Countercurrent gas/liquid flow and mixing: Implications for water disinfection

Experimental and numerical results are presented from investigations into the hydrodynamics of a bench scale bubble column reactor. Countercurrent bubble column reactors are most commonly used in water disinfection for effecting mass transfer of ozone to the aqueous phase. In the reactor column used in this study, gas is introduced at the bottom of the column via a spherical diffuser and water is introduced to the top of the column through a manifold packed with glass spheres. Residence time distribution (RTD) studies were conducted for a range of gas flow rates chosen to span the dispersed flow bubble regime. A multiphase computational fluid dynamics (CFD) model was used to simulate the flow in the bubble column and to gain insights into the fluid dynamics of countercurrent flow bubble columns. The CFD model accurately predicted trends in mixing. Use of CFD in bubble column design and scale-up thus may yield better designs than those based on empirical relations.     

Similarity solutions for immiscible phase migration in porous media: an analysis of free boundaries

A fuel pollutant migrating in a water flow throughout a porous medium is distributed between the moving (continuous) and residual (discontinuous) phases. Usually, there is an equilibrium condition between these phases. In this study, the migration of a fuel slug confied within free boundaries moving in the porous medium is considered. This type of fuel migration pertains to circumstances in which convective fuel transport dominates fuel dispersion when fuel saturation approaches zero. A one-dimensional self-similar model is developed, describing the movement of fuel saturation fronts in a porous medium against and with the water flow direction. Several analytical solutions are found revealing the effects of the pore size, fuel viscosity, fuel mass, and the capillary number on the fuel migration in the porous medium.     

Dispersion of multi-walled carbon nanotubes in PDMS/PB blend

In this study, the sequential dispersion of multi-walled carbon nanotubes (CNTs) in PDMS/PB (polydimethylsiloxane/polybutene) blends and the change of blend morphology by the dispersion of CNTs were investigated by rheological and morphological observations. The dispersion of CNTs into PDMS/PB blend was accomplished by the dilution of the CNT master (2?wt.% CNT in PDMS) in PDMS/PB blend using an extensional mixer. The morphological study shows that under the extensional flow, CNTs in the dispersed CNT master phase are mainly broken up by tip-streaming and the continuous pinching-off of PDMS drops during morphology evolution enhances the dispersion of CNT. It has been shown that CNTs can be disentangled as in the case of dispersing CNTs in a Boger fluid. Rheological data and TEM observations show that it is not simply a mixing of two phases and the CNTs in the master phase can be dispersed in the single CNT level.     

On the use of conventional cocurrent and countercurrent effective permeabilities to estimate the four generalized permeability coefficients which arise in coupled,two-phase flow

In the case of coupled, two-phase flow of fluids in porous media, the governing equations show that there are four independent generalized permeability coefficients which have to be measured separately. In order to specify these four coefficients at a specific saturation, it is necessary to conduct two types of flow experiments. The two types of flow experiments used in this study are cocurrent and countercurrent, steady-state permeability experiments. It is shown that, by taking this approach, it is possible to define the four generalized permeability coefficients in terms of the conventional cocurrent and countercurrent effective permeabilities for each phase. It is demonstrated that a given generalized phase permeability falls about midway between the conventional, cocurrent effective permeability for that phase, and that for the countercurrent flow of the same phase. Moreover, it is suggested that the conventional effective permeability for a given phase can be interpreted as arising out of the effects of two types of viscous drag: that due to the flow of a given phase over the solid surfaces in the porous medium and that due to momentum transfer across the phase 1-phase 2 interfaces in the porous medium. The magnitude of the viscous coupling is significant, contributing at least 15% to the total conventional cocurrent effective permeability for both phases. Finally, it is shown that the nontraditional generalized permeabilities which arise out of viscous coupling effects cannot equal one another, even when the viscosity ratio is unity and the surface tension is zero.     

