Simulation of packed-bed chromatography utilizing high-resolution flow fields: comparison with models

A computer simulation of a section of the interior region of a liquid chromatographic column is performed. The detailed fluid flow profile is provided from a microscopic calculation of low Reynolds number flow through a random packed bed of nonporous spherical particles. The fluid mechanical calculations are performed on a parallel processor computer utilizing the lattice Boltzmann technique. Convection, diffusion, and retention in this flow field are calculated using a stochastic-based algorithm. This computational scheme provides for the ability to reproduce the essential dynamics of the chromatographic process from the fundamental considerations of particle geometry, particle size, flow velocity, solute diffusion coefficient, and solute retention parameters when retention is utilized. The simulation data are fit to semiempirical models. The best agreement is found for the "coupling" model of Giddings and the four-parameter Knox model. These models are verified over a wide range of particle sizes and flow velocities at both low and high velocity. The simulations appear to capture the essential dynamics of the chromatographic flow process for non-dimensional flow velocities (Péclet number) less than 500. Since the same packing geometry is utilized for different particle size studies, the interpretation of the parameter estimates from these models can be extended to the physical column model. The simulations reported here agree very well with a number of experiments reported previously.     

循环流化床锅炉内颗粒速度分布的实验研究

为了研究操作参数对循环流化床锅炉内颗粒速度分布的影响,在冷态模型装置上使用PV6A型颗粒速度光纤测量仪、毕托管对循环流化床锅炉炉膛内的颗粒速度进行了测量与分析。结果表明:在流化风速为2.57 m/s、循环质量流率为0.58 kg/(m2.s)、一次风量为2 300 m3/h、二次风量为1 500 m3/h时,循环流化床锅炉炉膛内颗粒浓度分布、压降、流化状态、质量循环都达到一个较稳定的水平,呈现典型的环核分布特征。     

High-velocity transport of nanoparticles through 1-D nanochannels at very large particle to channel diameter ratios

We explore the possibility of generating high-velocity flows of nanoparticles through flat-rectangular nanochannels, which are only 50% deeper than the diameter of the particles. Using the shear-driven flow principle, 200-nm particles can, for example, be transported through a 300-nm-deep channel at velocities up to 35 mm/s (upper limit of our current setup). Working under high-pH conditions, the velocity of the carboxylated nanoparticles still respects the small-molecule velocity law, despite the high degree of confinement to which the particles are subjected. The high degree of confinement is also found to lead to a reduced band broadening. When injecting sharply delimited particle plugs, the plate heights observed for the flow of 0.2-microm particles through a 0.3-microm channel (with plate heights of the order of 1-2 microm) are, for example, approximately 1 order of magnitude smaller than for the flow of 1.0-microm particles through a 1.4-microm channel. It is also found that the band broadening is, within its statistical variation, independent of the fluid velocity over a large range of particle velocities (5-35 mm/s). The flow method distinguishes itself from pressure-driven field-flow fractionation and hydrodynamic chromatography in that the mean particle velocity is independent of the particle size over the entire range of possible particle to channel diameter ratios.     

Effects of porous boundaries on peristaltic transport through a porous medium

Summary Peristaltic pumping by a sinusoidal traveling wave in the porous walls of a twodimensional channel filled with a viscous incompressible fluid through a porous medium is investigated theoretically and graphically. It has been considered that the fluid is entering the flow region through one plate at the same rate as it is leaving through the other plate. A perturbation solution is obtained, which satisfies the momentum equation for the case in which the amplitude ratio is small. It has been noticed that the mean axial velocity and the reversal flow increase by increasing the permeability parameterW. The mean axial velocity and the reversal flow decrease by increasingV until at the upper quarter of the channel it increases by increasingW. Also, the fluid motion is nonsymmetric. Numerical results are reported for various values of the physical parameters of interest.     

