Coalescence-dispersion process theory

With this process the main objective is to produce the same interfacial areas per unit volume on both scales, in order to achieve the same mass transfer. The analysis based on turbulence theory has been confirmed by the knowledge gained in practice in the form of the scale-up criterion P/V = const. This applies to dispersing processes in liquid/liquid and gas/liquid systems. Because of the numerous factors that influence the process (e.g., coalescence properties, physical properties of mixtures, anomalous flow characteristics, static pressure, etc.), substantial... 

Classical theories of emulsion stability focus on the manner in which the adsorbed emulsifier film influences the processes of flocculation and coalescence by modifying the forces between dispersed emulsion droplets. They do not consider the possibility of Ostwald ripening or creaming nor the influence that the emulsifier may have on continuous phase rheology. As two droplets approach one another, they experience strong van der Waals forces of attraction, which tend to pull them even closer together. The adsorbed emulsifier stabilizes the system by the introduction of additional repulsive forces (e.g., electrostatic or steric) that counteract the attractive van der Waals forces and prevent the close approach of droplets. Electrostatic effects are particularly important with ionic emulsifiers whereas steric effects dominate with non-ionic polymers and surfactants, and in w/o emulsions. The applications of colloid theory to emulsions stabilized by ionic and non-ionic surfactants have been reviewed as have more general aspects of the polymeric stabilization of dispersions. ... 

Delichatsios and Probstein (D4-7) have analyzed the processes of drop breakup and coagulation/coalescence in isotropic turbulent dispersions. Models were developed for breakup and coalescence rates based on turbulence theory as discussed in Section III and were formulated in terms of Eq. (107). They applied these results in an attempt to show that the increase of drop sizes with holdup fraction in agitated dispersions cannot be attributed entirely to turbulence dampening caused by the dispersed phase. These conclusions are determined after an approximate analysis of the population balance equation, assuming the size distribution is approximately Gaussian. 

Flow-induced coalescence is accelerated by the same factors that favor drop breakup, e.g., higher shear rates, reduced dispersed-phase viscosity, etc. Most theories start with calculation of probabilities for the drops to collide, for the liquid separating them to be squeezed out, and for the new enlarged drop to survive the parallel process of drop breakup. As a result, at dynamic equilibrium, the relations between drop diameter and independent variables can be derived. 

Theoretical models for the dieleetrie properties of heterogeneous mixtures [for instance, Eq. (20), or extensions of this model] are commonly applied in order to explain or predict the dieleetrie behavior also of emulsions (106, 158). However, in the present theories a homogeneous distribution of the dispersed phase is required. This requirement is rarely fulfilled in a real emulsion system where the inherent instability makes the emulsions go through different stages on the way towards complete phase separation. Proeesses like sedimentation, flocculation, and coalescence continuously alter the state of the system (Fig. 36). These processes also influence the dielectric properties (159—162). Thus, the dielectric properties of one given sample may vary considerably over a period of time (160), depending on the emulsion rate. 

Ti2 is the shear stress, <7 is the interfacial tension, is the volume fraction of the dispersed phase, Epf is the bulk breaking energy, and P, is the probability that a collision between two close particles will result in coalescence leading to phase coarsening. It is clear from the expression that the particle size at equilibrium diminishes as the shear stress increases, the interfacial tension decreases, and the volume fraction of the dispersed phase decreases. This theory has been verified experimentally for several immiscible blends where a master curve of particle size as a function of composition was found to follow a + dependence [11]. Fortelny et al. [12] have propos an expression (Equation 1.5) that accounts for a drop breakup (the first term in Equation 1.5) and a coalescence process (the second term in Equation 1.5) ... 

In this chapter, we present a detailed review of deactivation of particle-oil antifoams, with particular emphasis on hydrophobed silica-polydimethylsiloxane antifoams about which most studies have been made. The available evidence suggests that the phenomenon concerns disproportionation of antifoam drops during processes of splitting and coalescence, which occur as the antifoam is either dispersed or interacts with foam films. We speculate here about the likely causes of this phenomenon and describe theories that attempt to predict foam volume growth in the presence of deactivating antifoam. 

Liquid-liquid dispersion is among the most complex of all mixing operations. It is virtually impossible to make dispersions of uniform drop size, because of the wide range of properties and flow conditions. Our chapter provides a fundamental framework for analysis and understanding of dispersion and coalescence, based often on idealized experiments and theories. This framework can be applied to more complicated processes, including scale-up. Throughout the chapter, references are made to state-of-the-art information, often not yet proven in practice. The chapter concludes with commercialization advice and recommendations. 

For fine aerosol particles, X 1.0 and the agglomeration rate is the collision rate. However, for hqnid-hqnid systems, the coalescence efficiency is often small and rate limiting. Therefore, classical agglomeration theory (e.g., Smolnchowski eqnation) cannot be directly applied to liquid-liquid dispersions. Coalescence is known as a second-order process ( n ) since the coalescence rate is proportional to F(d, d0n(d)n(d0, where n(d) and n(d ) represent an appropriate measure of the number of drops of size d and d, respectively. 

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