Phase separation driving forces

For all of the general techniques of Figure 2, the separations are achieved by enhancing the rate of mass transfer by diffusion of certain species relative to mass transfer of all species by bulk movement within a particular phase. The driving force and direction of mass transfer by diffusion is governed by thermodynamics, with the usual limitations of equilibrium. Thus, both transport and thermodynamic considerations are crucial in separation operations. The rate of separation is governed by mass transfer, while the extent of separation is limited by thermodynamic equilibrium. Fluid mechanics also plays an important role, and applicable principles are included in other chapters. 

This refers to the process of thinning and disruption of the liquid film between the droplets, with the result that two or more droplets fuse into a larger droplet. The limiting case for coalescence is the complete separation of the emulsion into two distinct liquid phases. The driving force for coalescence is the surface or film fluctuations this results in a close approach of the droplets whereby the van der Waals forces are strong and prevent their separation. 

For the separation of gas mixtures (permanent gases and/or condensable vapors) where the feed and permeate streams are both gas phase, the driving force across the membrane is the partial pressure difference. The membrane is typically a dense film and the transport mechanism is sorption-diffusion. The dual-mode transport model is typically used with polymer materials that are below their glass transition temperature. 

The need for low levels of 3-isomer in 2-thiophenecarboxyhc acid [527-72-0] which is produced by oxidation of 2-acetylthiophene [88-15-3] and used in dmg appHcations, has been the driving force to find improved acylation catalysts. The most widely used oxidant is sodium hypochlorite, which produces a quantity of chloroform as by-product, a consequence that detracts from its simplicity. Separation of the phases and acidification of the aqueous phase precipitate the product which is filtered off. Alternative oxidants have included sodium nitrite in acid solution, which has some advantages, but, like the hypochlorite method, also involves very dilute solutions and low throughput volumes. 

Part (a) is the driving force for the adsorption. If only (a) were present, adsorbed chains would lie flat on the surface. Parts (b) and (c) are the opposing forces (b) accounts for the entropy loss of a bond on the surface as compared to the solution, (c) represents the separation into a concentrated surface phase and a dilute solution. Part (d) arises from polymer-polymer, solvent-solvent and polymer-solvent interactions, which usually favour accumulation of segments. At equili-... 

In processing, it is frequently necessary to separate a mixture into its components and, in a physical process, differences in a particular property are exploited as the basis for the separation process. Thus, fractional distillation depends on differences in volatility. gas absorption on differences in solubility of the gases in a selective absorbent and, similarly, liquid-liquid extraction is based on on the selectivity of an immiscible liquid solvent for one of the constituents. The rate at which the process takes place is dependent both on the driving force (concentration difference) and on the mass transfer resistance. In most of these applications, mass transfer takes place across a phase boundary where the concentrations on either side of the interface are related by the phase equilibrium relationship. Where a chemical reaction takes place during the course of the mass transfer process, the overall transfer rate depends on both the chemical kinetics of the reaction and on the mass transfer resistance, and it is important to understand the relative significance of these two factors in any practical application. 

The physical process of melt ascent during two-phase flow models is typically based on the separation of melt and solid described by Darcy s Law modified for a buoyancy driving force. The melt velocity depends on the permeability and pressure gradients but the actual microscopic distribution of the melt (on grain boundaries or in veins) is left unspecified. The creation of disequilibria only requires movement of the fluid relative to the solid. 

Membranes act as a semipermeable barrier between two phases to create a separation by controlling the rate of movement of species across the membrane. The separation can involve two gas (vapor) phases, two liquid phases or a vapor and a liquid phase. The feed mixture is separated into a retentate, which is the part of the feed that does not pass through the membrane, and a permeate, which is that part of the feed that passes through the membrane. The driving force for separation using a membrane is partial pressure in the case of a gas or vapor and concentration in the case of a liquid. Differences in partial pressure and concentration across the membrane are usually created by the imposition of a pressure differential across the membrane. However, driving force for liquid separations can be also created by the use of a solvent on the permeate side of the membrane to create a concentration difference, or an electrical field when the solute is ionic. 

The scope of coverage includes internal flows of Newtonian and non-Newtonian incompressible fluids, adiabatic and isothermal compressible flows (up to sonic or choking conditions), two-phase (gas-liquid, solid-liquid, and gas-solid) flows, external flows (e.g., drag), and flow in porous media. Applications include dimensional analysis and scale-up, piping systems with fittings for Newtonian and non-Newtonian fluids (for unknown driving force, unknown flow rate, unknown diameter, or most economical diameter), compressible pipe flows up to choked flow, flow measurement and control, pumps, compressors, fluid-particle separation methods (e.g.,... 

In addition to the previously mentioned driving forces that determine the bulk state phase behavior of block copolymers, two additional factors play a role in block copolymer thin films the surface/interface energies as well as the interplay between the film thickness t and the natural period, Lo, of the bulk microphase-separated structures [14,41,42], Due to these two additional factors, a very sophisticated picture has emerged from the various theoretical and experimental efforts that have been made in order to describe... 

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