Deformation and osmotic swelling of an elastic membrane capsule in Stokes flows by the immersed interface method

Although permeable and deformable capsules are found in many applications in biological and industrial systems, studies on computational modeling of these capsules are still rather lacking. In this work, the osmotic swelling of a deforming capsule immersed in a diluted binary solution of a non-electrolyte solute under Stokes flows is simulated using the immersed interface method (IIM). The approximate jump conditions for solute concentration are calculated with the use of the Kedem–Katchalsky relations. The capsule membrane is considered to be either semi-permeable or fully permeable, and the material of capsule membrane is assumed to be Neo-Hookean. The employed properties of fluid and membrane lie in the range of a typical biological system. The numerical validation tests indicate that the present calculation procedure has achieved good accuracy in modeling the swelling and deformation of permeable capsules. The capsule swelling (with mass transfer across the membrane) and deformation are tested for different solute concentration fields and membrane permeability properties. Our numerical investigations show that the initial solute concentration field and the membrane permeability properties have much influence on the swelling/deformation of a permeable capsule under Stokes flows.     

Direct numerical simulation of complex multi-fluid flows using a combined front tracking and immersed boundary method

In this paper a simulation model is presented for the Direct Numerical Simulation (DNS) of complex multi-fluid flows in which simultaneously (moving) deformable (drops or bubbles) and non-deformable (moving) elements (particles) are present, possibly with the additional presence of free surfaces. Our model combines a Front Tracking (FT) model developed by van Sint Annaland et al. (2008. Numerical simulation of dense gas-solid fluidized beds: a multiscale modeling strategy. Ann. Rev. Fluid Mech. 40, 47-70.) and an Immersed Boundary (IB) model developed by van der Hoef et al. (2008. Numerical simulation of dense gas-solid fluidized beds: a multiscale modeling strategy. Ann. Rev. Fluid Mech. 40, 47-70.) The FT part circumvents the explicit computation of the interface curvature. The IB part incorporates both particle-fluid and particle-particle interaction via a direct forcing method and a hard sphere Discrete Particle (DP) approach. In our model a fixed (Eulerian) grid is utilised to solve the Navier-Stokes equations for the entire computational domain. The no-slip condition at the surface of the moving particles is enforced via a momentum source term that only acts in the vicinity of the particle surface. For the enforcement of the no-slip condition Lagrangian force points are used, which are distributed evenly over the surface of the particle. Dissipative particle-particle and/or particle-wall collisions are accounted via a hard sphere DP approach using a three-parameter particle-particle interaction model accounting for normal and tangential restitution and tangential friction. The capabilities of the hybrid FT-IB model are demonstrated with a number of examples in which complex topological changes in the interface are encountered.     

Numerical study of a hybrid membrane cell with semi and fully permeable membrane sub-sections

Hybrid membrane cells with up to 128 sections, each one comprising a fully and a semi-permeable membrane sub-section and, the limit case of a cell with an infinite number of membrane sections were studied by numerical methods. These hybrid cells separate a feed stream into two parts: a solvent stream which crosses the semi-permeable membranes and a concentrate stream which crosses the fully permeable membranes. The concentrate stream has a cleaning effect on the mass boundary layer over the semi-permeable membranes. The numerical results show that concentration polarization in hybrid cells is much lower than the polarization in conventional cells. Additionally, a highly concentrated solution is recovered. The cell with an infinite number of membrane sections (n) has the best performance: the lowest polarization and the highest concentration in the concentrate stream. As n increases to infinite, the concentration in the concentrate stream tends to the concentration over the semi-permeable membrane, i.e., to the maximum concentration inside the mass boundary layer. The number of membrane sections needed to achieve a performance similar to that of a cell with an infinite number of sections is very high, greater than 128. The velocity of the concentrate stream also plays an important role. As this velocity is increased (until an upper limit), the cleaning effect of the boundary layer intensifies but the purity of the concentrate stream decreases (dilution effect). An intermediate value for the velocity of the concentrate stream (between the lower and upper limit) should be used to optimize both effects.     

