Modeling surface tension effects

The dynamic surface tension of a monolayer may be defined as the response of a film in an initial state of static quasi-equilibrium to a sudden change in surface area. If the area of the film-covered interface is altered at a rapid rate, the monolayer may not readjust to its original conformation quickly enough to maintain the quasi-equilibrium surface pressure. It is for this reason that properly reported II/A isotherms for most monolayers are repeated at several compression/expansion rates. The reasons for this lag in equilibration time are complex combinations of shear and dilational viscosities, elasticity, and isothermal compressibility (Manheimer and Schechter, 1970 Margoni, 1871 Lucassen-Reynders et al., 1974). Furthermore, consideration of dynamic surface tension in insoluble monolayers assumes that the monolayer is indeed insoluble and stable throughout the perturbation if not, a myriad of contributions from monolayer collapse to monomer dissolution may complicate the situation further. Although theoretical models of dynamic surface tension effects have been presented, there have been very few attempts at experimental investigation of these time-dependent phenomena in spread monolayer films. 

Fig. 13. Comparison of the model (K19) with the experimental data for bubble formation in viscous liquids without surface-tension effect.

This model is a modification of the model developed by Kumar and Kuloor (K18) for bubble formation in inviscid fluids in the absence of surface-tension effects. The need for modification arises because the bubble forming nozzles actually used to collect data on bubble formation in fluidized beds differ from the orifice plates in that they do not have a flat base. Under such conditions the bubble must be assumed to be moving in an infinite medium and the value of 1/2 is more justified than the value 11/16. 

In this sub-section the embedded interface method (frequently referred to as a front tracking method) developed for direct numerical simulations of viscous multi-fluid flows is outlined and discussed. The unsteady model is based on the whole held formulation in which a sharp interface separates immiscible fluids, thus the different phases are treated as one fluid with variable material properties. Therefore, equations (3.14) and (3.15) account for both the differences in the material properties of the different phases as well as surface tension effects at the phase boundary. The bulk fluids are incompressible. The numerical surface tension force approximation used is consistent with the VOF and LS techniques [222] [32], hence the major novelty of the embedded interface method is in the way the density and viscosity fields are updated when the fluids and the interface evolve in time and space. 

Various recent fin tube models include surface tension effects [89, 93, 94, 95, 96, 97]. The best model for design purposes, because of its relative simplicity, is due to Rose [95]. His expression for the heat transfer enhancement ratio a7- (defined as the average heat transfer coefficient for the finned tube divided by the average value for the smooth tube, both based on the smooth tube surface area at fin root diameter and for the same film temperature difference (Ts - Two)) for trapezoidal-shaped fins is [89] ... 

Heat transfer coefficients for condensation processes depend on the condensation models involved, condensation rate, flow pattern, heat transfer surface geometry, and surface orientation. The behavior of condensate is controlled by inertia, gravity, vapor-liquid film interfacial shear, and surface tension forces. Two major condensation mechanisms in film condensation are gravity-controlled and shear-controlled (forced convective) condensation in passages where the surface tension effect is negligible. At high vapor shear, the condensate film may became turbulent. 

Two theories have been proposed to predict flow of a saturated or nearly saturated liquid through an orifice, namely, an equilibrium flow theory and a metastable flow theory. In the equilibrium model it was assumed that the vapor bubbles formed throughout the stream cross section at the section where the saturation pressure is reached [ ]. Experimental measurements of the flow of saturated water have shown that the mass flow rates are considerably higher than predicted by calculations based on the equilibrium theory. Surface tension effects have been used to explain the variance between the experimental results and the predicted values. It is postulated that vapor bubble formation is retarded because of the surface tension. 

Modeling interfacial tension effects are important because it is a potentially large force which is concentrated on the interface. There are two different approaches to modeling surface tension forces. The first one is CSF defined as... 

Experimental data show that the ratio of the solvation energy in the liquid phase to the sum of the stepwise enthalpies of solvation up to a given cluster size converges with as few as five or six solvent molecules for many different cations clustered both to water and to ammonia. These observations end support to the very simple Bom concept that to first order, solvation can be modeled by the immersion of a sph e of fixed radius and charge in a stmc-tureless dielectric continuum. Higher-order corrections to this simple picture come from consideration of surface tension effects. Convergence of these ratios to approximately the same value is indicative of the fact that, beyond the first solvation shell, the majority of the contribution to solvation is from electrostatic interactions between the central ion cavity and the surrounding medium. 

Note DFT/PaSD with void model, self-consistent model of a mixture of voids, cylindrical and slit-shaped pores, self-consistent regularization with respect to both PoSD (fy(i p)) and PaSD ((l)( z)) with the model of voids, (5 ), Aw=Sgg j-/(5 ) - 1, f)pHH e fractal dimension with Frenkel-Halsey-Hill equation accounting for adsorbate surface tension effects (Quantachrome Instruments software), Ag j is the gelatin adsorption in mg per gram of silica. 

An estimate of the fission threshold can be obtained from the energy required to distort the nucleus into an extreme shape which results in complete separation into fragments. It has been shown that this calculation can be based on the liquid-drop model of the nucleus. The two principal contributions to the distortion energy of the nucleus are the surface-tension effect from the nuclear forces between the constituent... 

The only study in which the combined effects of non-Newtonian characteristics and temperature gradient on bubble motion have been explored is that of Chan Man Fong and De Kee (1994). They studied the migration of bubbles in the presence of a thermal gradient for second-order and Carreau model fluids. They found that the surface tension effects are only important for small bubbles. Likewise, Dang et al. (1972) have elucidated the role of non-Newtonian characteristics in reactive systems. 

Bianco and Marmur [143] have developed a means to measure the surface elasticity of soap bubbles. Their results are well modeled by the von Szyszkowski equation (Eq. III-57) and Eq. Ill-118. They find that the elasticity increases with the size of the bubble for small bubbles but that it may go through a maximum for larger bubbles. Li and Neumann [144] have shown the effects of surface elasticity on wetting and capillary rise phenomena, with important implications for measurement of surface tension. 

Same definitions as 5-26-M. ILff = effective viscosity from power law model, Pa-s. <3 = surface tension liquid, N/m. 

The continuum model, in which solvent is regarded as a continuum dielectric, has been used to study solvent effects for a long time [2,3]. Because the electrostatic interaction in a polar system dominates over other forces such as van der Waals interactions, solvation energies can be approximated by a reaction field due to polarization of the dielectric continuum as solvent. Other contributions such as dispersion interactions, which must be explicitly considered for nonpolar solvent systems, have usually been treated with empirical quantity such as macroscopic surface tension of solvent. 

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