Internal circulation effect

Typical spray simulations do not resolve the temperature and species gradients around each droplet to compute the rate of evaporation. Instead, evaporation rates are estimated based on quasi-steady analysis of a single isolated drop in a quiescent environment [27, 28]. Multiplicative factors are then applied to consider the convective and internal circulation effects. 

Spray Towers A spray tower consists of an empty shell into the top of which the liquid is sprayed by means of nozzles of various kinds the droplets thus formed are then allowed to fall to the bottom of the tower through a stream of gas flowing upwards. The use of sprays appears to offer an easy way of greatly increasing the surface area exposed to the gas, but the effectiveness of the m.ethod depends on the production of fine droplets. These are difficult to produce and suffer from the disadvantage that they are liable to entrainment by the gas even at low gas velocities. The surface area may also be reduced as a result of the coalescence of the droplets first formed. As a consequence of these effects, the large increase in surface area expected may not be achieved, or if achieved m.ay be accompanied by serious entrainment and internal circulation of the liquid so that true counter-current flow is not obtained. A single spray tower is suitable for easy absorption duties. For difficult duties, a number of towers in series can be used. 

Example 4.7 A fully turbulent, baffled vessel is to be scaled up by a factor of 512 in volume while maintaining constant power per unit volume. Determine the effects of the scaleup on the impeller speed, the mixing time, and the internal circulation rate. 

Slow internal circulation suggests sluggish slow turnover of fluid Inadequate mixing Draft tube effect... 

The derivations of Hadamard and of Boussinesq are based on a model involving laminar flow of both drop and field fluids. Inertial forces are deemed negligible, and viscous forces dominant. The upper limit for the application of such equations is generally thought of as Re 1. We are here considering only the gross effect on the terminal velocity of a drop in a medium of infinite extent. The internal circulation will be discussed in a subsequent section. 

The surface viscosity effect on terminal velocity results in a calculated drag curve that is closer to the one for rigid spheres (K5). The deep dip exhibited by the drag curve for drops in pure liquid fields is replaced by a smooth transition without a deep valley. The damping of internal circulation reduces the rate of mass transfer. Even a few parts per million of the surfactant are sometimes sufficient to cause a very radical change. 

Not until the above effects can be mathematically related can we expect to progress beyond the experimental stage. To predict such items as size of drop formed at a nozzle, terminal velocity, drag curves, changes of oscillations, and speed of internal circulation, one must possess experimental data on the specific agent in the specific system under consideration. Davies (Dl, D2) proposes the use of the equation... 

Accounting for the influence of surface-active contaminants is complicated by the fact that both the amount and the nature of the impurity are important in determining its effect (G7, L5, Rl). Contaminants with the greatest retarding effect are those which are insoluble in either phase (L5) and those with high surface pressures (G7). A further complication is that bubbles and drops may be relatively free of surface-active contaminants when they are first injected into a system, but internal circulation and the velocity of rise or fall decrease with time as contaminant molecules accumulate at the interface (G3, L5, R3). Further effects of surface impurities are discussed in Chapters 7 and 10. For a useful synopsis of theoretical work on the effect of contaminants on bubbles and drops, see the critical review by Harper (H3). Attention here is confined to the practically important case of a surface-active material which is insoluble in the dispersed phase. The effects of ions in solution or in double layers adjacent to the interface are not considered. 

As for other types of fluid particle, the internal circulation of water drops in air depends on the accumulation of surface-active impurities at the interface (H9). Observed internal velocities are of order 1% of the terminal velocity (G4, P5), too small to affect drag detectably. Ryan (R6) examined the effect of surface tension reduction by surface-active agents on falling water drops. 

These flow transitions lead to a complex dependence of transfer rate on Re and system purity. Deliberate addition of surface-active material to a system with low to moderate k causes several different transitions. If Re < 200, addition of surfactant slows internal circulation and reduces transfer rates to those for rigid particles, generally a reduction by a factor of 2-4 (S6). If Re > 200 and the drop is not oscillating, addition of surfactant to a pure system decreases internal circulation and reduces transfer rates. Further additions reduce circulation to such an extent that shape oscillations occur and transfer rates are increased. Addition of yet more surfactant may reduce the amplitude of the oscillation and reduce the transfer rates again. Although these transitions have been observed (G7, S6, T5), additional data on the effect of surface active materials are needed. 

For circulating fluid particles without shape oscillations the internal resistance varies with time in a way similar to that discussed in Chapter 5 for fluid spheres. The occurrence of oscillation, with associated internal circulation, always has a strong effect on the internal resistance. If the oscillations are sufficiently strong to promote vigorous internal mixing, the resistance within the particle becomes constant. 

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