The Role of Capillarity in Two-Phase Flow through Porous Media

When determining experimentally relative permeability and capillary pressure as a function of saturation, a self-consistent system of macroscopic equations, that includes Leverett's equation for capillary pressure, is required. In this technical note, such a system of equations, together with the conditions under which the equations apply, is formulated. With the aid of this system of equations, it is shown that, at the inlet boundary of a vertically oriented porous medium, static conditions pertain, and that potentials, because of the definition of potential, are equal in magnitude to pressures. Consequently, Leverett's equation is valid at the inlet boundary of the porous medium, provided cocurrent flow, or gravity-driven, countercurrent flow is taking place, and provided the porous medium is homogeneous. Moreover, it is demonstrated that Leverett's equation is valid for flow along the length of a vertically oriented porous medium, provided cocurrent flow, or gravity-driven, countercurrent flow is taking place, and provided the porous medium is homogeneous and there are no hydrodynamic effects. However, Leverett's equation is invalid for horizontal, steady-state, forced, countercurrent flow. When such flow is taking place, it is the sum of the pressures, and not the difference in pressures, which is related to capillary pressure.     

A CLOSED SYSTEM OF EQUATIONS FOR DENSE TWO-PHASE FLOW AND EXPRESSIONS OF SHEARING STRESS OF DISPERSED PHA’E AT A WALL

In this paper, each of the two phases in dense two-phase flow is considered as continuous medium and the fundamental equations for two-phase flow are described in Eulerian form. The generalized constitutive relation of the Bingham fluid is applied to the dispersed phase with the analysis of physical mechanism of dense two-phase flow. The shearing stress of dispersed phase at a wall is used to give a boundary condition. Then a mathematical model for dense two-phase flow is obtained. In addition, the expressions of shearing stress of dispersed phase at a wall is derived according to the fundamental model of the factional collision between dispersed-phase particles and the wall.     

Mathematical model of convective heat transfer between flows of finely dispersed media in adjacent channels with permeable walls

The discussion is concerned with a mathematical model for convective heat transfer between the flows of finely dispersed media moving in adjacent channels separated by a permeable wall where portions of the fluid phases are exchanged many times between the flows. Numerical solutions are given for a countercurrent flow of a suspension and a liquid. Equations are derived and curves constructed to show the distribution of the flow velocity and the suspension porosity along the length of the channels as well as the dependence on time of the temperatures of the flows.     

Slip ratio in dispersed viscous oil-water pipe flow

In this article, dispersed flow of viscous oil and water is investigated. The experimental work was performed in a 26.2-mm-i.d. 12-m-long horizontal glass pipe using water and oil (viscosity of 100 mPa s and density of 860 kg/m³) as test fluids. High-speed video recording and a new wire-mesh sensor based on capacitance (permittivity) measurements were used to characterize the flow. Furthermore, holdup data were obtained using quick-closing-valves technique (QCV). An interesting finding was the oil-water slip ratio greater than one for dispersed flow at high Reynolds number. Chordal phase fraction distribution diagrams and images of the holdup distribution over the pipe cross-section obtained via wire-mesh sensor indicated a significant amount of water near to the pipe wall for the three different dispersed flow patterns identified in this study: oil-in-water homogeneous dispersion (o/w H), oil-in-water non-homogeneous dispersion (o/w NH) and Dual continuous (Do/w & Dw/o). The phase slip might be explained by the existence of a water film surrounding the homogeneous mixture of oil-in-water in a hidrofilic-oilfobic pipe.     

多孔介质在压力梯度作用下的热质耦合数值模拟

多孔介质干燥导致热质耦合传输过程。本文基于连续介质力学的宏观尺度,对多孔介质的热、湿和气三者耦合迁移进行数值模拟,研究压力梯度对热质传输的影响。多孔介质传质机理主要为水汽和空气的对流和扩散传输、吸附水在含湿量梯度作用下的自由扩散和其在温度梯度即Soret效应驱动下的流动。采用Galerkin加权余量的有限元方法,提出了...     

Heat and mass transfer in a dispersive medium

Macroscopic equations for the conservation of heat (or the mass of a diffusing impurity) in a continuous medium containing distributed particles of a dispersed phase are formulated neglecting the effect of random fluctuations of the medium and particles by the transfer process. The problem of convective heat conduction or diffusion near an isolated particle is also formulated, the solution of which permits calculation of all the parameters entering into the indicated equations. This problem has been solved in the particular case of small Peclet numbers, which characterize heat and mass exchange in the vicinity of a single particle.     

