Interfacial instability theory

Gouda J.H., and Joos P. (1975). Application of Longitudinal Wave Theory to Describe Interfacial Instability. Chemical Engineering Science 30 521-528. 

The characterisation of mass transfer is essential for the design of the micro-reactor. In liquid-liquid flows most studies have focused on the estimation of overall mass transfer coeflicients, while no model based on theory has been developed so far. The overall volumetric mass transfer coeflicient (kua) is a characteristic parameter of a system used to evaluate the performance of the contactors, and is a combination of the mass transfer coefficient (kp), which depends mainly on the difiusivity of solute, characteristic diffusion length and interfacial hydrodynamics, and of the specific interfacial area (a), which depends on the flow pattern. The prediction of the overall volumetric mass transfer coeflicient remains difficult due to secondary phenomena, tike interfacial instabilities. 

Gouda, J.H. and Joos, R, Application of longitudinal wave theory to describe interfacial, instability, Chem. Eng. Sci., 30, 521, 1975. 

The determination of the interfacial tension is performed by means of a recently developed rheo-optical technique [22] based on Tomotika s theory of fibril break-up [33] When a long fluid filament is present in a quiescent fluid matrix, interfacial instabilities due to thermal fluctuations will occur. These so-called Rayleigh instabilities will start to grow and will eventually disintegrate the fibril. Tomotika derived the following formula for the break-up time iB of a Newtonian fibril immersed in a quiescent Newtonian matrix [33]... 

Interfacial instability due to fluctuations of the electric potential is investigated by Felderhof [493]. A theoretical description of the stability of an evaporating liquid surface is given by Prosperetti and Plesset [510]. They established that at large evaporation flow rates, the instability is very strong with growth time of a millisecond or less. This theory... 

Clearly, then, the chemical and physical properties of liquid interfaces represent a significant interdisciplinary research area for a broad range of investigators, such as those who have contributed to this book. The chapters are organized into three parts. The first deals with the chemical and physical structure of oil-water interfaces and membrane surfaces. Eighteen chapters present discussion of interfacial potentials, ion solvation, electrostatic instabilities in double layers, theory of adsorption, nonlinear optics, interfacial kinetics, microstructure effects, ultramicroelectrode techniques, catalysis, and extraction. 

One leading explanation attributes the anomalous melt flow behavior (i.e., flow discontinuity and oscillation) to constitutive instabilities [65]. In other words, the anomalies would be constitutive in nature and non-interfacial in origin. Such an opinion has not only been expressed phenomenologically by Tordella [9b] and many other rheologists but found support from several theoretical studies [65-67]. However, these theories only attempt to describe inherent bulk flow behavior. Thus, a connection between the anomalous flow phenomena and constitutive instabilities was often explored without any account for possible molecular processes in the melt/wall interfacial region. 

This is very important, because the interface is stable in the presence of the diffusion-limited current, that is, the maximum current available, flowing across the interface. In other words, the flow of current or ions across the interface is not directly responsible for the interfacial turbulences, which in fact makes the strong contrast of the electrochemical instability with the instability associated with interfacial chemical reactions of the type treated within the framework of the linear stability theory [9,10,30]. 

An interdisciplinary team of leading experts from around the world discuss recent concepts in the physics and chemistry of various well-studied interfaces of rigid and deformable particles in homo- and hetero-aggregate dispersed systems, including emulsions, dispersoids, foams, fluosols, polymer membranes, and biocolloids. The contributors clearly elucidate the hydrodynamic, electrodynamic, and thermodynamic instabilities that occur at interfaces, as well as the rheological properties of interfacial layers responsible for droplets, particles, and droplet-particle-film structures in finely dispersed systems. The book examines structure and dynamics from various angles, such as relativistic and non-relativistic theories, molecular orbital methods, and transient state theories. 

Equations [84] and [85] suggest that the droplet size in the steady state is essentially determined by competition of the interfacial tension and the viscous shear stress, as considered in the classical Taylor theory " for an instability criterion of a single droplet. However, the behavior of the normal stress difference (eqn [83b]) is not fully understood from this theory. Concerning this point, Doi and Ohta proposed a phenomenological model for the interface anisotropy and spedfic interfacial area in blends having the characteristic length determined only by the shear. The predictions of the Doi-Ohta model are consistent with the experimental observation (eqns [83]-[85]) as well as the scaling behavior observed for... 

---