S.A.K. Jeelani

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

Abstract 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.

Prediction of sedimentation and coalescence profiles in a decaying batch dispersion

Abstract The variation in heights of the sedimenting and coalescing interfaces and of the boundary between the sedimentation and dense-packed zones in a batch dispersion can be predicted from flux and volume balances only involving a single measurement of the separation time. It is assumed that no interdrop coalescence occurs in the sedimentation zone and that the coalescence rate in the dense-packed zone initially increases linearly with time until sedimentation is complete but is proportional to the square root of the dense-packed height after sedimentation has ceased. The variation in the heights of the sedimentation and dense-packed zones have been individually measured by observing the boundary between the two and found to agree well with that predicted. For a given system the results may even be expressed as a single reduced plot which is independent of the initial dispersion hold-up and average drop size.

Dimple formation in the thin film beneath a drop or bubble approaching a plane surface

Abstract The fourth-order differential equation governing the shape of the dimple as a function of time during the drainage of thin liquid film, derived by Hartland (1969, Chem. Engng Prog. Symp. Ser. No. 91, 65 , 82-89), is solved numerically. The required four boundary conditions are obtained from the geometric symmetry of the system and the shape of the drop or bubble. The present theory applies to both large and small films, and predicts the drainage for any axisymmetric initial profile. In particular, planar and parabolic initial profiles quickly predict identical development of the dimpled profile as do bell-shaped initial profiles. Similarly, the initial film thickness does not affect the subsequent development of the dimpled film. Comparison with the experimental profiles measured by Hartland (1969) for large drops and by Platikanov (1964, J. phys. Chem. 68 , 3619-3624) for air bubbles shows good agreement.

Effect of interfacial tension gradients on emulsion stability

Drainage of the films between droplets in a dispersion depends on the velocities of the surfaces. Dispersion stability and instability are explained in terms of a surface mobility m which is proportional to the surface velocity. Its value is given by m = mc + mg = mc(1 + mg/mc) in which mc = 3μrd/2μdhi and mg = mc(πr3f/2ƒhi)(∂σ/∂r)fi. When the interfacial tension gradient (∂σ/∂rfi is negative, the surface mobility is negative when mg/mc < − 1 which greatly reduces the drainage, so the dispersion is stable. This is the normal situation when a surfactant is present at the interface. Demulsifier molecules penetrate the interface within the film thereby lowering the interfacial tension sufficiently to create a positive interfacial tension gradient (∂σ/∂r)fi so mg and the surface mobility m are positive. The coalescence time is then very small. The drainage is then greatly increased and the dispersion becomes unstable.

Foam formation during CO2 desorption from agitated supersaturated aqueous surfactant solutions

Abstract The behaviour of foams formed during desorption of CO 2 from an agitated supersaturated aqueous surfactant solution was investigated. A model allowing for the interfacial coalescence of gas bubbles is presented which predicts the variation in height of the foam formed during desorption. Experimental data obtained from a 49 mm diameter batch desorber at different initial absorption pressures, in which variation with time in the height of the foam, cumulative volume of desorbed gas and the bubble diameter are measured, demonstrate that the model parameters also describe the foam decay after the completion of gas desorption.

PREDICTION OF VELOCITY PROFILES OF SHEAR THINNING FLUIDS FLOWING IN ELASTIC TUBES

Non-Newtonian fluid flow characteristics in inflatable and collapsible elastic tubes are relevant to bio-fluid mechanics and other applications. The radial velocity profiles in an elastic tube during steady laminar flow of a shear thinning aqueous solution of 1.5% carboxy methyl cellulose (CMC) were investigated using ultrasound Doppler velocimetry. The shear rate–dependent viscosities obtained using a rheometer were well represented by the Carreau model. Measured storage and loss moduli indicated the CMC solution to be inelastic up to 2% concentration. The velocity profiles were predicted by integrating the theoretical equation derived by equating the shear stress along the tube radius involving pressure drop to that of the Carreau model using its parameters. The agreement between predicted and measured velocity profiles was good. The predicted pressure drop is about the same as the experimental value at lower flow rates. In contrast, the measured pressure drop is lower than that predicted at higher flow rates due to inflation of the tube. Good agreement between estimation (Hagen-Poiseuilles law) and measurement (tube shape image analysis) for the detection of elastic tube expansion while increasing flow rates is found.

Use of submerged jets in gas desorption from supersaturated solutions

Abstract The behaviour of foams formed during desorption of CO 2 from batch supersaturated aqueous surfactant solutions is investigated. A model allowing for the interfacial coalescence of gas bubbles is presented which predicts the variation in height of the foam during and after desorption. Desorption of CO 2 is initiated by submerged water and nitrogen jets issuing downwards from a nozzle. Equations are derived for the decrease with time in nozzle upstream pressure and jet velocity for both isothermal and adiabatic gas expansion and are verified with experimental data. For both water and nitrogen gas jets, the volume percentage of CO 2 desorbed is found to increase with the initial nozzle upstream pressure and the average jet velocity until a maximum value is reached. The aqueous surfactant solution is sometimes even subsaturated after the completion of desorption. A minimum jet velocity is required to initiate desorption. For a given initial nozzle upstream pressure, the instantaneous jet velocity is an order of magnitude higher for a gas due to its compressibility than that for a liquid. So a shorter time is required for the desorption of the same volume of CO 2 for a gas jet than for a liquid jet. Decreasing the distance of the nozzle from the bottom of the liquid pool increases the volume of CO 2 desorbed. Equations predicting the variation in height of the foam with time are verified with experimental data.