Microfluidic particle sorter employing flow splitting and recombining

This paper describes an improved microfluidic device that enables hydrodynamic particle concentration and size-dependent separation to be carried out in a continuous manner. In our previous study, a method for hydrodynamic filtration and sorting of particles was proposed using a microchannel having multiple branch points and side channels, and it was applied for continuous concentration and separation of polymer particles and cells. In the current study, the efficiency of particle sorting was dramatically improved by geometrically splitting fluid flow from a main stream and recombining. With these operations, particles with diameters larger than a specific value move toward one sidewall in the mainstream. This control of particle positions is followed by the perfect particle alignment onto the sidewall, which increases the selectivity and recovery rates without using a liquid that does not contain particles. In this study, a microchannel having one inlet and five outlets was designed and fabricated. By simply introducing particle suspension into the device, concentrations of 2.1-3.0-microm particles were increased 60-80-fold, and they were collected independently from each outlet. In addition, it was demonstrated that the measured flow rates distributed into each side channel corresponded well to the theoretical values when regarding the microchannel network as a resistive circuit.     

On-chip high-speed sorting of micron-sized particles for high-throughput analysis

A new design of particle sorting chip is presented. The device employs a dielectrophoretic gate that deflects particles into one of two microfluidic channels at high speed. The device operates by focussing particles into the central streamline of the main flow channel using dielectrophoretic focussing. At the sorting junction (T- or Y-junction) two sets of electrodes produce a small dielectrophoretic force that pushes the particle into one or other of the outlet channels, where they are carried under the pressure-driven fluid flow to the outlet. For a 40 microm wide and high channel, it is shown that 6 microm diameter particles can be deflected at a rate of 300/s. The principle of a fully automated sorting device is demonstrated by separating fluorescent from non-fluorescent latex beads.     

An analytical model for bedload layer thickness

A theoretical study has been carried out to determine the thickness of the bedload layer in an open channel turbulent flow with non-cohesive sediment, which is very crucial in sediment transport problems as this is treated as saltation height of a sediment particle and the reference level in suspension studies. A new expression of viscous shear stress is proposed, which is a function of effective viscosity of sediment–fluid mixture, velocity gradient and volumetric concentration of sediment particles. During particle collisions, impact shear stress is generated, which is another important parameter near the sediment bed. By including both the shear stresses, an expression for the thickness of the bedload layer is developed. The predicted bedload layer thickness is a function of viscous coefficient, impact coefficient, particle diameter, relative mass density of sediment particle, maximum bed concentration and non-dimensional shear stress. It agrees reasonably well when compared with a wide class of experimental data under different hydraulic conditions.     

Direct numerical simulation of ellipsoidal particles in turbulent channel flow

This paper investigates the behaviour of elongated, axi-symmetric ellipsoidal particles, their interaction with turbulence, and the effects of the ellipsoids on turbulence in a turbulent channel flow with Re _τ = 150. The simulations are carried out with full four-way coupling using the point-source approach: the particles are affected by the fluid, the particles affect the fluid, and the particles can collide with each other or the wall using a realistic collision algorithm. The trajectories of the ellipsoids are tracked by solving the translational and rotational equations of motion in a Quaternion framework and are closed with hydrodynamic drag and torque laws. To specifically identify the effect of particle shape, simulations of single phase channel flow are compared to simulations with spherical particles and to simulations with ellipsoids. In all cases, the driving pressure drop, to establish a flow with Re _τ = 150, is kept constant. Both the spherical particles and the ellipsoidal particles have a Stokes number of 5. Although the volume fraction is very low, 0.00725 and 0.0219 % for the spheres and ellipsoids, respectively, there is some effect of the particles and the ellipsoids on the turbulence. Although the transport terms in the turbulent kinetic energy equation of the fluid are hardly affected, the turbulence kinetic energy itself decreases by 6.0 % for the flow laden with spherical particles and 4.8 % for the ellipsoidal particles. The homogeneous dissipation of turbulence kinetic energy by the fluid decreases due to the addition of particles, and the production also decreases. The particles dissipate turbulence kinetic energy of the fluid phase, predominantly in the near-wall region. Because there is a high average slip velocity in the stream-wise direction between the particles and the fluid in the near-wall region, the root mean square of the particle velocity is higher than that of the fluid velocity in this direction. In the other directions, the root mean square velocities of the particles are significantly lower than of the fluid. There is, however, a positive slip velocity between the particles and the fluid in the wall-normal direction, indicating that the particles move towards the wall with a higher momentum than that they return to the centre of the channel with. As a result, there is a 4–5 times higher concentration of particles near the wall than in the centre of the channel. As both the spherical and the ellipsoidal particles are very small, there is no major difference in their overall behaviour. However, in the near-wall region, there are some profound differences. The collision mechanism of ellipsoids with the walls is significantly different compared to spheres, the former predominantly inducing rotation resulting from a collision and the latter predominantly moving away from the wall after colliding. This is confirmed by the strong rotation as well as large root mean square of rotation of the ellipsoidal particles in the near-wall region. This results in a slight inward shift of the peak of the root mean square velocities of the fluid and the ellipsoidal particles as well as the peak in slip velocity, driving the momentum transfer, compared to the simulations with the spheres. Finally, the statistics of the orientation show that the ellipsoids align in the stream-wise direction in the near-wall region, because of the fluid boundary layer as well as the particle–wall collisions, but that there is no significant orientation of the ellipsoids outside of the near-wall region.     

