Transport of solvents

Mechanism The mechanism of leaching may involve simple physical solution or dissolution made possible by chemical reaction. The rate of transport of solvent into the mass to be leached, or of soluble fraction into the solvent, or of extract solution out of the insoluble material, or some combination of these rates may be significant. A membranous resistance may be involved. A chemical-reaction rate may also affec t the rate of leaching. 

Solvent-polymer compatibility problems are often encountered in industry, such as in the selection of gaskets or hoses for the transportation of solvents. A rough guide exists to aid the selection of solvents for a polymer, or to assess the extent of polymer-liquid interactions. A semi empirical approach has been developed by Hildebrand based on the principle of like dissolves like. The treatment involves relating the enthalpy of mixing to a solubility parameter, S, and its related quantity, 8, called the cohesive energy density. 

As the permeability of the membrane for ions of different charge signs largely varies, salt diffusion through a membrane is accompanied by the establishment of a membrane potential. These concentration or dialysis potentials play an important part in the study of membrane phenomena. With the above described model, the phenomenon of electro-endosmosis i.e. the transport of solvent across a membrane under the influence of an electric field, can easily be explained also. 

The final colligative property, osmotic pressure,24-29 is different from the others and is illustrated in Figure 2.2. In the case of vapor-pressure lowering and boiling-point elevation, a natural boundary separates the liquid and gas phases that are in equilibrium. A similar boundary exists between the solid and liquid phases in equilibrium with each other in melting-point-depression measurements. However, to establish a similar equilibrium between a solution and the pure solvent requires their separation by a semi-permeable membrane, as illustrated in the figure. Such membranes, typically cellulosic, permit transport of solvent but not solute. Furthermore, the flow of solvent is from the solvent compartment into the solution compartment. The simplest explanation of this is the increased entropy or disorder that accompanies the mixing of the transported solvent molecules with the polymer on the solution side of the membrane. Flow of liquid up the capillary on the left causes the solution to be at a hydrostatic pressure... 

The mechanism of particle filtration by screen filters has been the subject of many studies because it is relatively easily described mathematically Bungay has published a review of this work [49], Ferry [50] was the first to model membrane retention by a screen filter in his model pores were assumed to be equal circular capillaries with a large radius, r, compared to the solvent molecule radius. Therefore, the total area of the pore is available for transport of solvent. A solute molecule whose radius, a, is an appreciable fraction of the pore radius cannot approach nearer than one molecular radius of the pore overall. The model is illustrated in Figure 2.32. 

Mass-transport limitations are common to all processes involving mass transfer at interfaces, and membranes are not an exception. This problem can be extremely important both for situations where the transport of solvent through the membrane is faster and preferential when compared with the transport of solute(s) - which happens with membrane filtration processes such as microfiltration and ultrafiltration - as well as with processes where the flux of solute(s) is preferential, as happens in organophilic pervaporation. In the first case, the concentration of solute builds up near the membrane interface, while in the second case a depletion of solute occurs. In both situations the performance of the system is affected negatively (1) solute accumulation leads, ultimately, to a loss of selectivity for solute rejection, promotes conditions for membrane fouling and local increase of osmotic pressure difference, which impacts on solvent flux (2) solute depletion at the membrane surface diminishes the driving force for solute transport, which impacts on solute flux and, ultimately, on the overall process selectivity towards the transport of that specific solute. 

Osmosis involves the transfer, by a concentration gradient, of a solvent through a membrane into a mixture of solute and solvent. The membrane is almost non-permeable to the solute. In reverse osmosis, transport of solvent in the opposite direction is effected by imposing a pressure, higher than the osmotic pressure, on the feed side. Using a non-porous membrane, reverse osmosis successfully desalts water. 

In the solution-diffusion model, the transport of solvent and solute are independent of each other, as seen in Equations 4.1 and 4.2. The flux of solvent through the membrane is linearly proportional to the effective pressure difference across the membrane (Equation 4.1) ... 

Transfer of water molecules (in evaporation control), transport of solvent across monolayers at oil-water interfaces (in Ostwald-ripening of emulsions) and transfer of ions across such interfaces (as models for ion conduction in bilayers and membranes) can often be treated in terms of surface concentration fluctuations. Their magnitudes can be expressed in standard deviations (cr for the standard deviation in the surface concentration), which are measures of the probability that random holes are formed in the layer, allowing material transport. We have presented the formal treatment in sec. 1.3.7. From this section we can immediately obtain = IcTOr / 0 ), for a Gibbs monolayer, with... 

Considering the membrane process as a binary system, the transport of solvent (e.g., water), and solute are involved. Designating solute and solvent by subscripts A and B, Eq. (5) can be written for solvent B as... 

In the presence of solutes with small molecular weights, concentration polarization is likely to occur but with much less effect than in the case of ultrafiltration as explained in Section 12.2.1. A theoretical model concerning separation of sucrose and raffinose by ultrafiltration membranes has been proposed by Baker et al. [53] which assumes transport of solvent and solute exclusively through pores. This model can apply to ceramic nanofilters as they exhibit a porous structure with a pore size distribution. The retention characteristics of a given membrane for a given solute is basically determined by its pore-size distribution. The partial volume flux jy through the pores which show no rejection to the solute can be expressed as a fraction of the total volume flux fy. 

Although the transport of solvents, such as water, which usually occurs in a direction opposite the solute, could be formulated in similar terms, it is more common to report the so-called water-transport number, which is the ratio of the water flux to the solute flux. A negative value of the water-transport number indicates transport of solvent in the same direction as the solute. Ideally, the absolute value of the water transport number should be less than 1.0. 

An alternative to a flash devolatilization unit is the oil heated thin film or WFE. In this equipment, the molten polymer/solvent solution is throttled to the WFE comprising a rotating set of blades that draws the melt into a thin film. In this manner, very good heat transfer from the oil heated surface is obtained and the thin film minimizes diffusion distances and allows rapid mass transfer of volatiles out of the melt. Both vertical and horizontal WFE units are in commercial production and are effective for small-to-medium-sized plants with moderate viscosity melts. Larger units require very large motors to strip viscous resins. Like flash devolatilization units, bubble formation and collapse are essential to effective mass transport of solvent from the polymer melt. 

The MF process is used to reject particles in the range of 0.05-10 pm, while UF rejects the particles on the order of 1-50 nm. The transport of solvent, carried out by convection, is directly proportional to the applied transmanbrane pressure, which can be described, among other models, by the Hagen-Poiseuille model. 

Fig. 5.10 Schematic representation of the tortuous path exhibited by the crystalline HOPE phase to the transport of solvent [60]...

The control over supersaturation is one of the essential aspects of crystallisation. Because of the limited thermal stability of many biopharmaceutical products, evaporation of the solvent is often a less desired method since the heat transfer to the system is associated with temperature gradients. Therefore, alternative methods to remove the solvent have been proposed. One of these techniques is osmotic dewatering in which solvent removal is a pressure driven transport of solvent through solvent-selective membranes. The membrane part of the process is analogous to ultrafiltration for macromolecules or to reverse osmosis for small solutes. 

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