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A model for Ostwald ripening of oil-in-water emulsion in the presence of small amount of surfactants is presented. It accounts for the transfer of oil from small to larger drops when the interfacial resistance is rate controlling. In this case, the continuous breakdown and reformation of the micellar structure during mass transfer through the interface, is assumed to be the rate-controlling step. A discretized population balance equation for the change in the number concentration of drops due to Ostwald ripening is solved using the method of characteristics. The third moment of the distribution (average volume) is found to increase linearly with time, consistent with available experimental observations, before reaching an abrupt equilibrium. The rate of change of drop volume is found to be strongly dependent on the solubility and is fairly insensitive to the volume fraction. The transients of the drop size distributions indicate an initial rapid decrease in the small droplets with a corresponding increase in the larger drops followed by a very slow change in the number distributions at longer times. The rate constants involved can be roughly correlated with the components of several experimental measurements, and allow comparison with the data of Kabalnov (Langmuir 10 (1994) 680), but only at small surfactant concentrations. The numerical agreement is not good but it is able to predict the anomalous direction of change with increased surfactant concentrations. The basis of the lack of numerical agreement is discussed.

Transient breakage drop-size distributions have been experimentally measured using an image analysis technique. The transient distributions show self-similar behavior. The breakage rate and daughter-drop distribution functions have been determined using an inverse-problem approach which takes advantage of this self-similarity. The inverse-problem results show that the breakage rate is not a power law function of the drop size. The breakage rate is found to increase sharply with the drop size and the stirrer speed while decreasing sharply with increase in the interfacial tension. It is also found to decrease with increase in the dispersed phase viscosity, though the dependence on the viscosity is weaker than on the other variables. The daughter drop distribution was found to be relatively insensitive to the stirrer speed and interfacial tension, but was found to depend on the dispersed phase viscosity. As the drop viscosity increases, the breakage becomes more erosive in nature, leading to a broader size distribution of daughter drops. Generalized correlations for the breakage rate and daughter-drop distribution which account for the effect of physical properties and experimental conditions are presented. These relations will be very useful in predicting the drop-size distributions in stirred dispersions. Models for the breakage functions are compared with those determined in this study and the model predictions of the transient-size distributions are compared with the experimental data.

A model for transitional breakage probability of droplets in agitated lean fiquid-liquid dispersions is proposed based on the mechanism of breakage of droplets due to their oscillations resulting from relative velocity fluctuations. A universal transitional breakage probability in terms of non-dimensionalized drop diameter is derived for all dispersed phases whose density and viscosity are almost the same as that of continuous phase. The maximum stable drop diameter ds derived from the model, shows a dependence of NWe−0.6. It is shown that a “power law” approximation Kvn is valid for transitional breakage probability for d/ds up to 2. The exponent 2.67, predicted by this model corresponds rather well with an estimate of 2, obtained from experimental observations. A functional relation for the rate constant K in terms of the parameters and physical properties of the system is derived. A universal non-dimensionalized equilibrium drop-size distribution for agitated lean liquid-liquid dispersions is derived by analytical solution of a population balance equation simplified by order of magnitude estimates. Interestingly enough, this analytical solution is the same as the Gaussian distribution suggested empirically by Chen and Middleman.

A generalized isothermal effectiveness factor correlation has been proposed for catalytic reactions whose intrinsic kinetics are based on the redox model. In this correlation which is exact for asymptotic values of the Thiele parameter the effect of the parameters appearing in the model, the order of the reaction and particle geometry are incorporated in a modified form of Thiele parameter. The relationship takes the usual form: and predicts effectiveness factor with an error of less than 2% in a range of Thiele parameter that accommodates both the kinetic and diffusion control regimes.

Boundary value problems involving oblique or mixed second derivative boundary conditions[1,3] arise in the description of heat (or mass) transfer in stationary media which are peripherally cooled (or leached) by a fluid in which the temperature (or concentration) is varying significantly in the direction of flow. By decomposing the energy equation into a pair of first order systems Ramkrishna and Amundson have shown[1] how the originally non-selfadjoint boundary value problems can be reduced to selfadjoint problems. The foregoing decomposition allows for an elegant analytical solution of the boundary value problems which is also numerically efficient. This paper relaxes certain redundant constraints imposed earlier on the method of solutions[1] and demonstrates the power of the method by actual numerical calculations for a constant heat source function.

Based on the generalized treatment of isothermal mean effectiveness factor presented by Aris, an experimental factor Φ exp has been obtained, the numerical value of which could be ascertained from experimental measurements of reaction rate and other pertinent properties of the fluid-particle system. It is shown that if Φ exp ⩽ 0·03, the experimental data reflect solely the influence of intrinsic kinetics of the system. Based on available kinetic information pertaining to a phthalic anhydride process, the variation of Φ exp with temperature, catalyst activity and external diffusion has been presented. Finally a plot of Φ exp against generalized Thiele parameter for low orders of reaction, has been used to check the consistency and absence or otherwise of pore diffusion limitation in experimental data reported in existing literature.

The process of thermal decomposition of calcium carbonate has been treated as one governed by simultaneous heat and mass transfer, under quasi steady state conditions, to the decomposition interface. It is believed that the surface chemical reaction is very fast and as such does not interfere in the determination of the overall decomposition rate. Rigorous expressions, based on heat transfer rate, have been derived, based on the system properties, for the prediction of decomposition times for definite geometric shapes such as spheres and cylinders. The good agreement observed between the actual and predicted values bears out the soundness of the decomposition scheme assumed for the process. The expression derived are: Based on an analysis of simultaneous heat and mass transfer rates the following correlation is obtaiend: This equation bears very close resemblance to the theoretical expression for the evaporation of small spheres into quiet air. This equation may be rearranged to provide: which is a modified form of the usual correlation for simultaneous heat and mass transfer based on Chilton-Colburn analogy. The mathematical treatment has been extended to a two-phase solid system (Mg CO 3 -Ca CO 3 ) characterized by finite but different equilibrium decomposition temperatures. The mathematical analysis involves the solution of simultaneous differential equations. This has been done numerically by the modified Runge-Kutta method with the help of an IRM computer. The confirmation of the proposed equation must await future experimental data for the two-phase system.

The cell model developed by Amundson and co-worker has been applied to compute the bulk and particle temperatures and partial pressure along the length of a packed bed reactor where an exothermic non-catalytic solid-gas reaction, viz. proceeds under adiabatic conditions. The kinetic data previously obtained have been used in the numerical computation procedure adopted in programming on a CDC 3200 computer. By linearizing the transient equations around the steadystate, the stability problem has been investigated by examination of the Lienard-Chipart criterion. The condition of sectional stability has been obtained as: which is a more conservative condition that the usual van Heerden's slope conditions, at the specified cell. An approximate but safe stability condition applicable over the entire bed at any stage of conversion has been obtained as Experimental work is in progress.

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