Dispersed Phase Flow Research Articles

The growth rate of gas hydrate from refrigerant R12

Experimental and theoretical investigations were presented dealing with three phase direct-contact heat transfer by evaporation of refrigerant drops in an immiscible liquid. Refrigerant R12 was used as the dispersed phase, while water and brine were the immiscible continuous phase. A numerical solution is presented to predict the formation rate of gas hydrates in test column. The solution provided an acceptable agreement when compared with experimental results. The gas hydrate growth rate increased with time. It increased with increasing dispersed phase flow rate. The presence of surface-active sodium chloride in water had a strong inhibiting effect on the gas hydrate formation rate.

ポリマー粒子の最前線 マイクロチャンネルを用いた均一径ポリマー微粒子の合成とその用途開発

A new scheme for the polymer beads production using a microfluidic technique is described. This technique is based on the fact that droplets formation at a junction in microchannels is caused by shear stress acting on the dispersed-phase flow by the continuous-phase flow. The Reynolds number in a microchannel was very low which indicated the flow in the microchannel was laminar, therefore, uniform droplet formation was generated. The diameter of the droplets is widely varied from 50% to 300% to the diameter of the dispersed phase flow. Various monomers were used as a dispersed phase, and aqueous solution of polyvinyl alcohol as a continuous phase. Droplets produced in the microchannel were introduced from the drain to the server, and then polymerized by the thermal polymerization method or photo polymerization method. The droplet diameter was monodisperse with CV of less than 5%. Various polymer beads were produced by changing the geometry of the microchannel structure. By using this technique, two colored polymer beads, with different electrical potential for the electronics paper, were produced. We are now approaching to the mass production of the two colored polymer beads which is used for the manufacturing of electronic papers.

Two-way coupling model for shock-induced laminar boundary-layer flows of a dusty gas

The present paper describes a numerical two-way coupling model for shock-induced laminar boundary-layer flows of a dust-laden gas and studies the transverse migration of fine particles under the action of Saffman lift force. The governing equations are formulated in the dilute two-phase continuum framework with consideration of the finiteness of the particle Reynolds and Knudsen numbers. The full Lagrangian method is explored for calculating the dispersed-phase flow fields (including the number density of particles) in the regions of intersecting particle trajectories. The computation results show a significant reaction of the particles on the two-phase boundary-layer structure when the mass loading ratio of particles takes finite values.

Dust-cloud structures behind a shock wave moving over a deposited layer of fine particles*

Abstract The present paper investigates dispersed-phase flow structures of a dust cloud induced by a normal shock wave moving a constant speed over a flat surface deposited with fine particles. In the shock-fitted coordinates, the general equations of dusty-gas boundary layer flows are formulated within the framework of a multi-fluid model and parametic numerical studies of the carrier- and dispersed-phase flow field are performed. The problem associated with crossing particle trajectories and the formation of local particle accumulation regions are solved by using the full Lagrangian method for the dispersed phase. The basic features of the near-wall two-phase flow under consideration including the role of saffman force in the particle entrainment and the development of discontinuities or singularities in the particle density profiles are discussed. The effects associated with account of the non-uniformity of particle size and the finiteness of the particle knudsen numbers are studied in detail

The impact of mass transfer and interfacial expansion rate on droplet size in membrane emulsification processes

