Koaleszenz in dichtgepackten Gas/Flüssig‐ und Flüssig/Flüssig‐Dispersionen
Authors: Hartland S. 
Published: July 2012

AbstractThe height of a steady state dispersion formed in a vertical vessel increases with the throughput of the disperse phase. Since the cross‐sectional area of the disengaging interface remains constant, the volume rate of coalescence per unit area of the interface must increase as the throughput increases. There are three possible ways in which this may occur:

The films are formed between the drops or bubbles shortly after entering the dispersion and gradually become thinner, due to drainage, as they pass through the dispersion until the critical film thickness is reached when the bubbles coalesce with their homophase. If the disperse phase throughput is increased, so the dispersion height increases to keep the residence time of the bubbles and films between them constant, the critical thickness being reached at the disengaging interface. If there is no change in hold‐up of the disperse phase this model, in its simplest form, infers a linear increase in dispersion height with throughput. It is more likely to apply to gas/liquid foams than liquid/liquid dispersions, since the bubbles in a foam do not move relative to each other and the films remain intact, once formed. This is only true close to the disengaging interface in a liquid/liquid dispersion, as in the bulk there is usually considerable turbulence and relative motion of the drops.
The drops (or bubbles) coalesce together in the dispersion to give larger drops. If the coalescence time remains constant the volume rate of coalescence at the disengaging interface will increase as the drop volume increases. This model also infers an increase in height with throughput since the residence time increases to allow the drops to grow in size.
The coalescence time of drops at the disengaging interface is itself influenced by the dispersion height. Close to this interface is a region in which the drops are packed so closely that forces are transmitted from drop to drop. These forces are mainly gravitational, arising from the net weight of the drops above and partly due to the rate of change of momentum of the freely moving drops as they strike this layer. The coalescence time of a drop in a close‐packed dispersion does in fact decrease as the force pressing on it increases, since the area of the draining film cannot increase as it is constrained by the presence of surrounding drops (as distinct to a free drop for which the coalescence time, τ increases with applied force F, because the area of the film, A increases and hence also the coalescence time according to the approximate equation

in which k is constant for a given fluid/liquid system). Thus, if the thickness of the close‐packed layer increases with the disperse phase throughput so will the volume rate of coalescence at the disengaging interface. In addition, some binary coalescence occurs in the turbulent zone and the drops pass from this zone into the close‐packed zone when they have grown in size.The design engineer is interested in the rate at which a foam decays and the steady state height of a dispersion which is continuously produced. The rate of growth of the dispersion is important when the plant is started up or when operating conditions change. Although it is difficult to predict the behaviour of a dispersion from basic principles because of the complex nature of the phenomena involved, it is perhaps possible to predict the behaviour of one phase in its lifetime by observing the behaviour of another phase. For example, the steady state height and rate of growth may be predicted from measurements made on the decaying dispersion. The decay is usually easiest to observe as a sample of the dispersion can be removed from the plant and allowed to settle, or the two phases mixed together in a vessel under appropriate conditions before being allowed to separate.—The volume rate of coalescence V at the disengaging interface where the disperse phase hold‐up is εi is

so the coalescence time τi may be obtained if the drop diameter di is known. The growth in drop diameter, d, with residence time t within the dispersion is given by:

so the binary coalescence time τb may be obtained if the initial drop diameter do is known. The determination of coalescence times from batch data is discussed. Mathematical models for predicting the steady state dispersion height and the decay and growth of unsteady state dispersions are applied to recent experimental data.