Dispersion Height Research Articles

Stopped-flow injection analysis. The influence of diffusion on dispersion of normal and reverse flow injection

A relationship is derived to enable the comparison of the dispersion heights of normal and reverse flow injection analysis (FIA). A single channel flow system is employed in the absence of a chemical reaction. The stopped-flow injection method is used to probe the influence of molecular diffusion on the overall dispersion of normal and reverse FIA, which appeared to demonstrate fundamentally different diffusion behaviors. Small discrepancies are observed between the dispersion heights, which are enhanced by the stopped-flow period, especially when unmatched matrix ionic compositions of the indicator and counter solutions were involved. For these conditions, the diffusion flux rate is enhanced considerably, displaying a peak, in addition to the transient, for both methods. The influence of diffusion on the dispersion characteristics of normal and reverse FIA is discussed theoretically. Diffusion in the proposed model is postulated to oppose dispersion by convection. The latter initiates concentration gradients in the injection zone and propagates it with flow time over the dispersion zone profile. The diffusion flux then reacts in order to confine the indicator dispersion for normal FIA and to enhance it for reverse FIA. This model is consistent with the experimental results and accounts for most of the phenomena encountered. Probably owing to the influence of secondary flow phenomena, the use of coiled tubes has suppressed the effects of diffusion on the overall dispersion behavior.

Estimation of turbulence parameters for application in air pollution modelling

Profile relationships based on Monin-Obukhov similarity theory have been used to compute, turbulence parameters, viz., friction velocity, u., and friction temperature, 0*., at the surface with available routine meteorological observations for the city of Delhi during day time. In order to make the method more realistic a radiation model has been coupled with the iterative procedure adotped for the similarity approach. The multifarious applications of turbulence parameters, viz., the computation of convective velocity scale w*., stability parameter wind velocity and eddy-diffusivity profiles and the most important though qualitatively known, the vertical dispersion height, of dz diffusing cloud have been presented and discussed at length.

Prediction of steady‐state dispersion height in the disengaging section of an extraction column from batch settling data

AbstractThe decay of a dense dispersion formed under calm conditions is given by Experiments in a batch vessel with different liquid‐liquid systems and initial drop diameters show that the dimensionless constant K is equal to 26,000. This agrees with the value previously determined from the variation in steady‐state dispersion height with throughput in spray columns, the analogous equation being The results can thus be used to predict the height of the dispersion formed in the disengaging section of extraction columns.

Choice of model for predicting the dispersion height in liquid/liquid gravity settlers from batch settling data

The design of liquid/liquid gravity settlers has attracted increasing interest in recent years due to the industrial importance of solvent extraction. Batch settling tests are easier to perform than continuous pilot plant runs, but require sophisticated interpretation if the behaviour of a steady-state dispersion is to be predicted. Both batch and continuous dispersions contain sedimentation and dense-packed zones in which the drops grow in size through binary coalescence and finally disappear when they coalesce with their bulk homophase. The rate of droplet sedimentation is a function of the drop size and dispersed phase hold-up, whereas the interfacial coalescence rate is dependent on the height of the dense-packed zone and the drop size at the coalescing interface. At the steady state the dense-packed height may shrink to zero if the interfacial coalescence is virtually instantaneous. On the other hand, the whole of the dispersion may be dense-packed if the conditions in the feed stream lead to a volume rate of sedimentation which is higher than the dispersed phase throughput. Similar extreme behaviour also occurs in batch dispersions under corresponding conditions. The variations in height of the sedimentation and dense-packed zones, and hence the total dispersion height with the throughput in a continuous settler, can thus be predicted using parameters determined from experimental batch sedimentation and coalescence data. A procedure based on the shape of the batch decay curves, hold-up and volume rates of sedimentation and interfacial coalescence is proposed for selecting the appropriate model which is verified with available experimental data.

