Enhancement of laminar mixing by optimal control methods

Calculus of variations is applied to the problem of optimal mixing of two immiscible fluids in a laminar flow where stretching of the interface between the liquids is treated as an objective function. Under the action of an optimal control, the system behaves like that driven by a negative surface tension, i.e., an initially flat interface evolves in long tongues that are stretched and twisted by the flow. The method was tested for mixing by Stokes flow in lid-driven two-dimensional rectangular cavity.     

微通道中气体/离子液体两相流动与分散性能

离子液体在气-液反应与分离过程中有良好的应用前景,研究气体/离子液体两相体系的微分散过程对于发展新型气-液分散技术和设备具有重要意义。研究了N₂/[Bmim]BF₄体系在同轴环管微通道中的流动和分散行为。实验结果表明,在不同的气相和液相流速下,N₂/[Bmim]BF₄体系分别呈现气泡流、气泡-气柱过渡流、气柱流和气柱-环隙流过渡流4种流型。通过考察分散相尖端尺寸和气相、液相流速对气-液体系流型的影响,作出了相应的流型图。通过考察气相、液相流速对稳定气-液分散流型下的气相分散尺寸的影响,揭示了分散气相行为的机理,并建立了描述气相分散尺寸的数学模型。     

Dispersed plug flow model for steady-state laminar flow in a tube with a first order sink at the wall

Steady state, laminar flow transport in a tube with a first order sink at the wall involves two dimensions—radial and axial. In this paper, a novel iterative technique has been proposed for reducing such a two-dimensional model to an equivalent one-dimensional dispersed plug flow model. The latter yields an analytical expression for the equivalent axial dispersion and a simple, closed form, but approximate, analytical solution of the original two-dimensional problem. The operating range in which this analytical solution is useful has been investigated for a system with mass transfer at the wall.     

Uniform flux heat transfer in concentric laminar flow of two immiscible liquids

The energy equation was solved exactly for fully developed steady laminar flow in a circular pipe of two immncible Newton liquids with a concentric cylindrical interface between them, assuming invariant physical properties of the liquids, uniform heat flux at the wall and fully developed temperature profiles. It is shown that, even if the viscosity of the annular liquid is orders of magnitude smaller than that of the core liquid, the improvement in heat transfer to the core liquid by infection of the annular liquid cannot exceed a factor of 1 8     

Residence time distribution of the liquid in two-phase cocurrent downflow in packed beds: Air/newtonian and non-newtonian liquid systems

New data on the liquid residence time distribution for two-phase downflow of air-Newtonian and non-Newtonian liquids through packed beds of porous and non-porous particles are presented. The piston-dispersion-exchange model is used to describe the liquid flow. With porous particles the dynamic evolution of the tracer concentration in the particles is described in terms of diffusion phenomena. The axial dispersion is very important in the case of two-phase downflow of air-water (trickle flow regime) and air-CMC systems through fixed beds with porous particles, and is negligible in the case of non-porous particles. With the porous particles, a key value is the effective diffusion coefficient of the tracer in the pores of the particles.     

Optimization of fluid dynamics for maximum fouling prevention

Experimental results with ultrafiltration of coloured solutions show, as a general rule, that “quo;gel formation”quo; develops as stripes in the flow direction on flat sheet membranes.

However, secondary flows in the bulk fluid cannot be detected with the experimental accuracy possible in Newtonian liquids.

An attempt to explain the phenomena important to ultrafiltration in laminar flow is made by theories explaining the phenomena by instability in the boundary layer at the membrane surface.     

两种混合模式下PS-MAMA微量组分在聚合物熔体中的分散

通过苯乙烯(St) 和3-异丙烯基-α,α-二甲基苄基异氰酸酯(TMI) 共聚制备了共聚物P(St-co-TMI),然后与9-(N-甲氨基甲基)蒽(MAMA)反应合成了具有示踪特性的聚苯乙烯大分子示踪剂(PS-MAMA)。采用PS-MAMA作为微量组分,在自制的间歇混合器中考察了两种混合模式下其在聚苯乙烯(PS)和聚甲基丙烯酸甲酯(PMMA)中的分散行为。结果表明:对于左右两个转子同时异向转动的匀速混合模式,虽然可以在较短时间内使微量组分在转子壁面和混合腔体内壁之间形成稳定的层状分布,但是随着混合时间的延长,层与层之间的混合较慢;而对于交替异向转动的方波混合模式,尽管在混合初期,层内和层间的浓度分布都不均匀,但是流场的交替变化加快了微量组分PS-MAMA 在聚合物熔体中的分散。因此,方波混合模式的混合效果要优于匀速混合模式的。     