Mass‐transfer enhancement by a reversible chemical reaction across the interface of a bubble rising under Stokes flow

Mass transfer around a bubble rising in a liquid under Stokes regime is investigated when a reversible chemical reaction, , is taken into account. Four dimensionless parameters control the interfacial transfer rate: the Péclet and Damköhler numbers, the ratio of the diffusion coefficient of both species, and the reaction equilibrium constant. The mass‐transfer equations are solved numerically with a finite element technique. A boundary layer approach is also proposed and solved with a coupled technique of finite difference and Chebyshev‐spectral method. The equilibrium constant and the ratio of diffusion coefficients have a strong influence on the coupling between the chemical reaction and mass transfer leading to an increase of the Sherwood number. The interaction between the chemical reaction and advection is clearly established by the simulations. Conditions corresponding to Péclet number larger than the Damköhler number reduces the effect of the chemical reaction. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3376–3388, 2014     

DEM-LES study of 3-D bubbling fluidized bed with immersed tubes

Based on Euler-Lagrange frame, a true three-dimensional numerical simulation of bubbling fluidized bed embedded with two immersed tubes is presented. The solid phase is composed of 178,200 particles of diameter and simulated by discrete element method (DEM, a soft-sphere approach). The gas phase is computed through solving the volume-averaged four-way coupling Navier-Stokes equations in which the Smagorinsky SGS tensor model is used in large eddy simulation (LES). Particle-tube collision is particularly treated as a transformation of DEM. The volume segmentation of a particle sphere for void fraction calculation is solved via a numerical sub-division approach. The numerical results are compared with the experimental results for validation. The results obtained with and without the LES model are also compared. The numerical results show a strong correlation between gas-particle interaction, particle-particle interaction, pressure drop, particle back mixing motion and bubble motion, and all of them follow a similar pattern of synchronous periodic variation though the periodicity may vary depending on different flow conditions. The effects of SGS tensor on evolution of fluidized bed are found in various aspects. Finally, the distribution of particle-tube impact frequency is given.     

Numerical Studies of Convective Mass Transfer Enhancement in a Membrane Channel by Rectangular Winglets☆

Numerical calculations were conducted to simulate the flow and mass transfer in narrow membrane channels with and without flow disturbers. The channel consists of an impermeable solid wall and a membra...     

New mechanism of gas transport at the interface solid/liquid

It was recently shown that an abnormally fast transport of CO molecules takes place at the electrode/electrolyte interface of Pt and PtRu electrodes in H₂SO₄ and HClO₄ solutions. In the present paper, this phenomenon is tested for other gases, such as hydrogen and oxygen. The fast transport is also observed at the solid/electrolyte solution interface of other electrode materials and at the glass/electrolyte interface. Several experiments are shown, demonstrating that mass transfer takes place at a velocity, which is more than one order of magnitude higher than expected for usual diffusion conditions.Assuming radial mass transfer at the interface of a Pt disc, the activation energy, E_a = 23 kJ mol⁻¹, was calculated from Arrhenius plots. The same value was measured in H₂SO₄ and HClO₄ as supporting electrolytes. The mass transport parameter, Y, at 298 K was 4.8 × 10⁻³ cm² s⁻¹ and 2.9 × 10⁻³ cm² s⁻¹ in 0.5 M H₂SO₄ and 1 M HClO₄ respectively.     

Electrodiffusion diagnostics of laminar flows using the delay-time method

Electrodiffusion diagnostics are widely used for measurement of local wall shear stresses in liquid flows. At present, this method requires special electrolytes, so the applications are limited to laboratory conditions. Another problem concerns the dependence of the limiting diffusion current on the electrode surface state and on the bulk concentration of the electroactive species. In this paper, it is shown that the delay time between generation of the electroactive species and their detection on the downstream electrode, is directly related to the local wall shear stress value. Thus, the measurements of the delay-time open a new way for the study of near-wall hydrodynamics. This new method has been confirmed experimentally using an electrolyte containing the conventional hexacyanoferrate(III/II) redox couple, as well as with the chlorine (chloric(I))/chloride couple in an electrolyte similar to seawater.     

