A.J. Karabelas

A conductance probe for measuring liquid fraction in pipes and packed beds

Al~tract--The performance of ring electrodes measuring the conductance of gas--liquid mixtures in pipes and packed beds is studied experimentally and theoretically. With relatively closely spaced pairs of rings, one can detect liquid segregation, i.e. stratified and annular distribution, as well as a uniform liquid distribution if the mean liquid fraction is available. Conversely, reliable cross-sectionally-averaged holdup data can be obtained if the liquid distribution pattern is known. Measurements in packed beds and pipes are qualitatively very similar. Existing theoretical expressions are employed to interpret the conductance measurements. Moreover, a new analytical solution for an annular liquid distribution is presented, which is particularly helpful in assessing the spatial probe sensitivity in the axial direction. The latter is found to be quite satisfactory. In general, agreement between the data and theoretical predictions is fair to excellent, providing the necessary confidence for practical applications. Two successful applications of the technique to packed beds are reported.

STATISTICAL CHARACTERISTICS OF FREE FALLING FILMS AT HIGH REYNOLDS NUMBERS

Abstract The characteristics of films flowing inside a vertical pipe are studied experimentally. Using an accurate wire conductance technique the film thickness is measured over the Re range 509–13,090. The mean film thickness data are in good overall agreement with established relations. Extensive statistical analysis shows that film thickness fluctuations have a stochastic character. The description given by Dukler and co-workers, of a relatively well-defined substrate in between the large waves, is confirmed up to Re ≈ 7000. At higher Re the substrate tends to lose its identity, due to amplification of the small waves on its surface. Moreover, data on standard deviation, h max and h min indicate that at Re > 5000 the amplification of large waves essentially stops, and that the substrate thickness tends to increase. The calculated probability density functions of film thickness, the spectral density functions, the skewness and kurtosis provide new reliable information for the statistical description of film thickness fluctuations. Finally, by identifying the wave peaks it is found that the total number of waves is nearly constant, in the range of Re studied, and that the distribution of wave peaks becomes bimodal at Re ≳ 4000.

On the steady-state size distribution of dispersions in breakage processes

Breakage processes are considered in the absence of agglomeration or coagulation. A new method is proposed, based on a population balance type of formulation, applicable to systems (such as dispersions) that may be characterized by a maximum stable particle size. In this method, considerable simplification is achieved by means of a transformation that effectively eliminates the breakage frequency, thus allowing the convenient computation of steady state through solution of an integral equation. To compute the steady state, apart from the maximum size and the breakage kernel, only an estimate of the initial distribution is required. Two functional forms of binary breakage kernels which can represent a large variety of possible breakage mechanisms are proposed (by an appropriate selection of parameter values). For the sake of completeness, analytical solutions are also presented for several, relatively simple kernels. Finally, a study is made to assess the influence of initial conditions on the steady-state size distribution, which is helpful in tackling the inverse problem of determining the breakage kernel using limited experimental data.

Deposition of micron-sized particles on flat surfaces: effects of hydrodynamic and physicochemical conditions on particle attachment efficiency

An experimental study of micron-sized particle deposition on flat surfaces is presented, aimed at delineating the effects of hydrodynamic and physicochemical interactions on particle transport and attachment efficiency, and at obtaining a better understanding of the particle sticking probability, a concept employed in modelling particulate fouling of industrial heat exchangers. Dilute particle suspensions are employed in a parallel-plate-laminar-flow channel, and hydrodynamic and physicochemical conditions are systematically varied. Deposition rates are determined by optical microscopy and image analysis techniques. It is observed that if gravity forces are present (in a horizontal channel) they control deposition at low wall shear stresses. As the hydrodynamic wall shear stress increases particle deposition rates are significantly reduced due to the effect of hydrodynamic lift or drag forces inhibiting transport or attachment. In general, for hydrodynamic conditions similar to those encountered in industrial heat exchangers, it appears that the particle sticking probability is significantly lower than unity.