INTERFACIAL TRANSPORT OF ENERGY IN LAMINAR OPEN CHANNEL AND FILM FLOWS

A new dispersion theory applicable to interfacial transport is used to analyze unsteady two-dimensional thermal pollution in laminar open channel and film flows. A strip source across the width of the flow at a variable depth is considered. The unsteady state temperature distribution depends on three time variable coefficients which are the convection, dispersion and exchange coefficients and expressions for these coefficients are derived from first principles. The exchange coefficient in the theory depends on time, the thickness and position of the source and the interfacial transport rate. Furthermore, the convection and the dispersion coefficients are affected substantially by interphase transport. The results, which are relevant to reactor design and such separation processes as chromatography, are discussed in physical terms and are compared to those for laminar flow in tubes. The theory can be applied readily to turbulent flow systems but computing the coefficients is a more formidable job.     

INTERFACIAL TRANSPORT OF ENERGY IN LAMINAR OPEN CHANNEL AND FILM FLOWS

A new dispersion theory applicable to interfacial transport is used to analyze unsteady two-dimensional thermal pollution in laminar open channel and film flows. A strip source across the width of the flow at a variable depth is considered. The unsteady state temperature distribution depends on three time variable coefficients which are the convection, dispersion and exchange coefficients and expressions for these coefficients are derived from first principles. The exchange coefficient in the theory depends on time, the thickness and position of the source and the interfacial transport rate. Furthermore, the convection and the dispersion coefficients are affected substantially by interphase transport. The results, which are relevant to reactor design and such separation processes as chromatography, are discussed in physical terms and are compared to those for laminar flow in tubes. The theory can be applied readily to turbulent flow systems but computing the coefficients is a more formidable job.     

THEORETICAL PREDICTION OF GAS HOLDUP IN BUBBLE COLUMNS WITH NEWTONIAN AND NON-NEWTONIAN LIQUIDS

A simple model based on an energy balance which takes into account the friction losses at the gas-liquid interface and the slip velocity of single bubble is used to simulate the gas holdup in bubble columns containing Newtonian and non-Newtonian liquids which circulate in both laminar and turbulent flows. Experimental data available from the literature for bubble columns up to 7 m height and 1 m diameter with water and glycerol as Newtonian liquids and different solutions of CMC in a wide range of concentrations as non-Newtonian liquids are simulated with good agreement despite the simplifications made to describe the gas liquid flow regimes. Most of the differences between experimental and calculated gas holdup are justified on the basis of the simplifying assumptions.     

Taylor dispersion in fluidized channel flow

Taylor dispersion coefficients (D_t) were determined as a function of flow velocity ?u for flow of fluidized solids in a rectangular-sectioned channel under various conditions. Log—log plots of (D_t ?l D) versus ?u were found to be linear, as is the case for liquids in both turbulent and laminar flow. The experimental plots were compared with calculated values, based on solutions of the differential equations governing transport and mixing in the wake and emulsion phases, respectively. The calculated values were found to be reasonably consistent with the experimental data. It was concluded that mixing due to spreading of bubble wakes at the surface of the fluidized solids was a relatively unimportant lateral mixing mechanism.     

Residence Time Distribution of a Capillary Microreactor Used for Pharmaceutical Synthesis

The main drivers for application of small-scale reactors in the pharmaceutical industry are the possibility of rapid synthesis and screening of novel drugs as well as the readiness of the scale-up. The characterization of fluid flow pattern was performed through step-up and step-down residence time distribution experiments using a tracer at six different flow rates. Four single-parameter models were considered for representing deviations from ideal plug flow and ideal laminar flow in tubes. The model that provided the best results was the axial dispersion model and the Peclet and Reynolds numbers could be well correlated. Obtained Peclet values from 44 to 244 were close to Pe > 100, in which axial dispersion can be neglected and the reactor can be considered as plug flow reactor.     

NMR imaging of mass transport processes and catalytic reactions

NMR imaging and spectroscopy techniques are applied to study flow and filtration of liquids, gases and granular solids in various geometries and to the in situ studies of the interplay of mass transport and catalytic reactions in porous media. In particular, quantitative spatially resolved maps of flow velocities of liquids and gases in the channels of monoliths have been obtained. A comparative study of the filtration of water and propane through model porous media has revealed that the dispersion coefficients for water are dominated by the holdup effects even in a bed of nonporous glass beads. Similar experiments performed with the gravity driven flow of liquid-containing fine solid particles through a porous bed have yielded the distributions of particle velocities for various flow rates. The NMR imaging technique was employed to visualize the propagation of autocatalytic waves for the Belousov–Zhabotinsky reaction carried out in a model porous medium. It was demonstrated that the wave propagation velocity decreases as the wave crosses the boundary between the bulk liquid and the flooded bead pack. The images detected during the catalytic hydrogenation of -methylstyrene on a single catalyst pellet at elevated temperatures have revealed that the reaction and the accompanying phase transition alter the distribution of the liquid phase within the pellet.     