The specific interfacial area in external-circulation-loop airlifts and a bubble column-I. Aqueous sodium sulphite solution

In order to contribute to general knowledge of the performance and design of external-circulation-loop type airlift fermentors, the specific gas-liquid interfacial area a was studied. Three different measurement methods were applied, namely sulphite oxidation, light scattering and photographic. Two sizes of fermentors having downcomer-to-riser cross-sectional area ratios ( A d/ A r) of 0.111 and 0.444 were employed. Parallel studies in a bubble-column-type fermentor ( A d/ A r = 0) were carried out for comparison. Experimental data on the liquid circulation velocity, gas hold-ups in the riser and the downcomer and the average bubble diameter necessary for evaluation of a by the chemical and photographic methods were also measured and are reported. While the data for a obtained by the chemical and light scattering methods agree well, a significant discrepancy was found with the results obtained using the photographic method. The specific interfacial area is shown to be mainly dependent on the downcomer-to-riser cross-sectional area ratio and the superficial gas velocity. However, the effects of liquid velocity, dispersion height and sparger hole diameter have also been taken into account to facilitate comparison with other works.

The gas disengagement technique for studying gas holdup structure in bubble columns

AbstractBy recording the drop in dispersion height after stopping the gas supply, the fractions of large and small bubbles, the respective swarm rise velocities, and the contributions to the overall gas flow can be determined. Some problems of the analysis are discussed in detail. The efficiency of the technique is demonstrated for the results obtained with two different gas distributors in a bubble column of 30 cm diameter.

Effect of drop size and physical properties on dispersion height in the separating section of a liquid/liquid extraction column

AbstractThe height of the dispersion formed in the separating section of an extraction column is given byH = K/g (σ/Δρg)1/2 I/ϕo (Qd/A)2Since calm conditions prevail the height of the sedimentation zone can be neglected and the dispersion is essentially dense‐packed. The effect of physical properties was investigated in a spray column using nine different liquid/liquid systems. A distributor divided into seven equal sectors enabled the effect of drop size and dispersed phase flow rate to be independently investigated.

On power input and liquid‐phase mixing times in pneumatically‐agitated contactors: Response to critique of guy et al.

AbstractThe total power input to a pneumatically‐agitated gas—liquid contactor in principle is the sum of the contributions of isothermal gas expansion (p‐V work) and the changes in the potential and kinetic (ΔKE) energies of the flowing gas. The latter energy change is dependent, in part, on the pressure drop in the sparger orifices. Guy et al. (1986a) strongly infer that in practice ΔKE is never negligible compared to the p‐V work and claim that Bello et al. (1984) made a serious error in neglecting the ΔKE contribution in their cases, which error may have made their relative mixing time comparisons invalid.This communication shows that for the work of Bello et al. (1984), the ΔKE contribution was in fact negligibly small, whereas for the spargers used by Guy et al. (1986b) it was not. Furthermore, it is shown that the implication of Guy et al. (1986a) that bubble columns (BC) produce better or equivalent liquid‐phase mixing than do stirred tanks (ST) is not universally true. The relative performance of BC and ST contactors is highly dependent upon the dispersion height: diameter ratio of the former, which ratio was quite different in the works of Bello et al. (1984) and Guy et al. (1986b).

Prediction of steady state dispersion height from batch settling data

AbstractIn order to design continuous industrial settlers, it has in the past been necessary to obtain extensive pilot plant data, the interpretation of which required considerable experience before it could be used for scale‐up purposes. The idea of using batch settling tests has always seemed attractive, but the difficulty of reconciling unsteady‐ and steady‐state experiments has so far proved physically and mathematically insurmountable.In this study the variation in steady state height with dispersion throughput in a continuous settler is predicted from unsteady state data obtained in a small‐scale batch settler. Models are presented which relate the drop sedimentation and coalescence in batch and continuous dispersions, thus enabling the steady state settler behavior to be predicted from parameters obtained from the batch data. These models are verified with available experimental data and should greatly simplify the future design and scale‐up of continuous settlers.

Mass transfer modelling for GS heavy water plants: Part 1: Point efficiency on GS sieve trays

AbstractA model that takes into account the gas‐phase and liquid‐phase resistance to mass transfer has been developed, where the overall mass transfer coefficient (KOGa) is expressed as a function of the equivalent Sauter‐mean bubble diameter. This parameter was back calculated from mass transfer measurements made at a pilot plant on single pass sieve trays of 0.311 m diameter. Hydraulic parameters were measured for these trays as well. Mean bubble diameters were then correlated as a function of active area F‐factor and dispersion height for various tray geometries, and these correlations are used to predict point efficiencies on production plant trays up to 8.5 m in diameter.