A numerical study of stir mixing of liquids with particle method

The process of stir mixing of two viscous liquids is simulated using the moving particle semi-implicit (MPS) method. A mixing rate is defined within the particle method to characterize the level of mixing, as the number, position, period, and rotating speed of the stirring stick(s) and liquid viscosity are changed. The motions of liquid particles are tracked to reveal the flow field and mixing mechanisms. The variation of the mixing rate shows that the mixing rate is higher when the sticks are rotating monotonically at high speed, and an optimum position of the stick can be identified. The mixing rate does not enhance significantly when three or more sticks are employed, and the liquid viscosity has minor influences on the mixing rate. These results give useful qualitative suggestions on controlling the mixing rate during chemical reactions.     

The intensification of gas-liquid flows with a periodic, constricted oscillatory-meso tube

The experimental study of gas dispersion in a vertical periodically, constricted, oscillatory meso-tube (OMT) is herein presented. Water was continuously pumped through the OMT in the laminar flow regime along with an oscillatory flow component superimposed into the net flow in a range of fluid oscillation frequency (f) and centre-to-peak amplitude (x₀) of and 0-3 mm, respectively, in the presence of a very low superficial gas velocity . Bubble images were recorded with a CCD camera and analysed with Visilog^® software. A bimodal distribution of bubble size was in general observed but the bubble size was found strongly dependent on the oscillatory flow mixing conditions imposed into the fluid. A number fraction of micro-bubbles (with an equivalent diameter, D_eq, equal or bellow 0.2 mm) up to 60% was generated with increasing values of x₀ (i.e. 3 mm) and values of f in the range . Furthermore, it is demonstrated that the Sauter mean diameter, D₃₂, and the specific interfacial area, a, can be fined tune by setting both f and x₀ in this studied range. The high number fraction of micro-bubbles was concluded to have a positive impact in enhancing the liquid-side mass transfer coefficient, k_L. Globally, the differences in bubbles sizes were found to play a marginal effect in the global enhancement of the k_La in the meso-tube in comparison with the intensive contact experimented by the bubbles rising in the oscillatory flow. The higher order of magnitude of the k_L values found in this work (up to ) is promising for running numerous industrial gas-liquid flows processes through smaller and better, while aeration of biotransformations can be run more efficiently, as supported by our recent proof-of-concept studies carried out in the platform.     

Numerical simulation of a falling droplet surrounding by air under electric field using VOF method: A CFD study

This is a numerical study of a falling droplet surrounding by air under the electric field modeled with finite volume method by means of CFD. The VOF method has been employed to model the two-phase flow of the present study. Various capillary numbers are investigated to analyze the effects of electric field intensity on the falling droplet deformation. Also, the effects of electric potential on the heat transfer coefficient have been examined. The obtained results showed that by applying the electric field at a capillary number of 0.2 the droplet tends to retain its primitive shape as time goes by, with a subtle deformation to an oblate form. Intensifying the electric field to a capillary number of 0.8 droplet deformation is almost insignificant with time progressing; however, further enhancement in capillary number to 2 causes the droplet to deform as a prolate shape and higher values of this number intensify the prolate form deformation of the droplet and result in pinch-off phenomenon. Ultimately, it is showed that as the electric potential augments the heat transfer coefficient increases in which for electric potential values higher than 2400 V the heat transfer coefficient enhances significantly.     

