Chemical potential gradient based forc

We consider here the role of bulk flow parallel to the direction of the chemical potential gradient based force in phetse-equilibrium based open two-phase systems. Vapor-liquid systems of flash vaporization, flash devolatilization and batch distillation are considered first, followed by a liquid-liquid system for extraction. Solid-liquid systems for zone melting and normal freezing are studied thereafter to explore how bulk flow parallel to the force direction is essential to considerable purifleation of solid systems followed by solid-vapor systems as in drying. 

Chemical potential gradient based force in phase equilihrium fixed-hed processes... 

Bhatia [39] studied the transport of adsorbates in microporous random networks in the presence of an arbitrary nonlinear local isotherm. The transport model was developed by means of a correlated random walk theory, assuming pore mouth equilibrium at an intersection in the network and a local chemical potential gradient driving force. The author tested this model with experimental data of CO2 adsorption on Carbolac measured by Carman and Raal [40]. He concluded that the experimental data are best predicted when adsorbate mobility, based on the chemical potential gradient, is taken to have an activation energy equal to the isosteric heat of adsorption at low coverage, obtained from the Henry s law region. He also concluded that the choice of the local isotherm... 

The physicocheimcal basis for separation is the primary focus of Chapter 3. Separation happens via species-specific force driven relative displacement of molecules of one species in relation to other species into species-specific region in the separation system. Particles of different sizes/ properties similarly undergo relative displacements. To develop this perspective. Chapter 3 (Section 3.1) identifies various external forces and chemical potential gradient based... 

An approach that is conceptually simpler and does not require the prescription of transport to hydraulic or diffusion mechanisms was proposed by Janssen [47], and Thampan et al. [22] (hereafter TMT) based on the use of chemical potential gradients in the membrane. More recently, Weber and Newman [27] developed a novel model where the driving force for vapour-equilibrated membranes is the chemical potential gradient, and for liquid-equilibrated membranes it is the hydraulic pressure gradient. A continuous transition is assumed between vapour- and liquid-equilibrated regimes with corresponding transition from 1 to 2.5 for the electro-osmotic drag coefficient. 

Fig. 15 (a) DNA translocation through a protein pore in a-hemolysin. When the DNA enters the pore, the ionic current is blocked. This current blockage is used to detect the residence time of DNA bases in the pore [67]. (b) Chain translocation through a nanopore. The instantaneous translocation coordinate is s(t) and the bead velocity in the pore is v(t). The driving force is due to a chemical potential gradient within the pore, f = (ni — Adapted from [68]. Reproduced... 

For any membrane-based separation process to be successful, the membrane must possess two key attributes high flux and good selectivity. Flux, which depends directly on permeability, was treated in Sections 4.4.2 and 4.4.4. Selectivity depends in part on differences in permeant size and solubility in the membrane (Section 4.4.5). Separation will then occur because of differences in the transport rates of molecules within the membrane. This rate of transport is determined by the mobility and concentration of the individual components as well as the driving force, which is the chemical potential gradient across the membrane. 

Based on our previous studies of the dissolution and crystallization kinetics of potassium inorganic compounds based on linear nonequilibrium thermodynamics (Ji et al, 2010 Liu et al, 2009 Lu et al, 2011), we proposed to assume that the kinetic process of CO2 absorption by ILs comprised two steps surface reaction and diffusion, as shown in Fig. 17. Figure 17 demonstrates that when CO2 in the vapor phase and the ILs were in contact, the chemical reaction of CO2 with ILs occurred for the chemical absorption process of CO2 by ILs in the first step, which was named as the surface reaction layer, while for the physical mass transport process of CO2 by ILs in the first step, CO2 in the vapor phase would be transported into the IL phase, which was also named as the assumed surface reaction layer. As for the surface reaction layer, the driving force of the surface reaction was the chemical potential gradient of CO2 between CO2 at the vapor—Hquid interface and gas CO2. After that, in the second step, CO2 in the IL phase would... 

Pervaporation (PV) is a membrane-based process used to separate the components of a liquid mixture. It requires dense membranes. The liquid feed is heated up and placed in contact with the active layer, whereas a vacuum or a sweep gas is applied downstream. The driving force is a chemical potential gradient through the membrane cross section. The separation phenomenon is explained according to the solution-diffusion model. The selective separation depends on the different dissolution of feed molecules into the membrane matrix and their diffusivity. 

Fig. 19.2 The operation principle of the most common membrane separation processes, with membranes separating the feed (left) from the permeate phase (right). Circles and stars indicate volatile and non-volatile compounds, respectively. Driving forces acting upon solutes are indicated by arrows as gradients of pressure (P), activity (a) and electrostatic potential (V )- It shoidd be noted that all these driving forces are eventiudly based on a gradient of the chemical potential in its most general form...

The starting point for the mathematical description of diffusion in membranes is the proposition, solidly based in thermodynamics, that the driving forces of pressure, temperature, concentration, and electrical potential are interrelated and that the overall driving force producing movement of a permeant is the gradient in its chemical potential. Thus, the flux,. /,(g/cm2 s), of a component, i, is... 

Compare the phenomenological coefficient for mass transfer defined in terms of the concentration gradient with that based on a Newtonian force defined for the gradient of the chemical potential. 

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