Zweiphasenströmung in Kreiselpumpen für den hydraulischen Feststofftransport

A mathematical model of the trajectories of fluid and particles is developed based on the two dimensional equations of motion in plane flow for the impeller and the casing. The set of differential equations for plane flow is solved numerically using a 4th order Runge–Kutta method using the velocity profile of the fluid and the velocity components of the particles at the inlet of the impeller as initial conditions. The strong effect of the particle density ?_S and of the particle diameter d_S on the particle trajectory is analysed. Based on the solution of the equations of motion of both phases in the impeller and in the casing the velocity ratio of particles and fluid is calculated.     

In-line holographic particle image velocimetry for turbulent flows

A holographic system has been developed to measure the velocity field in three-dimensional flow regions. The system records the position of small tracer particles on two in-line holograms of the flow obtained simultaneously. Two exposures are recorded on each hologram. The flow velocity is derived from the displacement of the particles between exposures. A general design procedure is described for selecting the particle diameter and the concentration on the basis of the configuration of the flow facility and the resolution characteristics of the holographic imaging system. The system was implemented in a 2 ft x 2 ft (1 ft = 30.48 cm) water channel to measure the velocity field in a turbulent free-surface jet. The spatial resolution of the system is 1 mm, and the field of view is 100 mm, approximately. Measurements performed with this system are compared with results reported in the literature and are found to be in good agreement.     

Enhancement of air purification by unique W-plate structure in two-stage electrostatic precipitator: A novel design for efficient capture of fine particles

In this paper, a novel W-plate two-stage ESP was developed and investigated systematically through the experimental and simulated process. Numerical models and available calculation procedure of solving coupling electrostatic field, fluid field, and particle dynamics were established, whose accuracy was validated by experiments. The relationship among collection efficiency, gas velocity, and particle diameter was studied, and the distribution of electrostatic field, the evolution of EHD flow and fluid field, and particle dynamics, including particle charging, particle trajectory, transverse velocity, and particle concentration, were also investigated thoroughly. Results showed that W-plate two-stage ESP exhibited excellent number-based collection efficiency for fine particles which benefited from the reasonable structure design and the exceeding weak influence of EHD flow. Besides, the particle charging process suggested that the diameter decided the dominant charging mechanism, and the trajectory also played an important role in controlling the charging action. Compared with the behavior of each particle injected at different inlet positions, fine particles injected near the discharge wire got more charging number and quicker capture. Importantly, W-plate structure could exert its crucial role in capturing particles with the help of fluid field and inertial effect when inlet gas velocity increased rapidly. W-plate two-stage ESP had more than 90% number-based collection efficiency for >3 μm diameter particles and more than 75% number-based collection efficiency for 0.3–1 μm diameter submicron particles at 2 m/s gas velocity in both experimental and simulated investigations.     