Numerical simulation of pulsed fluidized bed with immersed tubes using DEM-LES coupling method

The present work is a 2-D numerical simulation of pulsed fluidized bed with immersed tubes using DEM-LES coupling method. The pulsed inflow of gas phase is modeled as U₀(1+sin(2πft)), in which four pulsating frequencies of f=5, 10, 15 and 20 of velocity inflow are used. The discrete element method (DEM) simulation for particle motion coupled with the large eddy simulation (LES) for gas phase is used. The fluidized bed with five immersed tubes of staggered arrangement and six immersed tubes of in-line arrangement is simulated, respectively. It is found that the pressure drop, the mean drag force and the mean pressure gradient force experienced by particles are forced oscillated. The different effects of pulsed fluidization on the circumferential distribution of particle-tube collision on the outer surface of tubes at different pulse frequencies and modes of arrangement of immersed tubes are numerically analyzed. Finally, it is found that the pulsed motion of fluid with high frequency leads to suppression of particle fluctuating motion.     

Numerical simulation of unsteady mass transfer by the level set method

Unsteady mass transfer to/from a single drop in the continuous phase is formulated and numerically simulated in a moving reference coordinate system by solving the motion and mass transfer equations of an accelerating drop coupled with a level set equation for capturing the interface. Numerical simulation demonstrates the evolution of mass transfer rate and average drop concentration. Numerical simulation of the flow field and the concentration field simultaneously in each time step is compared with experimental data on single drop motion and mass transfer in two typical solvent extraction systems. The numerical predictions are found in good accord with the experimental measurements. The present numerical procedure in which the flow field is solved in a coupled way with the concentration field gives more accurate prediction than the previous decoupling algorithm by the authors.     

Drying characteristics of porous material immersed in a bed of hygroscopic porous particles fluidized under reduced pressure

A relatively large wet material was immersed in a fluidized bed of hygroscopic porous particle (silica gel beads) under reduced pressure. And then the drying characteristics were compared with those in the case of inert particle (glass beads). The comparison of drying characteristics is performed experimentally and theoretically. In calculation, the water transfer from the sample to the fluidized bed was considered. The calculation results are in good agreement with the experimental data. The effects of the operational conditions (the pressure in the drying chamber and the temperature of the drying gas) on the drying characteristics were also examined in both fluidizing particles.The drying finishes earlier in the case of hygroscopic porous particle than in the case of inert particle regardless of pressure in the drying chamber, since the water transfer from the sample facilitates the drying in the case of hygroscopic porous particles. The temperature decrement in drying appears in the case of inert particle. This phenomenon is also observed in the case of hygroscopic porous particle, but the decrement degree of the temperature is much smaller than that in the case of inert particle. The difference of the minimum temperature in the sample in drying between the cases of hygroscopic porous particle and inert particle is very slight for different pressures in the drying chamber.     

球形胶囊内约束熔化过程的LBM模拟

为了准确预测球形胶囊内部材料的相变性能,为后续相变微胶囊浆体的多尺度研究提供微观相变信息,采用格子Boltzmann方法（LBM）,引入浸入式移动边界处理方案,借鉴糊状区和热焓理论,构建了适于相变模拟的数值模型,模拟了球形胶囊内部固液相变过程,讨论了不同粒径尺度下熔化机制的区别。结果表明,利用LBM方法得到的预测结果与可视化实验数据吻合较好,清晰地呈现出球体上部温度热分层和下部液相强对流共存的特性。随着粒径尺度的不断减小,胶囊内部对流作用逐渐减弱,甚至当粒径小于3 mm时,其内部对流作用可忽略。     

Pseudo-steady state method on study of xylose hydrogenation in a trickle-bed reactor

A new approach to assess the overall mass transfer coefficients in a partial wetting trickle-bed reactor was proposed and tested in hydrogenation of xylose. An effective data-acquiring procedure featured by recycling a large volume of liquid feed has been adopted after the steady state operation. Since the volume of the fresh feed taken for recycling was so large that the xylose feed concentration decreased slowly during the prolonged recycling period, the pseudo-steady state was therefore achieved. By relating outlet and inlet xylose contents in liquid flow of the reactor, the reaction results varied with xylose feed concentration were simulated. The coefficients of the two reactants, hydrogen and xylose, were correlated simultaneously with a steady state reaction model. The estimated coefficients fell in the range of trickle-bed reactors at low flow rates and manifested a partial wetting status.     

