Dispersed phase geometry

Many composite materials are composed of just two phases one is termed the matrix, which is continuous and surrounds the other phase, often called the dispersed phase. The properties of composites are a function of the properties of the constituent phases, their relative amounts, and the geometry of the dispersed phase. Dispersed phase geometry in this context means the shape of the particles and the particle size, distribution, and orientation these characteristics are represented in Figme 16.1. 

The last remaining parameter in the DPM is the individual rising velocity of a dispersed phase droplet in a certain apparatus geometry. The velocities of both phases are related to the two-layer model [65] which is expressed as ... 

When two liquids are immiscible, the design parameters include droplet size distribution of the disperse phase, coalescence rate, power consumption for complete dispersion, and the mass-transfer coefficient at the liquid-liquid interface. The Sauter mean diameter, dsy, of the dispersed phase depends on the Reynolds, Froudes and Weber numbers, the ratios of density and viscosity of the dispersed and continuous phases, and the volume fraction of the dispersed phase. The most important parameters are the Weber number and the volume fraction of the dispersed phase. Specifically, dsy oc We 06(l + hip ), where b is a constant that depends on the stirrer and vessel geometry and the physical properties of the system. Both dsy and the interfacial area aL remain unaltered, if the same power per unit volume (P/V) is used in the scale-up. 

The mechanical properties of rapidly polymerizing acrylic dispersions, in simulated bioconditions, were directly related to microstructural characteristics. The volume fraction of matrix, the crosslinker volume in the matrix, the particle size distribution of the dispersed phase, and polymeric additives in the matrix or dispersed phase were important microstructural factors. The mechanical properties were most sensitive to volume fraction of crosslinker. Ten percent (vol) of ethylene dimethacrylate produced a significant improvement in flexural strength and impact resistance. Qualitative dynamic impact studies provided some insight into the fracture mechanics of the system. A time scale for the elastic, plastic, and failure phenomena in Izod impact specimens was qualitatively established. The time scale and rate sensitivity of the phenomena were correlated with the fracture surface topography and fracture geometry in impact and flexural samples. 

Dal-Cin MM, Lick CN, Kumar A, and Lealess S, Dispersed phase back transport during ultrafiltration of cutting oil emulsions with a spinning disc geometry, J. Membr. Sci. 1998 141 165. 

Conceptually, the framework of the theory permits description of interphase heat and mass transfer with reaction occurring in either or both phases. In theory one can use this approach to study the affects of partial mixing of the dispersed phase on extent of reaction for non-first-order reactions which occur in the droplets. Analyses can be made for mass-transfer-controlled reactions and selectivity for complex reactions. Difficulties in the solution of the resulting integro-diflferential equations have restricted applications at present to partial solutions. For example, the effects of partial droplet mixing on extent of reaction were studied for uniform drops. Mass transfer from nonuniform drops for various reactor geometries was studied for dispersions with drop breakage only or drop coalescence only. 

The process relationship for the target quantity 32 (or for a) can be formulated either with extensive or intensive quantities. The difference lies in the choice of the process parameter. The dispersion characteristic formulated with extensive quantities uses as the process parameter the extensive quantity stirrer speed and leads, assuming a given geometry (stirrer type D/d, H/d, h/d = const), to the following dependence (the index d indicating the physical properties of the dispersed phase, no index indicating the physical properties of the continuous phase) ... 

Garstecki et al. conducted careful experiments [13] in which they varied (i) the geometry of the device, (ii) the rates of flow of the two fluids, (iii) the viscosity of the continuous fluid and (iv) the value of the interfacial tension. These experimental results verified that at low values of the Capillary number - which are t5 ical to those t5 ical for flows in microsystems -indeed the mechanism of break-up is similar to that observed in the flow-focusing system. Namely, as the tip of the dispersed phase enters the main channel, and fills its cross-section, the hydraulic resistance to flow in the thin films between the interface and the walls of the obstructed microchannel creates an additional pressure drop along the growing droplet. This pressure drop has a primary influence on the d5mamics of break-up namely, once the main channel is obstructed by the growing droplet, the upstream interface of... 

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