Koaleszenz in dichtgepackten Gas/Flüssig‐ und Flüssig/Flüssig‐Dispersionen

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.

Effect of geometrical arrangement and interdrop forces on coalescence time

AbstractAccording to the Reynolds' equation the time taken for a thin film to reach a critical thickness at which rupture occurs is a function of the film area and applied force. It follows that the coalescence time of a liquid drop is greatly affected by its geometrical configuration. If the drop is unconstrained the coalescence time increases when a vertical force is applied to the drop, but if the drop is constrained by the presence of surrounding drops its coalescence time decreases as the applied force increases. This explains why the rate of coalescence at the disengaging interface of a close‐packed dispersion increases with the dispersion height. The coalescence time for a planar film is usually less than for the spherical film formed between a drop and its homophase which explains why near‐horizontal surfaces inserted into close‐packed dispersion increase the rate of coalescence. The coalescence time of a drop in a close‐packed dispersion decreases as it approaches the disengaging interface. This means that the volume rate of coalescence at the interface may equal the disperse phase throughout without the necessity for interdrop coalescence. When the applied pressure is much greater than the van der Waals pressure, as in a close‐packed dispersion, the critical film thickness is itself a function of the film area and applied force, but this has little effect on the above conclusions. When the applied pressure is much less than the van der Waals pressure, as in a loose‐packed dispersion, the critical film thickness is only a function of the film area and the affect of the applied force on the coalescence time is then increased.

Effect of interdrop forces on the coalescence of drops in close-packed dispersions

The effect of a vertical force on the shape of a drop constrained by the presence of other drops in a horizontal array is considered. From the areas of the draining films above and below the drop and the forces acting on them, the coalescence time may be calculated relative to that of the draining film beneath a single drop subjected only to the weight of the drop. Calculations show that the coalescence time of a constrained drop decreases as the applied force increases, whereas that of an unconstrained drop increases. This suggests a relationship between the height of a close-packed droplet dispersion and the coalescence time of a drop at the disengaging interface.

A model for coalescence in a two-dimensional close-packed dispersion

The effect of a vertical force on the shape of a two-dimensional drop constrained by the presence of other drops in a horizontal row is considered. From the areas of the draining films above, below and to the side of the drop and the forces acting on them, the coalescence time may be calculated in relation to that of the draining film beneath a single drop subjected only to the weight of the drop. Calculations show that the coalescence time of a constrained drop decreases as the applied force increases, whereas that of an unconstrained drop increases. This suggests a relation between the height of a close-packed droplet dispersion and the coalescence time of a drop at the disengaging interface.

Vermischungseffekte in Flüssig/Flüssig‐Extraktionskolonnen

AbstractAxial mixing in liquid/liquid countercurrent extractors. Methods are considered for the determination of longitudinal mixing in many countercurrent extractors. It is found that only the single phase mixing of the continuous phase can be accurately determined; with certain reservations this also applies to the disperse phase. In the case of RDC and ARD in particular, correlations are available which permit calculation of Bodenstein numbers for both phases. Such scale‐up calculations are not recommended for many extractors. It is very important to establish adequate correlations for calculation of mixing of the disperse phase in order to obtain exact dispersion heights in connection with those of the continuous phase.

On the hydrodynamics of sieve plates without downcomers.: I. Dynamic nature of the gas—liquid dispersions

The random fluctuations of the pressure drop across the gas—liquid dispersion have been recorded at a point near the centre on sieve plates without downcomers. A 300 mm; diameter single plate column was used. Different plate designs have been investigated using the system air—water. The statistical properties of the froth pressure drop time—histories were evaluated by a digital method. Operating regimes were defined in terms of the statistical properties evaluated. The relation between the standard deviation of the froth pressure drop fluctuations and the average liquid hold-up was established. The frequencies of the macroscopic periodic stationary waves (occuffing under certain conditions) have been studied as a function of the dispersion height and gas flow rate.