The theory of solute extraction in viscous single-drop systems is extended to show (1) the dependence of the asymptotic Nusselt number on the Peclet number from N p , = 0, the molecular diffusion limit, to N p , = 00, the Kronig and Brink limit, and (2) the dependence of the diffusion entry region Nusselt number on the Peclet number and the initial concentration profile.A numerical solution of the diffusion equation, limited to dilute solute concentrations and salute transport by viscous convection and molecular diffusion, is presented from which the nature of the Nusselt number is deduced. The observed oscillatory behavior of the Nusselt number in the diffusion entry region, as N p , +cs, is given a simple physical interpretation in terms of the circulation period of the drop liquid.The model is based upon the Hadamard stream function which theoretically is limited to creeping flow; however some experimental evidence indicates that flow fields similar to the Had0ma.d stream function exist at continuous phase Reynolds numbers of the order of ten. It is customary to analyze and correlate the results of single-drop extraction experiments in terms of mathematical models. For example, experiments with viscous drops normally are related to either the stagnant-drop model, at the extreme of vanishing circulation or to the Kronig and Brink (10) model at the opposite extreme; whereas ex-L. J ! $ Johns, Jr., is with Dow ChFmical Company, Midland, Michigan. &ann is with the University of Maryland, College Park, Mary-R. B. land. periments with turbulent drops frequently are related to the Handlos and Baron model ( 1 5 ) .This paper presents the solution to a viscous %ow model which reduces to the stagnant-drop and the Kronig and Brink models in the respective limits, that is, N p s = 0 and Np. + co, and complements these models on the interval 0 < N p e < co. A mathematical formulation of the model will be given after a brief summary of the problem and a presentation of the major assumptions.

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The problem of immiscible displacement of oil ganglia arises in connection with oil bank formation and attrition during enhancwd oil recovery with flooding. A stochastic simulation method is developed here, which enables prediction of the fate of solitary ganglia during immiscible displacement in water-wet unconsolidated granular porous media. This method takes into account the local topology of the porous medium; the initial size, shape and orientation of the oil ganglion and the capillary number. For each ganglion size, hundreds of realizations are performed with random ganglion shapes for a 100 x 200 sandpack. These results are averaged to obtain probabilities of mobilization, breakup and stranding as fudctions of capillary number and ganglion size. Axial and lateral dispersion coefficients are obtained as functions of the average ganglion velocity. The results from the solitary ganglion analysis can he used with the ganglion population balance equations developed in a companion publication (Payatakes, Ng and Flumerfelt, 1980) to study the dynamirs of oil bank formation.

V 7 =space time, s $ = dimensionless reactant concentration 4 = porosity = stoichiometric coefficient (moles reactant consumediinole of mineral reacted) Subscripts b = breakthrough h = homogeneous phase reaction i = reactant species .i = mineral species n S = surface reaction = last of the moving fronts Hekim, Y., and H. S. Fogler, "Acidization VI. On the Equilibrium

When a liquid whose viscosity decreases as its temperature increases is made to undergo a simple shearing flow the wall speed, or the centreline temperature, is a double valued function of the wall stress. This is called the base solution curve and the turning point is called the nose of the curve. The question we address is this: is there a point of neutral stability on this curve? The answer turns out to depend on whether the wall speed or the wall stress is the control variable.We introduce an eigenvalue problem which explains the shape of the base curve. It leads to a useful definition of the nose and to a rule which forecasts when a nose ought to arise. It then helps us determine where the neutral points lie. The result is this: if the wall speed is the control variable there are no points of neutral stability; if the wall stress is the control variable the nose of the curve is a point of neutral stability. This supports our conviction that in a physical experiment the wall speed must be the control variable, it cannot be the wall stress. Because the wall stress plays the same role here as does the Frank-Kamenetskii number in thermal ignition we conclude that thermal ignition is not a good model of fluid frictional heating.