Interfacial pressure model

Considering the interfacial pressure model, the flow rates should be between the higher and lower limits. APpiow can be evaluated by considering the pressure loss in the microchannels. Assuming that the pressure at the opened outlet is atmospheric pressure, Patm, then the pressure P of each phase from the pressure loss AP is expressed as follows ... 

Thermodynamics of the ITIES was developed by several authors [2-6] on the basis of the interfacial phase model of Gibbs or Guggenheim. General treatments were outlined by Kakiuchi and Senda [5] and by Girault and Schiffrin [6]. At a constant temperature T and pressure p the change in the surface tension y can be related to the relative surface excess concentrations Tf " of the species i with respect to both solvents [6],... 

When protein solutions are shaken, insoluble protein is often seen to separate out (Bull and Neurath, 1937). The coagulation occurs at the interface and may be observed when protein is allowed to adsorb from solution at a quiescent interface (Cumper and Alexander, 1950) or when spread protein monolayers are compressed (Kaplan and Frazer, 1953). This is an interesting type of phase separation in which a three-dimensional coagulum is formed from the two-dimensional monolayer, once a certain critical value of the interfacial pressure is exceeded. The concentration of protein in the monolayer when the critical pressure is reached may be thought of as the solubility in the interface under those conditions. When this concentration is exceeded, precipitation occurs. A simple model may help to illustrate how free energy considerations govern the coagulation. 

The terms pk)Ai — Pk)vk) oik + < k)Ai otk are referred to as the interfacial pressure difference effect (or the concentration gradient effect) and the combined interfacial shear and volume fraction gradient effect [67] [115], respectively. The interfacial pressure difference effect is normally assumed to be insignificant for the two-fluid model [54, 4, 125, 119]. That is, for two-phase flows one generally assumes that... 

Stuhmiller JH (1977) The Influence of interfacial pressure forces on the character of two-phase flow model equations. Int J Multiphase Flow 3 551-560 Sussman M, Smereka P, Osher S (1994) A Level-Set Approach for Computing Solutions to Incompressible Two-Phase Flow. J Comput Phys 114 146-159. Sussman M, Smereka P (1997) Axisymmetric free boundary problems. J Fluid Mech 341 269-294. 

Fig.2.11. Dependencies of the adsorption in state 1 (1 and L1) and 2 (2 and L2) on the interfacial pressure for the two-state model at the water/air (solid lines), and water/hexane (dotted lines) interfaces according to [87]...

Interfacial film properties between water and model oils containing asphaltenes or resins were investigated, when the concentration of asphaltenes or resins and the aromaticity of the oil phase were varied. Interfacial tension (IFT) or interfacial pressure (IFP), interfacial viscosity (IFV), and... 

The model seems to over-predict the experimental results for the bigger channels and this is attributed to the fact that the interfacial pressure drop calculated by Eq. (2.2.30) assumes ideally semi-spherical caps, which is not the case at all experimental conditions. By substituting the constant C in Eq. (2.2.31) to C = 1.7, the correlation was able to predict pressure drop during plug flow in the channels with 0.5, 1, and 2 mm ID with mean relative error of 14 % (red highlighted symbols). 

Jovanovic et al. [80] proposed a pressure drop model which account for frictional pressure losses in the discrete and continuous phases (Appjuc) and the interfacial pressure drop (Apj) ... 

The distribution of stress around discontinuous fibers in composites has been studied by a number of researchers. Theoretical analyses have been performed by Cox [82] and Rosen [83]. In these models only fiber axial stress distribution and the fiber-matrix interfacial shear stress distribution are determined. Amirbayat and Hearle [84] studied the effect of different levels of adhesion on the stress distribution, that is, no bond, no adhesion, perfect bond, and the intermediate case of limited friction. They also considered the inhibition of slippage by frictional forces resulting from interfacial pressure due to Poisson s lateral contractions of the matrix but did not consider the shrinkage of the matrix during curing. 

Interfacial pressures below 2 inN/m increased linearly with surfactant concentration (activity) (Fig. 4.39). The linear relationship is in agreement with a thermodynamic model of adsorption developed by Lucassen-Reynders [105] and others [106-108]. For surfactants which are strong 1 1 electrolytes, the model suggests the limiting form of the equation of state ... 

The film pressure of a myristic acid film at 20°C is 10 dyn/cm at an area of 23 A per molecule the limiting area at high pressures can be taken as 20 A per molecule. Calculate what the film pressure should be, using Eq. IV-36 with / = 1, and what the activity coefficient of water in the interfacial solution is in terms of that model. 

The behavior of insoluble monolayers at the hydrocarbon-water interface has been studied to some extent. In general, a values for straight-chain acids and alcohols are greater at a given film pressure than if spread at the water-air interface. This is perhaps to be expected since the nonpolar phase should tend to reduce the cohesion between the hydrocarbon tails. See Ref. 91 for early reviews. Takenaka [92] has reported polarized resonance Raman spectra for an azo dye monolayer at the CCl4-water interface some conclusions as to orientation were possible. A mean-held theory based on Lennard-Jones potentials has been used to model an amphiphile at an oil-water interface one conclusion was that the depth of the interfacial region can be relatively large [93]. 

In model equations, Uf denotes the linear velocity in the positive direction of z, z is the distance in flow direction with total length zr, C is concentration of fuel, s represents the void volume per unit volume of canister, and t is time. In addition to that, A, is the overall mass transfer coefficient, a, denotes the interfacial area for mass transfer ifom the fluid to the solid phase, ah denotes the interfacial area for heat transfer, p is density of each phase, Cp is heat capacity for a unit mass, hs is heat transfer coefficient, T is temperature, P is pressure, and AHi represents heat of adsorption. The subscript d refers bulk phase, s is solid phase of adsorbent, i is the component index. The superscript represents the equilibrium concentration. 

As both phases occupy the full flow field concurrently, two sets of conservation equations correspond to these two phases and must be complemented by the set of interfacial jump conditions (discontinuities). A further topological law, relating the void fraction, a, to the phase variables, was needed to compensate for the loss of information due to model simplification (Boure, 1976). One assumption that is often used is the equality of the mean pressures of the two phases, ... 

The role of various surfactant association structures such as micelles and lyotropic liquid crystals (372), adsorption-desorption kinetics at liquid-gas interfaces (373) and interfacial rheology (373) and capillary pressure (374) on foam lamellae stability has been studied. Microvisual studies in model porous media indicate... 

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