Interphase Rheology

Rheological methods of measuring the interphase thickness have become very popular in science [50, 62-71]. Usually they use the viscosity versus concentration relationships in the form proposed by Einstein for the purpose [62-66], The factor K0 in Einstein s equation typical of particles of a given shape is evaluated from measurements of dispersion of the filler in question in a low-molecular liquid [61, 62], e.g., in transformer oil [61], Then the viscosity of a suspension of the same filler in a polymer melt or solution is determined, the value of Keff is obtained, and the adsorbed layer thickness is calculated by this formula [61,63,64] ... 

Koelman and Hoogerbrugge (1993) have developed a particle-based method that combines features from molecular dynamics (MD) and lattice-gas automata (LGA) to simulate the dynamics of hard sphere suspensions. A similar approach has been followed by Ge and Li (1996) who used a pseudo-particle approach to study the hydrodynamics of gas-solid two-phase flow. In both studies, instead of the Navier-Stokes equations, fictitious gas particles were used to represent and model the flow behavior of the interstial fluid while collisional particle-particle interactions were also accounted for. The power of these approaches is given by the fact that both particle-particle interactions (i.e., collisions) and hydrodynamic interactions in the particle assembly are taken into account. Moreover, these modeling approaches do not require the specification of closure laws for the interphase momentum transfer between the particles and the interstitial fluid. Although these types of models cannot yet be applied to macroscopic systems of interest to the chemical engineer they can provide detailed information which can subsequently be used in (continuum) models which are suited for simulation of macroscopic systems. In this context improved rheological models and boundary condition descriptions can be mentioned as examples. 

Shang et al. (1995) show that the work of adhesion between a silica filler surface and a polymer matrix is directly related to the dynamic viscosity and moduli. Additionally, at lower frequencies there is a greater influence of the work of adhesion. The influence is shown to be described well by an effective increase in interphase thickness due to the increase in the work of adhesion, such that polymer chains are effectively immobilized around the filler, and the friction between the immobilized layer and the polymer then governs the dynamic rheology. It was noted that the immobilized layer could be reduced in extent at higher frequencies. 

Krotov, V. V., Rheological analysis of the Marangoni effect for an ideal interphase layer, Colloid Journal, Vol. 48, No. 1, 1986. 

Thermodynamics also plays a dominant role in the interphasial phenomena, viz. the interfacial tension coefficient, thickness of the interphase, Al, the rheological properties of the interphase, the adhesion, etc. It is worth recalling that most... 

Most polymer blends are immiscible. Their flow is complex not only due to the presence of several phases having different rheological properties (as it will be demonstrated later, even in blends of two polymers the third phase, the interphase, must be taken into account), but also due to strain sensitivity of blend morphology. Such complexity of flow behavior can be best put in perspective by comparing it to flow of better understood systems, suspensions, emulsions, and block copolymers. 

Oldroyd [1953, 1955], Choi and Schowalter [1975],OosterbroekefflZ. [1980, 1981] and many others considered the interphase between the dispersed phase and the matrix liquid to be a physical, three-dimensional entity endowed with its own specific rheological properties. These considerations led to calculations of two relaxation times for Newtonian emulsions [Choi and Schowalter, 1975] ... 

Two types of coalescence must be recognized, the hrst being determined by equilibrium thermodynamics e.g., liquid-liquid miscibility, interfacial tension coefficient, rheological conditions of the interphase, etc.), the second, dynamic one, being also affected by the rheology. In the following text, only the second type will be discussed. 

Functionalized Polyolefins and Aliphatic Polyamide Blends Interphase Interactions, Rheology, and High Elastic Properties of Melts... 

The viscosity of blends varies not only with the composition but with flow conditions as well, which depend on the temperature and shear rate (20,41,65). A decisive effect on PA/PO rheology is caused by the chemistry of interphase processes (41). Blends of PA with ungrafted PO, or uncompatibilized blends, are characterized by a decreased melt viscosity in comparison with the additive... 

Finally, one can consider that the measured adhesive strength of an assembly conld be expressed as a fnnction of three terms relating, respectively, to (1) the interfacial molecnlar interactions, (2) the mechanical and rheological properties of bnlk materials, and (3) the characteristics of the interphase. The first two terms have received a great deal of attention dnring recent decades, as a result of studies in the physical chemistry of surfaces and fractnre mechanics. The third term constitutes the real challenge for a proper and complete understanding of adhesion. 

In a destabilization scheme, one first assesses the degree of stability of the emulsion. There is a need to know how much time and energy are cmcial for the process, the phase compositions, and the emulsifier(s) ehemisliy. For flie experienced engineer, this information flien allows some de-duetions on the eonfiguration of emulsifiers around the droplets, and the rheological properties of bofli flie interfa-eial film on the droplet and the interphase lamella between droplets. The viscosities of the emulsions and eontinuous oil phase are also important for deeisions on destabilization (96). 

At high dilution, the morphology of an immiscible blend is controlled by the viscosity ratio (2), the capillarity number (k), and the reduced time (t ) as defined in Eq. 9.8. The interfacial and rheological properties enter into k and t. As the concentration increases, the coalescence becomes increasingly important. This process is also controlled by the interphase properties. 

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