [47], see also [48] is a good representation of typical biological storage reactions (C2.14.8). 

This represents a system of simultaneous equations equal in number to the number of rows of the square matrix, Each equation consists, on the left, of the sum of the products of the members of a row of the square matrix and the corresponding members of the W-column matrix and, on the right, of the member of that row in the third matrix. With this set of equations solved for Wj, the net flux at any surface Aj is given by... 

The net flux from gas G is GSiOfTd Ti ) + GS g Tg — T/) which, with replacement of the last term using Eq. (5-172), gives the single term... 

Physically, diffusion occurs because atoms, even in a solid, are able to move - to jump from one atomic site to another. Figure 18.4 shows a solid in which there is a concentration gradient of black atoms there are more to the left of the broken line than there are to the right. If atoms jump across the broken line at random, then there will be a net flux of black atoms to the right (simply because there are more on the left to jump), and, of course, a net flux of white atoms to the left. Pick s Law describes this. It is derived in the following way. 

The area of the surface across which they jump is I2, so the net flux of atoms, using the definition given earlier, is ... 

The design problem of a TMB consists on setting the flow rates in each section to obtain the desired separation. Some constraints have to be met to recover the less-adsorbed component A in the raffinate and the more retained component B in the extract. These constraints are expressed in terms of the net fluxes of components in each section (see Fig. 9-1). In section I, both species must move upwards, in sections II and III the light species must move upwards, while the net flux of the more retained component must be downwards, and in section IV the net flux of both species have to be downwards, i.e.. 

For the case of a binary system with linear adsorption isotherms, very simple formulas can be derived to evaluate the better TMB flow rates [19, 20]. For the linear case, the net fluxes constraints are reduced to only four inequalities, which are assumed to be satisfied by the same margin /3 (/3 > 1) and so ... 

Increasing the switch time interval is equivalent to decrease the solid flow rate and the net fluxes of components in all sections of the TMB unit will be pushed in the same direction of the liquid phase. This implies that, first, the more retained species will move upwards in section III and will contaminate the raffinate stream and the less retained species will move upwards in section IV, will be recycled to section I, and will contaminate also the extract stream. The decrease of the switch time interval will have similar consequences. The equivalent solid flow rate will increase and the net fluxes of component in all four sections of the TMB unit will be pushed in the opposite direction of the liquid phase. This implies that, first, the less-retained species will move downwards in section II and will contaminate the extract stream and the more retained component will also move downwards in section I, will be recycled with the solid to the section IV, and will contaminate the raffinate stream. It is possible to obtain simultaneously high purities and recoveries in a SMB, but the tuning must be carefully carried out. 

The rate equations determine the rate of change of the probability of a particular configuration, a, within an ensemble of growing crystals. They must include the rate constants for adding or subtracting units, which are assumed to obey microscopic reversibility. The net flux between configurations a and a which occur with probability P(a) and P(a ) respectively, and differ by one unit is ... 

The magnitude and direction of the net flux density, F, of any gaseous species across an air-water interface is positive if the flux is directed from the atmosphere to the ocean. F is related to the difference in concentration (Ac), in the two phases by the relation... 

Seiler, W. and Crutzen, P. J. (1980). Estimates of gross and net fluxes of carbon between the biosphere and the atmosphere from biomass burning. Climat. Change 2, 226-247. 

Impurities travel from atmosphere to ice sheet surface either attached to snowflakes or as independent aerosols. These two modes are called wet and dry deposition, respectively. The simplest plausible model for impurity deposition describes the net flux of impurity to ice sheet (which is directly calculated from ice cores as the product of impurity concentration in the ice, Ci, and accumulation rate, a) as the sum of dry and wet deposition fluxes which are both linear functions of atmospheric impurity concentration Ca (Legrand, 1987) ... 

In a reaction at equilibrium, the forward and reverse reactions occur at equal rates, and there is therefore no net flux in either direction ... 

In vivo, under steady-state conditions, there is a net flux from left to right because there is a continuous supply of A and removal of D. In practice, there are invariably one or more nonequilibrium reactions in a metabolic pathway, where the reactants are present in concentrations that are far from equilibrium. In attempting to reach equilibrium, large losses of free energy occur as heat, making this type of reaction essentially irreversible, eg. 

All the transport properties derive from the thermal agitation of species at the atomic scale. In this respect, the simplest phenomenon is the diffusion process. In fact, as a consequence of thermal kinetic energy, all particles are subjected to a perfectly random movement, the velocity vector having exactly the same probability as orientation in any direction of the space. In these conditions, the net flux of matter in the direction of the concentration gradient is due only to the gradient of the population density. 

Infinite-cis experiments. In this type of experiment, the net flux of glucose from a limitingly high concentration on the cis face of the membrane is measured as a function of the concentration on the trans face. Both entry and exit infinite-m (ic) experiments can be performed, yielding two Am values, A i and K, respectively. Maximal fluxes are obtained when the concentration on the trans side of the membrane is zero. Since this is the zero-trans situation, = Fq and F o =... 

Further neglecting the first term allows integration from y = 0 at the wall (membrane surface) into the boundary layer. At the wall, the net flux is represented by convection into the permeate... 

Assuming that the target interface can be modeled as a quiescent, sharp boundary, with Eq. (30) initially at equilibrium there is zero net flux of species Red across the interface and each phase has a uniform composition of Red, CRed, (where the integer i = 1 or 2). The initial condition is identical to Eqs. (11) and (12). 

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