Mathematical Modelling of Particle Movement Ahead of the Solid—liquid Interface in Continuous Casting

Whether the particle with be trapped by the solid-liquid interface of not is dependent on its moving behavior ahead of the interface,so a mathematical model has been developed to investigate the movement of the particle ahead of the solid-liquid interface.Based on the theory for the boundary layer,the fluid velocity field near the solid-liquid interface was obtained,and the trajectories of particles were calculated by the equations of motion for particles.In this model,the drag force,the added mass force,the buoyance force,the gravitational force,the Saffman force and the basset history force are considered.The results show that the behavior of the particle ahead of the solid-liquid interface is affected by the physical property of the particle and fluid flow.And in the continuous casting process,if it moves in the stream directed upward or downward near vertical solid-liquid interface of in the horizontal flow under the solid-liquid interface,the particle with the diameter from 5μm to 60μm can reach the solid-liquid interface.But if it moves in horizontal flow above the solid-liquid interface,only the particle with the diameter from 5μm to 10μm can reach the solid-liquid interface.     

Simulation of an orifice scrubber performance based on Eulerian/Lagrangian method

A mathematical model based on Eulerian/Lagrangian method has been developed to predict particle collection efficiency from a gas stream in an orifice scrubber. This model takes into account Eulerian approach for particle dispersion, Lagrangian approach for droplet movement and particle-source-in-cell (PSI-CELL) model for calculating droplet concentration distribution. In order to compute fluid velocity profiles, the normal k− turbulent flow model with inclusion of body force due to drag force between fluid and droplets has been used. Experimental data of Taheri et al. [J. Air Pollut. Control Assoc. 23 (11) (1973) 963] have been used to test the results of the mathematical model. The results from the model are in good agreement with the experimental data. After validating the model the effect of operating parameters such as liquid to gas flow rate ratio, gas velocity at orifice opening, and particle diameter were obtained on the collection efficiency.     

A parametric study of dispersed laminar gas-particle flows through vertical and horizontal channels

Particle diameter, particle phase material density and inlet particle volume fraction are three important parameters governing the flow physics of dispersed gas-particle flows. In this work, an inhouse numerical solver is developed to investigate the effects of particle diameter (Stokes number), particle phase material density, inlet particle volume fraction and inlet phase velocities in the flow characteristics of gas-particle flows through vertical and horizontal channels and also in open domains. It is found that, for a constant inlet particle volume fraction, lower diameter particles attain a higher steady state velocity at any section inside the channel than the higher diameter particles; while the corresponding steady state gas velocity at any section increases with increase in particle diameter. On the other hand, for a constant particle diameter, the steady state gas phase velocity at any section decreases with increase in inlet particle volume fraction. Significant changes in both gas and particle velocity and volume fraction profiles have also been observed with inlet slip, i.e., when the velocities of both the phases at inlet are distinct as opposed to being equal, keeping all other flow and physical parameters invariant.     

WALL DEPOSITION OF SMALL SUSPENDED PARTICLES IN A TURBULENT CHANNEL FLOW

The diffusion of small suspended particles in a turbulent channel flow is studied by solving the transport advection-diffusion equation. The mean flowfield in the channel is simulated using a two-equation k-ε turbulence model. Deposition velocity is evaluated at different sections in the channel for different particle sizes and flow Reynolds numbers. The effects of turbulence dispersion and Brownian diffusion on particle deposition velocity are discussed. The variation of particle deposition velocity with particle diameter, density and flow Reynolds number are analyzed. The wall deposition velocities for different size particles are compared with those obtained by other models.     

Solid Flow Transition in Liquid and Three-Phase Fluidized Beds

Flow transition of solids in liquid and three phase fluidized beds of Newtonian and non-Newtonian fluids have been studied in a 15.2 cm-ID pyrex glass column. The relation between the fluid flow rate and the bed porosity in three phase fluidized beds have been determined in terms of effective volumetric flux of fluid phases from the modification of the Richardson and Zaki's equation. The modified particle Reynolds Number exhibited its maximum value with the variation of bed porosity in liquid and three phase fluidized beds. The drag coefficient changed its slope apparently at the bed porosity where the maximum value of the modified particle Reynolds number could be attained. At the flow transition condition, the continuity wave velocity, energy dissipation rate, and the continuity shock wave velocity found to have their maximum values. Also, the immersed heater-to-bed and wall-to-bed heat transfer coefficients, wall-to-bed mass transfer coefficient, liquid radial mixing coefficient and solid particle diffusivity in the literature data were found to have maximum values at the transition condition of liquid and three phase fluidized beds.     