In membrane emulsification, especially under conditions where droplets are forming with a narrow droplet size distribution, it is conjectured that the interfacial phenomena are determining the emulsification result. The process parameters of continuous phase flow and dispersed phase flux were analysed from the perspective of how they could be affecting the interfacial tension of the growing droplet. This work first reviews the applicability of current droplet formation models (force balance and spontaneous transformation based (STB)), describes the interfacial transport of surfactant molecules to an expanding oil–water interface, and models the flow of dispersed phase through a pore using MATLAB. The data from these calculations are then applied in a model to predict the final size of the droplets, which includes dynamic effects of mass transfer and expansion rate. The droplet detachment mechanism in membrane emulsification was modelled from the point of view of Gibbs free energy. An interactive finite element program called the surface evolver was used to test the model. A program was written and run in the surface evolver, which allows the user to track the droplet shape as it grows, to identify the point of instability due to free energy, and thus predict the maximum stable volume (MSV) attached to the pore. The final droplet size was found by applying a pressure pinch constraint (PPC), which is based on the division of the surface into two volumes, a droplet and a segment, which remains attached to the pore mouth. The relative size of these two volumes is such that the resulting radii of curvature of the droplet will maintain an equal Laplace pressure across the surface of both volumes. Predicted droplet sizes were compared to experimental data from the literature. It was found that changes in surfactant coverage caused by mass transfer coupled to the expansion rate of the oil–water interface have a significant and predictable effect on the final droplet size in membrane emulsification. The extent of the influence of the dispersed phase flux on dynamic interfacial tension was quantified using a dimensionless parameter, the mass transfer expansion ratio (MER). The MER can be used to predict the effect of increasing the depletion of surfactant on the relative final droplet size in membrane emulsification. This new insight into the role mass transfer and surface expansion play in membrane emulsification allows us to now predict à priori the final droplet size that would form for a particular set of conditions, and can lead to better process design methods in the future.

Lipoxygenase-1 Mass-Transfer Coefficient in Aqueous Two-Phase System Using Spray Extraction Column

Extraction of lipoxygenase-1 was investigated by using the aqueous two-phase system formed by sodium sulfate−poly(ethylene glycol)−buffer. The extraction was performed in a 47-mm inner diameter spray column, operating in a semibatch manner. The effects of dispersed-phase flow rate and phase compositions on fractional dispersed-phase hold up (eD) and volumetric mass-transfer coefficient (KDa) were respectively studied. It was found that the hold-up and volumetric mass-transfer coefficient increased with an increase in dispersed-phase velocity and decreased with increasing phase composition. Correlations have been developed by nonlinear regression for estimation of fractional dispersed-phase hold up and volumetric mass-transfer coefficients.

Hydrodynamic Behavior of a Rotating Disc Contactor Under Low Agitation Conditions

ABSTRACT The hydrodynamics of a rotating disc contactor (76.2 mm diameter, 19 stages, and operating height of 815 mm) has been investigated at limiting operational conditions of low holdup (φ ≤ 3%) and low agitation (Re R ≤ 22,000) for the water/n-heptane system in the absence of mass transfer. Water was chosen as the continuous phase, and it was kept stagnant inside the column. Local drop size distribution, local mean drop diameter, and total holdup have been measured at different flow rates of the dispersed phase (70 to 640 mL/min) and rotor speeds (0 to 700 rpm). Drop size distributions along the column were suitably described using the log-normal probability density function, and empirical expressions were derived to predict the parameters of the distribution curve as a function of operating conditions. An empirical expression was also proposed to predict the Sauter mean drop diameter along the column with a mean deviation of 3.4%. Statistical analysis has revealed no significant effect of the rotor speed on the total holdup, which changed solely with the dispersed phase flow rate for the operating conditions investigated.

Experimental and theoretical approaches on droplet formation from a micrometer screen hole

The droplet formation process from a micrometer screen hole under crossflow conditions was applied to study the droplet behavior in the high-promising processes of micromixing and membrane emulsification. Three working systems with different interfacial tension were used, and the effects of flow rates and interfacial tension on droplet formation were investigated. To elucidate the influence of systems’ properties and flow rates, a theoretical model based on force balance has been developed, in which a parameter of detachment period and a dimensionless number x meaning the drag force torque fraction have been defined to distinguish whether the influence of detachment period should be considered. It was found that the dispersed phase flow rate has little influence on the droplet diameter for the system with large interfacial tension of 51.0 mN/m. And the droplet size can be predicted with the torque balance equation directly. While for the systems with interfacial tension of 1.7 and 8.13 mN/m, respectively, the increase of the dispersed phase flow rate resulted in droplet size increment. Therefore, the effect of detachment period should be considered. Using the theoretical model, the detachment time t d can be fitted as a function of x, and the calculated droplet diameters are in good agreement with the experimental values.