A reduced‐order model for chemical species transport in a tube with a constant wall concentration

A two‐dimensional advection‐diffusion model accompanied with a parabolic velocity profile of Poiseuille flow is considered for the chemical species transport in a tube with a constant wall concentration. The Reynolds decomposition technique is applied to reduce it to an equivalent one‐dimensional model for advective‐dispersive transport in a tube through which the effective advection coefficient, the dispersion coefficient, and the effective Sherwood number are developed for the problem under study. The derived and the classical Taylor models are also compared in order to find the difference between the two arrangements. The reduced‐order model for the transport equation shows that the effective advection coefficient increases, whereas the dispersion coefficient in the tube decreases as compared to the classical Taylor equation. The effective Sherwood number for the steady state form of the developed model is found to be only a function of the Peclet number, which varies in the range of 3.215 ≤ Sh ≤ 4. These results find application in design of experiments and improve our understanding of mass transfer in microfluidic devices.     

Particle velocity in a stratified two-phase flow between inclined parallel plates

Fundamental investigations of coalescence processes in settlers with plate packages for the separation of liquid-liquid dispersions prompted an analysis of the drop motion on the interface of a stratified two-phase flow. Therefore, a physical model was developed, which permits the calculation of drop velocity along the interface of an inclined trickling film. Starting from a balance of forces around a single particle, the model provides the equation of motion for a steady motion of single particles in a stratified two-phase flow. Several assumptions and considerations were necessary to solve this equation, such as taking into account the influence of the wall and of flow resistance. The model calculation assumes Newtonian liquids and laminar, smooth trickling films. A comparison with experimental results confirms that the drop motion behaviour is well reproduced.     

Tracer Dispersion in Stirred Tank Reactors: Asymptotic Properties and Mixing Characterization

This article addresses the characterization of dispersion and homogenization phenomena in stirred vessels through the analysis of dispersion curves that can be obtained experimentally by means of conductivity measurements. New insights on mixing conditions can be achieved from the analysis of the qualitative and asymptotic properties of tracer dispersion curves. The results obtained are interpreted in the context of the spectral approach to the advection‐diffusion equation. It is shown that any flow model aimed at reproducing the experimentally determined dispersion curves must be at least two‐dimensional. Convection‐enhanced dispersion associated with the spectral structure of the advection‐diffusion equation is addressed.     

Gas/liquid dispersions with a SMX static mixer in the laminar regime

A Sulzer SMX mixer was used to disperse gas into viscous, Newtonian and non-Newtonian fluids. The investigation covered the effect of the dispersed phase volume fraction, the viscosity of the continuous phase, the mixer length and the power draw. The flow regime was kept laminar in all the experiments. The dispersion of gas was carried out with gas concentrations between 1% and 7% in volume. Using the “process viscosity” concept, it was possible to collapse all the measured sizes on a single master curve by using the energy consumption in the mixer as the common variable between the experiments. Comparison was made with a Kenics mixer. The SMX mixer was found to be better adapted to the dispersion task due to its internal structure.     

复色多相聚合物/ 油/ 水分散体系的悬浮稳定性及分散稳定性

采用Ｓｔｏｋｅｓ落球模型研究了两相密度差对油／水分散体系悬浮稳定性的影响规律,考察了水相粘度及水相界面张力对油／水分散体系分散稳定性的影响。结果表明：复色多相分散体系的悬浮稳定性主要由两相密度差决定,当两相密度差降至０．５ｋｇ／ｍ３时,可以制得悬浮稳定性很好的复色多相分散体系。水相粘度增大,悬浮稳定性提高。水相界面张力对丙烯酸酯－聚氨酯油相形成的分散体系影响较大,当其界面张力大于６９．５×１０－３Ｎ／ｍ时,分散稳定性好。只要粒子间不易相互融结,形成的复色多相分散体系便不发生渗色现象。     

Dispersion of liquid–liquid systems in a mixer with a reciprocating agitator

In this paper, the experimental results of dispersion of two immiscible liquids in a vibromixer are presented. The investigations covered three of the most important problems for vibro-mixing of liquid–liquid systems: the critical conditions, power consumption, and phase dispersion. The data obtained were presented in dimensionless correlations describing the influence of both: the operating conditions and physical properties of dispersed liquids on the process. Also new forms of dimensionless numbers for vibro-mixing are proposed.