Numerical study of particle dispersion in the wake of gas-particle flows past a circular cylinder using discrete vortex method

A numerical investigation on the particle dispersion in the wake of particle-laden gas flows past a circular cylinder at Reynolds number of 10⁵ is presented. In the numerical method, the Discrete Vortex Method with the diffusion velocity model is employed to calculate the unsteady gas flow fields and a Lagrangian approach is applied to track individual particles. A dispersion function is defined to represent the dispersion scale of the particle. The distributions of gas velocities and vortex blobs, the trajectories and dispersion functions as well as distributions for particles with various Stokes numbers ranging from 0.01 to 1000 are obtained. The numerical results show that: (1) very small sized particles with St = 0.01 can distribute both in the vortex core and around the vortex periphery, whereas intermediate sized particles with St = 1.0, 10 are distributed around the vortex periphery, and very large sized particles with St = 1000 do not feel the gas flow; (2) only at small Stokes number (St = 0.01, 0.1) the particles do not impact with the cylinder; (3) the particle's dispersion intensity decreases precipitously as St is increased from 0.01 to 10.     

水平集方法数值模拟单液滴的生成过程(英文)

液滴生成的动力学过程和机理,对溶剂萃取、喷墨打印机设计、飞行器保护等有重要意义。虽然已有很多相关的实验、理论和计算研究,但对涉及拓扑变形界面的该问题研究仍富有挑战性,常用的有限元等模拟方法还有待改进。1988年提出的水平集(Level set)方法,可以比较简方便地模拟多相变形界面问题,已成功用于多相流、结晶、浇铸、模式识别等过程的计算。作者在对水平集方法进行改进并用于相间传质模拟的基础上,本文数值模拟了单个液滴在毛细管口的生长和脱离过程。假设流体均为不可压缩液体或气体作层流流动,采用二维轴对称欧拉坐标和交错网格,利用控制容积法和SIMPLE算法离散求解藕合水平集函数的运动方程组。水平集函数的发展方程和重新初始化方程的空间与时间离散格式,分别采用5阶WENO(Weighted essentially nonoscillatory)和3阶TVD(Total variation diminishing)Runge-Kutta格式。初步计算了不同参数的单液滴在气体或另一不互溶液体中的生成过程,液滴的拓扑形状、两相流场和液滴大小与实验或文献报道的模拟结果基本吻合,为今后拓展模拟三维空间的不稳定运动液滴或气泡生成过程的流动和传递奠定了基础。     

气流横向冲刷圆壳管束换热的数值模拟

采用标准k-ε模型、SIMPLEC算法,研究了均匀速度进气和有扩张角进气横向冲刷管束的换热情况。比较了在充分发展流时均匀进气和不同扩张角进气横向冲刷管束的换热性能,分析了进口扩张角对换热的影响,进口扩张角影响了气流的分布,导致换热效果的不同。     

Combination of the direct-forcing fictitious domain method and the sharp interface method for the three-dimensional dielectrophoresis of particles

In this paper, we combine the direct-forcing fictitious domain (DF/FD) method and the sharp interface method (SI) to resolve the problem of particle dielectrophoresis in three dimensions. The flow field is solved with the DF/FD method. The electric field governed by a Laplace equation with a jump coefficient across the particle surface is solved with the sharp interface (SI) method, and the dielectrophoretic force on particles is then calculated with the Maxwell stress tensor (MST) method. The main feature of our method is that both hydrodynamic and dielectrophoretic forces on particles are calculated with the interface-resolved methods instead of the point-particle model. The accuracy of the SI/MST method for the dielectrophoretic force without the consideration of the flow is validated via two problems: the electrostatic force on the particle in a non-uniform electric field, and the electrostatic force between two particles. The capability of the proposed DF/FD-SI/MST method is demonstrated with two numerical examples: the aggregation of particles due to the conventional dielectrophoretic force, and the motion of particles due to both conventional and traveling wave dielectrophoretic forces.