Mass transfer performance and two-phase flow characteristic in membrane dispersion mini-extractor

In this experiment, a new membrane dispersion mini-extractor with a microfiltration membrane as the dispersion media was developed for liquid–liquid extraction processes. The performance of the new extractor was tested in six experimental systems with different dispersed phase media to measure the effects of flow rates on mixing and mass transfer characteristics, as well as the relationship between transmembrane pressure and dispersed phase flow rate. For all systems, the results showed droplet diameter decreasing with an increase of volume flow rate, and higher extraction efficiency due to the increase in specific interfacial area and decrease in diffusion distance. At higher flow rates, the droplet diameter reached a minimum value and the mass transfer efficiency could be as high as 100% with residence time less than 0.2 s. The mini-extractor's capacity reached around 500 m 3/(m 2 h) under the mass transfer efficiency of almost one theory stage. Because of its simple design, low cost production and increased efficiency, the membrane dispersion mini-extractor has potential for widespread industrial extraction process application.

Numerical Modeling of Inhaled Charged Aerosol Deposition in Human Airways

A new numerical modeling of inhaled charge aerosol has been developed based on a modified Weibel's model. Both the velocity profiles (slug and parabolic flows) and the particle distributions (uniform and parabolic distributions) have been considered. Inhaled particles are modeled as a dilute dispersed phase flow in which the particle motion is controlled by fluid force and external forces acting on particles. This numerical study extends the previous numerical studies by considering both space- and image-charge forces. Because of the complex computation of interacting forces due to space-charge effect, the particle-mesh (PM) method is selected to calculate these forces. In the PM technique, the charges of all particles are assigned to the space-charge field mesh, for calculating charge density. The Poisson's equation of the electrostatic potential is then solved, and the electrostatic force acting on individual particle is interpolated. It is assumed that there is no effect of humidity on charged particles. The results show that many significant factors also affect the deposition, such as the volume of particle cloud, the velocity profile and the particle distribution. This study allows a better understanding of electrostatic mechanism of aerosol transport and deposition in human airways.

Trajectories of Charged Drops in a Liquid−Liquid System: The Effect of Geometrical Scale-Up

The work in this paper builds on earlier research, which demonstrated the ability to predict charged drop motion in one-dimension and by using a single contactor geometry. Here we have extended this approach to compare the accuracy of the modeling methods in different sizes of contactor. The liquid-liquid system studied here comprised drops of water dispersed in sunflower oil The predicted drop trajectories are compared with those measured using video photography. Comparisons are presented for three different contactor sizes based on similar rectangular geometry. The largest contactor had dimensions of 100 x 100 mm 2 cross section and a maximum interelectrode distance of 142 mm, the smallest contactor was of 50 x 50 mm 2 cross section with a minimum interelectrode distance of 70 mm. The experimental variables studied included applied voltage, dispersed phase flow rate, interelectrode distance, field polarity, and contactor size. The space charge profiles and the electric field were calculated successfully, and good agreement between the predicted and the experimental trajectories was achieved in all cases. It is concluded that the predictive model can accurately accommodate geometries of different sizes and has the potential as a tool for scale-up design based on small scale experimentation.

Modeling of bubble break-up in stirred tanks

The Lagrangian code LAG3D for dispersed phase flow modeling was implemented with the introduction of bubble break-up model. The research was restricted on bubbles with diameter less than 2 mm, i.e. bubbles which could be treated as spheres. The model was developed according to the approach of Martinez-Bazan model. It was rearranged and adjusted for the use in the particular problem of flow in stirred tanks. Developed model is stochastic one, based on the assumption that shear in the flow induces the break of the bubble. As a dominant parameter a dissipation of the turbulent kinetic energy was used. Computations were performed for two different types of the stirrer: Rushton turbine, and Pitch blade turbine. The geometry of the tank was kept constant (four blades). Two different types of liquids with very big difference in viscosity were used, i.e. silicon oil and dimethylsulfoxide, in order to enable computation of the flow in turbulent regime as well. As a parameter of the flow, the number of rotations of the stirrer was varying. As a result of the computation the fields of velocity of both phases were got, as well as the fields of bubble concentration bubble mean diameter and bubble Sauter diameter. To estimate the influence of the break-up model on the processes in the stirred tank a computations with and without this model were performed and compared. A considerable differences were found not only in the field of bubble diameter, but also in the field of bubble concentration. That confirmed a necessity of the introduction of such model. A comparison with the experiments performed with phase Doppler anemometry technique showed very good agreement in velocity and concentration profiles of the gas phase. The results for the average bubble diameter are qualitatively the same, but in almost all computations about 20% smaller bubble diameter was got than in the measurements.