A Fractal-Fractional Model for the MHD Flow of Casson Fluid in a Channel

An emerging definition of the fractal-fractional operator has been used in this study for the modeling of Casson fluid flow. The magnetohydrodynamics flow of Casson fluid has cogent in a channel where the motion of the upper plate generates the flow while the lower plate is at a static position. The proposed model is non-dimensionalized using the Pi-Buckingham theorem to reduce the complexity in solving the model and computation time. The non-dimensional fractal-fractional model with the power-law kernel has been solved through the Laplace transform technique. The Mathcad software has been used for illustration of the influence of various parameters, i.e., Hartman number, fractal, fractional, and Casson fluid parameters on the velocity of fluid flow. Through graphs and tables, the results have been implemented and it is shown that the boundary conditions are fully satisfied. The results reveal that the flow velocity is decreasing with the increasing values of the Hartman number and is increasing with the increasing values of the Casson fluid parameter. The findings of the fractal-fractional model have elucidated that the memory effect of the flow model has higher quality than the simple fractional and classical models. Furthermore, to show the validity of the obtained closed-form solutions, special cases have been obtained which are in agreement with the already published solutions.     

PIV experimental investigation of entrance configuration on flow maldistribution in plate-fin heat exchanger

Flow characteristics of flow field in the entrance of plate-fin heat exchanger have been investigated by means of particle image velocimetry (PIV). The velocity fields were measured using the two-frame cross-correlation technique. A series of velocity vector and streamline graphs of different cross-sections are achieved in the experiment. The experimental results indicate that performance of fluid maldistribution in conventional entrance configuration is very serious, while the improved entrance configuration with punched baffle can effectively improve the performance of fluid flow distribution in the entrance. Based on the analysis of the fluid flow maldistribution, a baffle with small holes is recommended to install in the entrance configuration in order to improve the performance of flow distribution. When the punched baffle is proper in length, the small holes is distributed in staggered arrangement, and the punched ratio gradually increases from central axis to the boundary along with the baffle length, the performance of flow distribution in plate-fin heat exchanger is effectively improved by the optimum design of the entrance configuration. The flow maldistribution parameter S in plate-fin heat exchanger has been reduced from 1.21 to 0.209 and the ratio of the maximum velocity to the minimum θ is reduced from 23.2 to 1.76 by installing the punched baffle. The results validate that PIV is well suitable to investigate complex flow pattern and the conclusion of this paper is of great significance in the optimum design of plate-fin heat exchanger.     

Study of microscale hydraulic jump phenomenon for hydrodynamic trap-and-release of microparticles

Easy trap-and-release of microparticles is necessary to study biological cellular behavior. The hydraulic jump phenomenon inspired us to conceive a microfluidic device for the hydrodynamic trap-and-release of microparticles. A sudden height increase in a microfluidic channel leads to a dramatic decrease in flow velocity, allowing effective trapping of the microparticles by energy conversion. The trapped particles can be released by stronger inertial force based on simply increasing the flow velocity. We present a systematic, numerical study of trap-and-release of the microparticles using multiphase Navier-Stokes equations. Effect of geometry flow velocity, particle diameter, and adhesion force on trap-and-release was studied.     

Solid Flow Transition in Liquid and Three-Phase Fluidized Beds

ABSTRACT

Flow transition of solids in liquid and three phase fluidized beds of Newtonian and non-Newtonian fluids have been studied in a 15.2 cm-ID pyrex glass column. The relation between the fluid flow rate and the bed porosity in three phase fluidized beds have been determined in terms of effective volumetric flux of fluid phases from the modification of the Richardson and Zaki's equation. The modified particle Reynolds Number exhibited its maximum value with the variation of bed porosity in liquid and three phase fluidized beds. The drag coefficient changed its slope apparently at the bed porosity where the maximum value of the modified particle Reynolds number could be attained. At the flow transition condition, the continuity wave velocity, energy dissipation rate, and the continuity shock wave velocity found to have their maximum values. Also, the immersed heater-to-bed and wall-to-bed heat transfer coefficients, wall-to-bed mass transfer coefficient, liquid radial mixing coefficient and solid particle diffusivity in the literature data were found to have maximum values at the transition condition of liquid and three phase fluidized beds.