Physical approach to averaging theorems on phase interfaces in a dispersed multiphase medium

Within the framework of a procedure for scale-changing by averaging a representative elementary volume, theorems are developed to relate the averages of derivatives to the derivatives of averages over a surface, using elementary differential calculus. These theorems form the basis of a general macroscopic balance equation for a given quantity over interfaces of a dispersed multiphase medium. The equations of phase interfaces complement equations related to bulk phases describing transport in dispersed multiphase media.     

Stability of a stationary steam-water front in a porous medium

The instability of a plane front between two phases of the same fluid (steam and water) in a porous medium is considered. The configuration is taken to be initially stationary with the more dense phase overlying the less dense phase. The frontal region is assumed sharp, so that macroscopic boundary conditions can be utilized. This assumption precludes the existence of dispersion instabilities. The stabilizing influence of phrase transition as well as the implication of different macroscopic pressure boundary conditions on the stability of the front are discussed and illustrated.     

Analyzing and modeling the dynamic thermal behaviors of direct contact condensers packed with PCM spheres

Condensers serve as important components for humidification–dehumidification (HDH) desalination plants. Based on the interpenetration continua approach with volume averaging technique, a mathematical dynamic model for analyzing the heat and mass transfer within direct contact condensers with co-current or countercurrent flow arrangement was developed. It was validated against the experimental data from a small scale HDH desalination system. Comparisons including the productivities and the temperature profiles of gas, liquid, and solid phases show good agreement with the measurements. Phase change material (PCM) melting processes have little effect on water production rate for co-current flow arrangement, but the condenser packed with PCM capsules have higher water production rates than that packed with air capsules packed under given conditions. The relative humidity profile of the bulk gas shows contrary trend with the gas temperature profile. The direct contact condenser with countercurrent flow arrangement can provide much better heat and mass transfer between gas and water and produce about 16.3% more fresh water than the same condenser with co-current flow arrangement in 4 h under given conditions.     

Numerical simulation of fluid–particle hydrodynamics in a rectangular spouted vessel

A three-dimensional, Eulerian simulation was developed to describe isothermal, two-phase flow of the continuous (water) and dispersed (solid particles) phases in a rectangular spouted vessel. The mass and momentum conservation equations for each phase were solved using the finite volume technique, which treats each phase separately, while coupling them through drag, turbulence, and energy dissipation due to particle fluctuations. Particle–particle interactions via friction were also included.     

Water in water emulsions: phase separation and rheology of biopolymer solutions

Partially miscible polymers in solution do not separate into two macroscopic phases; in general they behave as viscoelastic fluids containing droplets of the minority phase dispersed into a continuous majority phase (emulsion type systems). Both phases contain two types of polymers and solvent in variable amounts. With time, the smaller droplets tend to merge into larger ones and eventually sediment. Provided the time stability of the emulsion is long enough and the size of the droplets does not exceed a few tens of microns, the emulsion can be characterized by conventional rheological methods as an effective medium, both in the linear regime (viscoelasticity) and under flow. We investigated a ternary system composed by two biopolymers, a protein (caseinate) and a polysaccharide (alginate) in aqueous solution and established an analogy between these phase separated solutions and immiscible blends of polymers. We first characterized the biopolymers and determined the phase diagram at room temperature that we interpreted within the framework of the Edmond and Ogston model. For the rheological investigations, starting with an initial composition of the system, we separated the two phases by centrifugation. The individual phases were then characterized through their viscoelastic and flow behaviors. By recombining variable amounts of these phases, thereby varying only their volume fractions, we were able to prepare stable emulsions with constituents having constant compositions. The effect of shear on these emulsions was investigated. After different shearing protocols, the size of the droplets was derived from the Palierne model and the flow curves were analyzed. The droplet sizes were compared to the critical capillary numbers and coalescence predictions. The flow curves and the dynamic viscosities of the emulsions were interpreted with a model recently proposed by Kroy et al. that extends earlier work of Oldroyd (1953), Schowalter et al. (1968), and Frankel and Acrivos (1970). Received: 11 September 2000/Accepted: 21 December 2000     