Quantitative analysis of coupling effects in cross-flow membrane emulsification

Membrane emulsification has attracted increasing experimental and theoretical interests over the last decade. On the experimental side, the parameters of this process have been thoroughly investigated and a linear relationship between the droplet size of an emulsion and the pore size of the membrane has been generally observed. Theoretical studies, however, have not provided an adequate description of many effects concerning droplet growth and detachment from membrane pores, such as the influence of the dynamic interfacial tension on the evolution of the droplet size. Most calculations have been based either on an algebraic torque balance equation or on a differential equation for the disperse phase flow rate through the membrane. The present paper offers a procedure for quantitative analysis which includes both the permeation of the disperse phase through the membrane pores and the mechanism of droplet detachment. The behavior of the droplet size of an emulsion versus the pore size of the membrane is determined with different sets of process parameters and it is compared satisfactorily with the experiments of Vladisavljevic and Schubert on Shirasu porous glass membranes. For the same membranes, the procedure is tested to pore sizes below 0.1 μm and a linear correlation is observed, similarly to micropore sizes.

Numerical analysis of the continuum formulation for the initial evolution of mixing layers with particles

Numerical analysis of the standard continuum description of a dilute dispersed phase as applied to a laminar, particle-laden, mixing layer during its initial evolution has been performed. The flow has been previously analyzed under the framework of linear stability analysis where both the continuous and the dispersed phases are considered as continua. Earlier studies had neglected the closure terms resulting from the averaging of the nonlinear transport term involved in the derivation of the dispersed-phase momentum equations. In this work, Lagrangian particle tracking was coupled to an incompressible Navier–Stokes solver to directly estimate the closure terms (referred to as the averaging-stress terms) and compare them to the other terms balancing the dispersed-phase continuum equations. Calculations were performed for particle Stokes numbers of 1, 10, and 50, and for a mass loading of one. Dispersed-phase flow quantities such as the number density and velocity were determined by averaging the data in the spanwise direction. A parametric study of the influence of the number of particles, for Stokes number of one, showed that an improved approximation to a continuum can be obtained by increasing the number of particles. Examining the momentum balance in detail revealed that the main contributors were the time-derivative, convective, and the interfacial force terms. The averaging stress was at least two orders of magnitude smaller for all the Stokes numbers studied. However, the averaging stress, though negligible in magnitude, showed a deterministic variation in the center of the mixing layer. The results lend support to the currently used continuum equations for analyzing the stability of laminar, particle-laden mixing layers, and possibly other free-shear flows such as jet and wake flows.

Enzyme mass-transfer coefficient in aqueous two-phase systems using static mixer extraction column.

Recent technical advances in aqueous two-phase systems (ATPS) have made this a sound technique for the extraction of biomacromolecules. The extraction of alpha-amylase was investigated using aqueous two-phase systems formed by sodium sulphate-polyethylene glycol (PEG) in water in a 47-mm inner diameter spray column packed with three types of static mixers. The effects of dispersed-phase flow rate, phase composition, column height and diameter were studied. The extraction column was operated in a semi-batch manner. It was found that the hold-up and volumetric mass transfer coefficients increased with an increase in dispersed (PEG-rich) phase velocity and decreased with increasing phase composition. Empirical correlations were developed for fractional dispersed-phase hold-up and volumetric mass transfer coefficients.

Prediction of the Hydrodynamics of Rotating Disc Contactors Based on a New Monte-Carlo Simulation Method for Drop Breakage.

