Transition-flow physics

As the pressure increases from low values, the pressure-dependent term in the denominator of Eq. (101) becomes significant, and the heat transfer is reduced from what is predicted from the free molecular flow heat transfer equation. Physically, this reduction in heat flow is a result of gas-gas collisions interfering with direct energy transfer between the gas molecules and the surfaces. If we use the heat conductivity parameters for water vapor and assume that the energy accommodation coefficient is unity, (aA0/X)dP — 150 I d cm- Thus, at a typical pressure for freeze drying of 0.1 torr, this term is unity at d 0.7 mm. Thus, gas-gas collisions reduce free molecular flow heat transfer by at least a factor of 2 for surfaces separated by less than 1 mm. Most heat transfer processes in freeze drying involve separation distances of at least a few tenths of a millimeter, so transition flow heat transfer is the most important mode of heat transfer through the gas. 

The microscopic understanding of tire chemical reactivity of surfaces is of fundamental interest in chemical physics and important for heterogeneous catalysis. Cluster science provides a new approach for tire study of tire microscopic mechanisms of surface chemical reactivity [48]. Surfaces of small clusters possess a very rich variation of chemisoriDtion sites and are ideal models for bulk surfaces. Chemical reactivity of many transition-metal clusters has been investigated [49]. Transition-metal clusters are produced using laser vaporization, and tire chemical reactivity studies are carried out typically in a flow tube reactor in which tire clusters interact witli a reactant gas at a given temperature and pressure for a fixed period of time. Reaction products are measured at various pressures or temperatures and reaction rates are derived. It has been found tliat tire reactivity of small transition-metal clusters witli simple molecules such as H2 and NH can vary dramatically witli cluster size and stmcture [48, 49, M and 52]. 

Stabilization of the Cellular State. The increase in surface area corresponding to the formation of many ceUs in the plastic phase is accompanied by an increase in the free energy of the system hence the foamed state is inherently unstable. Methods of stabilizing this foamed state can be classified as chemical, eg, the polymerization of a fluid resin into a three-dimensional thermoset polymer, or physical, eg, the cooling of an expanded thermoplastic polymer to a temperature below its second-order transition temperature or its crystalline melting point to prevent polymer flow. 

T and are the glass-transition temperatures in K of the homopolymers and are the weight fractions of the comonomers (49). Because the glass-transition temperature is directly related to many other material properties, changes in T by copolymerization cause changes in other properties too. Polymer properties that depend on the glass-transition temperature include physical state, rate of thermal expansion, thermal properties, torsional modulus, refractive index, dissipation factor, brittle impact resistance, flow and heat distortion properties, and minimum film-forming temperature of polymer latex... 

A plausible assumption would be to suppose that the molecular coil starts to deform only if the fluid strain rate (s) is higher than the critical strain rate for the coil-to-stretch transition (ecs). From the strain rate distribution function (Fig. 59), it is possible to calculate the maximum strain (kmax) accumulated by the polymer coil in case of an affine deformation with the fluid element (efl = vsc/vcs v0/vcs). The values obtained at the onset of degradation at v0 35 m - s-1, actually go in a direction opposite to expectation. With the abrupt contraction configuration, kmax decreases from 19 with r0 = 0.0175 cm to 8.7 with r0 = 0.050 cm. Values of kmax are even lower with the conical nozzles (r0 = 0.025 cm), varying from 3.3 with the 14° inlet to a mere 1.6 with the 5° inlet. In any case, the values obtained are lower than the maximum stretch ratio for the 106 PS which is 40. It is then physically impossible for the chains to become fully stretched in this type of flow. 

The onset of flow instability in a heated capillary with vaporizing meniscus is considered in Chap 11. The behavior of a vapor/liquid system undergoing small perturbations is analyzed by linear approximation, in the frame work of a onedimensional model of capillary flow with a distinct interface. The effect of the physical properties of both phases, the wall heat flux and the capillary sizes on the flow stability is studied. A scenario of a possible process at small and moderate Peclet number is considered. The boundaries of stability separating the domains of stable and unstable flow are outlined and the values of the geometrical and operating parameters corresponding to the transition are estimated. 

The issues of selection of the spatial wavelength and the deterministic character of the fine scale features of the microstructure are closely related to similar questions in nonlinear transitions in a host of other physical systems, such as macroscopic models of immiscible displacement in porous media - - the Hele Shaw Problem (15) - and flow transitions in fluid mechanical systems (16). 

A variety of mechanisms have since been suggested to explain the physical basis for the observed transition between flow patterns (Ishii, 1975 Taitel and Dukler, 1976b Taitel et al., 1980 Barnea, 1987 Taitel and Barnea, 1990). Dukler and Taitel (1991b) summarized the various mechanisms to explain such flow pattern transitions (Table 3.1), where the letters in Table 3.1 identify the theoretical curves shown in the accompanied graphs (Fig. 3.7) for different flow directions. A word of caution was given in the reference ... 

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