Breakage Rate Constants Research Articles

DROPLET COALESCENCE AND BREAKAGE RATES IN LIQUID EXTRACTION COLUMNS

Abstract A review is given of recent work on the measurement of droplet coalescence and breakage rates in a packed and a pulsed plate extraction column using a newly developed colorimetric technique. The results, which were interpreted in terms of second order coalescence and first order breakage rate constants, showed that the droplet interaction rates are considerably lower in the pulsed column. The rate constants can also be used to predict accurately the steady state droplet size distribution, and to study theoretically the effect of droplet coalescence and breakage on mass transfer rate. Deficiencies in the available mass transfer coefficient data for droplets, both individual and in “swarms”, are pointed out.

Droplet coalescence and breakage rates in a packed liquid extraction column

AbstractCoalescence rates for MIBK (methyl isobutyl ketone) droplets in water in a packed column have been measured directly using a novel colorimetric technique. Second‐order coalescence and first‐order breakage rate constants were derived from the results using a discrete population balance model and were correlated in terms of droplet diameter and dispersed‐phase holdup. It is shown that the rate constants can be used to predict the steady‐state droplet‐size distribution and coalescence rates. They were also used in a theoretical study of mass transfer for a typical polydisperse system, which showed that repeated droplet coalescence and breakage leads to some reduction in column height.

Material-depednent non-linear modeling of fine coal grinding

Fine grinding of lignite in a ball mill was shown to be non-linear in rate because of the presence of both weaker and stronger organic phases. Weaker phases were ground rapidly, whereas stronger phases were ground more slowly. Lignite grinding was modeled by evaluating two sets of time-independent linear breakage rate constants, one for the weaker phases and one for the stronger phases. The time of transition when the comminution rate became controlled by the stronger phases rather than the weaker phases was determined by observing changes in gas release rate and particle properties such as composition, shape, and porosity.

Isoelectric precipitation of soy protein. II. Kinetics of protein aggregate growth and breakage

Protein aggregate growth and breakage in agitated suspensions are modeled. The model includes growth of particles by a turbulent collision mechanism and breakage by a hydrodynamic shear mechanism. In the model, breakage results in the splitting of the particles into several small fragments. The model parameters are a growth rate constant and a breakage rate constant. Aggregate size distributions were measured with a Coulter counter and the data interpreted using a population balance that governs the steady-state particle size distribution in a continuous stirred tank reactor. Effects of changes in the operating variables pH, concentration, mean residence time, ionic strength, and mixing power input on the model kinetic parameters are investigated.

Continuous grinding in a small wet ball mill. Part V. A study of the influence of media shape

The influence of change in grinding media shape on the grinding behaviour of trace quantities of quartz within an environment of calcite in a small continuous wet ball mill has been studied using steel spheres, cubes, long, short and equi-cylinders, and hexagonal “cylinders” Their dimensions were chosen so that a unit of each shape weighed the same as a one-inch sphere. Standard charges of 90.5 lb. of each shape were used. The results show that the shape of grinding media had a significant effect on both the first-order breakage rate constants ( k′) and the breakage function. Spheres had the most selective rate function (i.e. relatively high breakage rates for coarser sizes and low for finer), and cubes and cylinders the least selective. Breakage functions for cylinders and cubes indicated that these shapes produced fewer fines in any single breakage event than spheres or hexagons. Media shape had a marked effect on the average residence time of particles in the mill but little effect on the type of flow through the mill. Simulated grinds using the dynamic model of breakage and the appropriate experimentally determined breakage functions, rate functions and distributions of residence time showed that spherical media handled the greatest throughput and produced the most closely sized product.

Continuous grinding in a small wet ball mill. Part IV. A study of the influence of grinding media load and density

TXX influence of changes in grinding media load and density on the grinding behaviour of trace quantities of quartz within an environment of calcite in a small continuous wet ball mill have been studied using (a) ball loads ranging from 45% to 100% of the standard load of 1-in. balls, (b) a standard load of 1-in. pebbles and (c) standard loads of equicylinders with specific gravities ranging from 2.82 to 9.49. A mill overload condition (125% ball load) has also been studied using a feed comprising 5% by weight of full-size-range quartz and 95% standard calcite. The results show that variations in breakage behaviour were best followed by a comparison of the adjusted breakage rate constants (k′) for individual sizes corresponding to a standard hold-up-weight. The changes in k′ with ball load could be explained in terms of changes in number of impacts per unit time and in the environmental size distribution. A reduction in the density of the grinding media caused a disproportionate decrease in k′ for the coarse sizes compared with the fine sizes, and breakage rates tended to zero for all sizes as the density of the medium approached that of the pulp. Whilst under some of the test conditions the flow of tracer solids behaved anomalously, under most conditions there was an approximately linear relationship between average residence time and total weight of media charged to the mill. Media density per se had no effect on breakage function, but there was a distinct change due to change in media shape.

Hydrodynamic shear breakage of DNA

AbstractThe rate of breakage of duplex DNA molecules by laminar flow through a capillary has been studied. For λb2b5c DNA (molecular wt., M = 25 × 106) the point at which breakage occurs is normally distributed around the center of the molecule with a standard deviation of 12.5% of the molecular length. At constant shear stress or shear rate, the breakage rate is independent of ionic strength. Thus, shear induced local denaturation is not a rate limiting, preliminary step in breakage. In experiments at constant temperature with varying solvent viscosity (controlled by added sucrose) the breakage rate is a function of shear rate, not of shear stress. The rate of opening of hydrogenbonded circles into linear molecules by hydrodynamic shear is also shown to be a function of shear rate and not of shear stress. The breakage rate at constant shear rate is not greatly dependent on temperature. The shear rate required to achieve breakage is inversely proportional to M1,2. The breakage rate constant, k varies as a very high power of the shear rate; at 25°C, d In k/d In Gm ∼ 15; at 10°C, d In k/d In Gm ∼ 26, where Gm is the maximum shear rate at the capillary wall. The unexpected result that breakage rate is mainly dependent on shear rate, not shear stress, supports a model in which the DNA molecule is distorted with a driving force which depends on the hydrodynamic shear stress, ηG, but the rate limiting step is segment diffusion into a highly extended configuration. The characteristic time to achieve this configuration is proportional to solvent viscosity, η, hence the breakage rate is dependent on ηG/η or G, the shear rate.

Continuous grinding in a small wet ball mill Part II. A study of the influence of hold-up weight

The effect of changes in the hold-up weight of calcite environment in a small continuous wet ball mill on the grinding behaviour of quartz tracer solids has been studied. The distribution of residence time and rate of breakage for the initial tracer size have been determined experimentally for hold-up weights varying from 1350 to 7640 g and the rates of breakage for sizes below the initial size have been determined by analogue computing techniques. The results show that the dimensionless distribution of residence time tended toward that of a more fully mixed system as the hold-up weight increased and that the first-order breakage rate constants were strongly dependent on the hold-up weight. The product of rate constant and hold-up weight remained approximately constant for each size below 590 μ but for the larger sizes increased considerably with increase in hold-up weight. However, the calcite steady-state product size distributions were only slightly influenced by large changes in the hold-up weight.