The objective of this study is to develop and evaluate a new Monte-Carlo simulation method to predict the hydrodynamics of rotating disc contactors (RDC) with continuous flows of liquid phases and with drop breakage. This method has the advantage of using individual drops controlled by breakage phenomenological parameters of probability of breakage, number of generated drops and their size distribution. Drop coalescence is ignored due to the very low hold-up and the high interfacial tension of the chemical system. The Monte Carlo stochastic method is applied by using the elements of generated vectors of random numbers having given distribution and with sequences of repeatable or non-repeatble. The limiting values are obtained from correlations that are based on single drop experiments. A stage-wise explicit calculation method with the use of a population balance is employed to follow the steady flow of dispersed phase. The generated results are compared with the experimental results obtained from a pilot RDC and a good agreement is observed. The changes of local hold-up and mean drop size along the column are also described reasonably.

CFD Simulation of Nonideal Dispersed Phase Flow in Stirred Extraction Columns

This paper will focus on hydrodynamic relations arising from single-droplet movement in a rotating disc extraction column (RDC) geometry. These relations can be regarded as the basis for a general estimation strategy for the determination of dispersed-phase flow parameters in connection with droplet population balance modeling. The droplet population balance based modeling of countercurrent liquid-liquid extraction column offers a considerable advance in describing the real droplet swarm behavior. The main problem encountered is the determination of the characteristic droplet model parameters, such as droplet rising velocity, axial backmixing, droplet breakage and droplet coalescence frequencies. The scope of this paper is to estimate fluid and particle residence times and thus the backmixing characteristics.

Development of The Drift-Flux Model for a Multi-Phase Flow Analysis.

A modified drift-flux model is developed for analyses of two dimensional gas-liquid and solid-liquid two-phase flows. The basic idea lies in a hypothesis that as far as the drift velocity is concerned, a dispersed phase wiI1 behave in a modified gravitation or acceleration field g' that includes, among others, the centrifugal acceleration effect due to curvatures of streamlines, without distinction between accelerations due to different forces. Therefore, the terminal velocity of the dispersed phase in the continuous phase can be obtained by simply replacing with g' the gravitation field g in the correlation of the terminal velocity obtained by a simple one dimensional experiment. Two-dimensional numerical analyses based on the drift-flux model were performed to analyze those dispersed phase flow structures in a tank filled with saturated water. By comparing the numerical results with the experimental observation, the validity of the drift-flux model for the case of multi-dimensional multi-phase flows was investigated.

Holdup measurements in a Scheibel column by means of an ultrasonic technique

AbstractAn ultrasonic technique developed by Bonnet and Tavlarides for dispersed phase holdup determination in liquid–liquid contactors has been applied in a 0·10 m diameter Scheibel extraction column. The column consists of three alternate mixing and packing sections of 0·03 and 0·055 m in height, respectively. The packings were built with polypropylene mesh with 96% voidage. The liquid–liquid systems were toluene (dispersed)/water (continuous) and MIBK (dispersed)/water (continuous); the Rushton‐type impellers were operated at 400, 500 and 600 rpm, and with four dispersed and continuous phase flow rates. In one of the mixing chambers two different holdup measuring devices were installed: two ultrasonic transducers and one controlled dispersion sampler. The values of dispersed phase holdup obtained by both methods were compared using statistical methods. It was found that at low agitation and for high interfacial tension, conditions for which the dispersion is not completely uniform, the difference was significant, whereas at high agitation and low interfacial tension the values obtained through both methods were statistically equal. This work demonstrates the applicability of the ultrasonic technique for holdup measurements to Scheibel columns, in which the only technique used so far was sampling. This ultrasonic technique allows us to solve the axial monitoring and control problems of these columns.

Aspects of Drop Behavior in a Rotating Disk Contactor

The motion of single liquid drops in a swarm of other drops in a rotating disk contactor has been observed by employing a (viscous) matched refractive index system (octanol/aqueous sucrose solution). The breakage probabilities of drops in a swarm have been observed and compared with those of single drops. Single drop velocity is different above and below rotors. The ratio of characteristic velocity (over the whole compartment) and terminal velocity at first decreases with increasing continuous-phase viscosity and then increases above 1.0, probably due to shape and drop orientation changes under the influence of agitation. Single drops in a swarm obey slip velocity relationships similar in form to that for the swarm, but the relationship between them is not yet clear. Single drop breakage probability in a swarm decreases as dispersed-phase flow rate increases and continuous-phase flow rate decreases if rotor speed exceeds the critical value for breakage, but the behavior is more complex if this is not the case