An assessment of the Silt Density Index based on RO membrane colloidal fouling experiments with iron oxide particles

Abstract RO membrane colloidal fouling experiments were performed in the laboratory under well controlled and realistic conditions. Iron oxide was selected as a typical inorganic colloidal foulant, due to its importance, as evidenced from well known manufacturer recommendations on iron concentrations in feed waters and from frequently encountered problems in membrane installations. A range of iron concentrations was identified where a linear relationship existed between flux reduction rate and concentration. The performance of the Silt Density Index (SDI) was tested on the basis of the RO fouling data obtained. The range of iron concentrations where measurable and meaningful SDI values could be obtained was remarkably close to membrane manufacturer recommendations. A notable sensitivity of the SDI was also observed with particles for which retention is negligible. However, on the basis of the RO fouling data obtained, it appears that the SDI is not conservative enough. Furthermore, since the SDI cannot predict fouling rates, it cannot discriminate between different types of membranes.

An assessment of low-order methods for solving the breakage equation

The population balance is a necessary vehicle for modeling processes that involve size reduction due to fragmentation (grinding) of solid particles. The online control and optimization of such processes require efficient algorithms for the numerical solution of the breakage equation. However, the plethora of available methods, relying on discretization of the integrodifferential breakage equation, is characterized by computational inefficiency in tackling complicated spatially dependent problems. For such cases, the method of moments, which transforms the continuous breakage equation to one with a few degrees of freedom, seems to be advantageous. The accuracy of several versions of the method of moments is examined in the present work by comparing them with analytical solutions of the breakage equation for typical cases. The results of this work allow the selection of the best method for a particular problem and the a priori estimation of the error associated with the use of a specific method. Finally, by revealing the weaknesses of the existing methods, the present results set the basis for pursuing improvements.

Longitudinal characteristics of wavy falling films

New data are presented on film thickness characteristics, over the Reynolds number range 370–11,020, and relatively long distances from liquid entry; i.e. 1.7–2.46 m. The mean film thickness δmean does not show a definite trend remaining roughly constant, while δmin has a tendency to slightly increase. Other quantities such as the standard deviation s, δmax and dominant wave velocity Vwave display a weak tendency to increase with longitudinal distance. This small variation of the aforementioned quantities suggests that the flow may not be fully developed, over the distances examined.

Calcium carbonate scaling in a plate heat exchanger in the presence of particles

Scale formation of CaCO3 in a plate heat exchanger is investigated in the presence of various types of added particles under isothermal conditions. The parameters examined include the degree of supersaturation, the type of particles, the flow velocity, the particle concentration and the direction of flow inside the heat exchanger. The key result of this work is the strong synergistic effect of fine aragonite particles on the deposition rate and the morphology of the deposits. On the contrary, the presence of fine titanium oxide and of relatively large calcite particles does not seem to affect the main scaling characteristics of CaCO3. � 2003 Elsevier Ltd. All rights reserved.

An investigation of liquid maldistribution in trickle beds

The influence of liquid maldistribution at the top of the packing on flow characteristics in packed beds of gas and liquid cocurrent downflow (trickle beds) is experimentally investigated. Particular attention is paid to the effect of gas and liquid flow rates on flow development. Tests are made in the trickling and pulsing flow regimes. A uniform, a half-blocked and a quarter-blocked liquid distributor is tested. Packings of various sizes and shapes are employed. Data are presented on pressure drop and liquid holdup as well as trickling to pulsing flow transition. Diagnosis of radial and axial liquid distribution is made by means of conductance probes. The effects of liquid foaming, bed pre-wetting, top-bed material, and blockage midway the bed on liquid distribution are also examined. Overall, liquid waves in the pulsing flow regime have a beneficial effect, promoting uniform liquid distribution in the bed cross section.

Progress towards modelling the CdS chemical bath deposition process

Progress is reported towards the development of a comprehensive model useful in process design and optimisation of CdS thin-film growth. Model equations are developed for the temporal variation of reactants concentrations as well as of the precipitating solid phase, both in the bulk and on the substrate. A combination of possible elementary mechanisms is employed and the resulting system of equations is solved numerically. Computational results show that the model is consistent with available experimental data, on film thickness evolution, suggesting that it may prove very useful for optimising the CBD process with respect to its design variables. To conclude the presentation, some aspects of the deposit morphology at the early stages of its growth are discussed. It appears that these first stages determine the properties of the final film.