Diffuse-interface method

D. Anderson, G. McFadden, A. Wheeler. Diffuse-interface methods in fluid mechanics. Ann Rev Fluid Mech 20 130, 1998. 

Anderson DM, McFadden GB, Wheeler AA (1998) Diffuse-interface methods in fluid mechanics. Annual Review of Fluid Mechanics 30 139-165... 

Surface Tension Simulation in Diffuse Interface Method Similar to surface tension modeling in the VOF method, both CSF and CSS methods are applicable, with minor adjustments, to the diffuse interface method. The CSF method is as follows ... 

Recently an alternative approach for the description of the structure in systems with self-assembling molecules has been proposed in Ref. 68. In this approach no particular assumption about the nature of the internal interfaces or their bicontinuity is necessary. Therefore, within the same formahsm, localized, well-defined thin films and diffuse interfaces can be described both in the ordered phases and in the microemulsion. This method is based on the vector field describing the orientational ordering of surfactant, u, or rather on its curlless part s defined in Eq. (55). 

The most reliable methods of the preparation of stable adsorbents involve, however, a covalent attachment of the polymeric stationary phases to the solid supporting material. In addition, the more diffuse interfaces formed in this case (see Sect. 2.2) are often favourable for the separation of proteins. 

The liquid-liquid free interface diffusion (FID) method, in which protein and precipitant solutions are carefully superimposed and left to slowly mix diffusively, was least used in the past due to handling difficulties. However, in the last 4 years the free interface technique has experienced a revival for both screening and optimization procedures. The... 

The average thickness E of the diffuse interface layer could be determined (see Table 1) by the above-mentioned two methods. The results obtained with the new method presented in this letter, i.e. by analysis of the negative deviation from Debye s theory (see Fig. 5), were denoted as Eq. The results derived from the negative deviation from Porod s law were denoted as Ep. It is obvious that Ed is close with Ep for various samples, but in each case the former is slightly higher and the reasons are thus not fully understood. With the increase of the average diameter of the colloidal nuclei, E (Ed and Ep) reasonably increased. 

We now briefly consider another important aspect of nonequilibrium thermodynamics, namely phase transformations and how they are modelled. Galenko and Jou198 develop a thermodynamic formalism for rapid phase transformations within a diffuse interface of a binary system in which the system is in a state of local nonequilibrium. The phase-field method, in which the phase- field variable O varies smoothly and continuously between one pure phase (in which O = +1) and another (in which -1), is used to derive... 

We adopted a second method called the Boltzmann-Matano interface method [see Eq. (5)], which is more accurate for the purely diffusive process. Notice that Ma et al. successfully employed this method, since the spreading profiles they measured exhibit little mass buildup at the front and negligible dewetting. 

Note that in all cases the initial strength is reestablished after the adhesive-bonded joint is dried. Thus, the drop in strength of adhesive-bonded joints operated in water is explained mainly by diffusion of water at the adhesive-substrate interface. Methods that increase water resistance decrease the rate of water diffusion along the interface, although it still takes place. Increase in the rate seems to be caused by both adsorption and diffusion mechanisms of the medium. 

Diffuse interface model Free-surface flow Front capmring Front tracking Interface tracking Interfacial flow Level set method Phase-field method Volume-of-fluid (VOF) method... 

In this contribution, first a number of fundamental concepts that are central to interface capturing are presented, including definitions of level set functions and unit normal and curvature at an interface. This is followed by consideration of kinematic and dynamic boundary conditions at a sharp interface separating two immiscible fluids and various ways of incorporating those conditions into a continuum, whole-domain formulation of the equations of motion. Next, the volume-of-fluid (VOE) and level set methods are presented, followed by a brief outlook on future directions of research and other interface capturing/tracking methods such as the diffuse interface model and front tracking. 

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