Two-phase pressure drop and flooding characteristics in a horizontal-vertical pulsed sieve-plate column

In this paper, an experimental investigation on the two-phase pressure drop has been carried out in a novel class of extractors entitled "horizontal-vertical pulsed sieve-plate column". The liquid-liquid systems used in this work are toluene–water, n-butyl acetate–water and butanol-water. The effects of operating parameters including the dispersed and continuous phases flow rates and pulsation intensity on total pressure drop under and at the flooding points have been studied. It is achieved that the pressure drop is strongly affected by the continuous and dispersed flow rates as well as pulsation intensity. In fact, the column experiences higher pressure drop with an increase in the values of Af, Q _c and Q _d. The interfacial tension is a physical property which has significant impact on pressure drop. Two theoretical-experimental correlations for prediction of pressure drop under and at the flooding in the column, and one correlation for maximum throughput are proposed by using dimensional analysis method with Average Absolute Relative Error (AARE) values of 2.15%, 3.56 and 6.85% respectively. Moreover, a particular approach for preventing flooding in pulsed extraction columns is developed based on evaluation of pressure drop through the column length.     

Numerical Simulation of Particle Dispersion in a Spatially Developing Mixing Layer

Although there have been several numerical studies on particle dispersion in mixing layers, most of them have been conducted for temporally evolving mixing layers. In this study, numerical simulations of a spatially developing mixing layer are performed to investigate particle dispersion under various conditions. The full compressible Navier--Stokes equations are solved with a high-order compact finite difference scheme, along with high-order time-integration. Accurate non-reflecting boundary conditions for the fluid flow are used, and several methods for introducing particles into the computational domain are tested. The particles are traced using a Lagrangian approach assuming one-way coupling between the continuous and the dispersed phases. The study focuses on the roles of the large-scale vortex structures in particle dispersion at low, medium and high Stokes numbers, which highlights the important effects of interacting vortex structures in nearby regions in the spatially developing mixing layer. The effects of particles with randomly distributed sizes (or Stokes numbers) are also investigated. Both instantaneous flow fields and statistical quantities are analyzed, which reveals essential features of particle dispersion in spatially developing free shear flows, which are different from those observed in temporally developing flows. The inclusion of the gravity not only modifies the overall dispersion patterns, but also enhances stream-crossing by particles. Received 7 June 2001 and accepted 19 February 2002     

Effects of a countercurrent gas flow on falling-film mode transitions between horizontal tubes

A liquid film falling between horizontal tubes is known to take the form of droplets, jets or sheets, depending on the liquid flow rate; the form of the flow is the so-called “falling-film mode”. Although previously neglected in studies of mode transition, a countercurrent gas flow often exists in falling-film heat exchangers, and its effect on the liquid flow might be important: it could impact the flow regime, lead to local “dryout,” and decrease the heat transfer rate. Experiments are conducted to explore the effects of a countercurrent gas flow and liquid feeding length on falling-film mode transitions for a liquid flowing over horizontal tubes. The effects on mode transition are shown to depend on fluid properties and are explained in terms of unsteadiness and film thickness. In general, transition hysteresis is reduced with an increasing gas velocity. A correlation is developed to predict the countercurrent gas flow effects on falling-film mode transitions. The liquid feeding length can affect mode transitions in quiescent surroundings and when a countercurrent gas flow imposed.     

Viscosity of the liquid phase in a dispersion

The motion of a dispersion (continuous medium and particles) may be described [1] via the equations ot conservation of matter and momentum for the two phases separately. Here it is necessary to know how the viscosity, pressure in the solid, and other quantities vary with the parameters of the motion. This difficulty occurs even for the very simple model where the internal stresses in the dispersed phase are taken as zero, as there is then an uncertainty as to the viscosity of the medium, which is not a material constant and is dependent on the concentration. There is also uncertainty as to the forces of interaction between the phases. There are numerous empirical relationships for these forces, and also a theoretical one [2]. Here an analogous method is applied to derive an expression for the viscosity of the liquid. This viscosity applies to a liquid filtering through a porous medium in the particular case where the concentration is such as to produce close packing of the solid particles. The result corresponds to standard formulas in the case of low concentrations.