Diffusional flux

There are two approaches to the kinetics of emulsion flocculation. The first stems from a relationship due to Smoluchowski [52] for the rate of diffusional encounters, or flux ... 

The estimation of the diffusional flux to a clean surface of a single spherical bubble moving with a constant velocity relative to a liquid medium requires the solution of the equation for convective diffusion for the component that dissolves in the continuous phase. For steady-state incompressible axisym-metric flow, the equation for convective diffusion in spherical coordinates is approximated by... 

Levich (L3, L4) has demonstrated that for NKt < 1, the local diffusional flux to the surface of the bubble is given by... 

To evaluate the average diffusional flux, the total mass-transfer rate from the entire surface of the bubble must be divided by that entire surface ... 

Here, J (a, t) is the instantaneous interfacial flux expressed as a state vector whose components are the diffusional and heat fluxes. Therefore, the expected value < J(a)> takes into account the variations in residence time among the entire bubble population. 

Since the total mass transfer rate of B is zero, there must be a bulk flow of the system towards the liquid surface exactly to counterbalance the diffusional flux away from the surface, as shown in Figure 10.1, where ... 

As a result of the diffusional process, there is no net overall molecular flux arising from diffusion in a binary mixture, the two components being transferred at equal and opposite rates. In the process of equimolecular counterdiffusion which occurs, for example, in a distillation column when the two components have equal molar latent heats, the diffusional velocities are the same as the velocities of the molecular species relative to the walls of the equipment or the phase boundary. 

Component Diffusional velocity Bulk flow velocity Total velocity Flux... 

Thus, the diffusional process does not give rise to equal and opposite mass fluxes. 

The relationship between the diffusional flux, i.e., the molar flow rate per unit area, and concentration gradient was first postulated by Pick [116], based upon analogy to heat conduction Fourier [121] and electrical conduction (Ohm), and later extended using a number of different approaches, including irreversible thermodynamics [92] and kinetic theory [162], Pick s law states that the diffusion flux is proportional to the concentration gradient through... 

The anions, which are not involved in the reaction v = 0, should not move in the steady state [i.e., in Eq. (4.17), J = 0]. This implies that the diffusional component of their flux to the surface should be fully compensated by a migration component away from the surface (Fig. 4.3). 

As the diffusional field strength depends on the coordinate jc in the diffusion layer, the diffusion flux density (in contrast to the total flux density) is no longer constant and the concentration gradients dCjIdx will also change with the coordinate x. 

It follows that convection of the hqnid has a twofold influence It levels the concentrations in the bnlk liquid, and it influences the diffusional transport by governing the diffusion-layer thickness. Shght convection is sufficient for the first effect, but the second effect is related in a qnantitative way to the convective flow velocity The higher this velocity is, the thinner will be the diffusion layer and the larger the concentration gradients and diffusional fluxes. 

The diffusional fluxes from segment to segment are indicated in Fig. 4.4. 

For small K, i.e., K = 0.5 in Fig. 17, the response of the equilibrium to the depletion of species Red] in phase 1 is slow compared to diffusional mass transport, and consequently the current-time response and mass transport characteristics are close to those predicted for hindered diffusion with an inert interface. As K is increased, the interfacial process responds more rapidly to the electrochemical perturbation in phase 1. The transfer of the target species across the interface generates an enhanced flux to the UME, causing... 

The percutaneous absorption picture can be qualitatively clarified by considering Fig. 3, where the schematic skin cross section is placed side by side with a simple model for percutaneous absorption patterned after an electrical circuit. In the case of absorption across a membrane, the current or flux is in terms of matter or molecules rather than electrons, and the driving force is a concentration gradient (technically, a chemical potential gradient) rather than a voltage drop [38]. Each layer of a membrane acts as a diffusional resistor. The resistance of a layer is proportional to its thickness (h), inversely proportional to the diffusive mobility of a substance within it as reflected in a... 

The term hID is often called the diffusional resistance, denoted by R. The flux equation, therefore, can be written as... 

Figure 4 Diffusion across a membrane with aqueous diffusional layers. cbI and cb2 are the concentrations of bulk solutions 1 and 2, respectively. The thicknesses of the aqueous diffusion layers are /i, and h2. The membrane has a thickness of hm. Equilibrium is assumed at the interfaces of the membrane and the aqueous diffusion layers. At steady state, the concentrations remain constant at all points in the membrane and in the aqueous diffusion layers. The concentration profiles inside the membrane and aqueous diffusion layers are linear, and the flux is constant.

If we assume that the thickness of the aqueous film is 8, the diffusional flux across the film is... 

In Section III, emphasis was placed on flux kinetics across the cultured monolayer-filter support system where the passage of hydrophilic molecular species differing in molecular size and charge by the paracellular route was transmonolayer-controlled. In this situation, the mass transport barriers of the ABLs on the donor and receiver sides of the Transwell inserts were inconsequential, as evidenced by the lack of stirring effects on the flux kinetics. In this present section, the objective is to give quantitative insights into the permeability of the ABL as a function of hydrodynamic conditions imposed by stirring. The objective is accomplished with selected corticosteroid permeants which have been useful in rat intestinal absorption studies to demonstrate the interplay of membrane and ABL diffusional kinetics (Ho et al., 1977 Komiya et al., 1980). 

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