Search

The evolution dynamics of wettability-induced jumping droplet is studied numerically by means of a high-density ratio based lattice Boltzmann method. The three phase moving contact line is modelled by a geometry based wetting formulation. We analyse the influence of pulse characteristics with respect to its nature, pulse width and double pulse actuation on the jumping dynamics. It is shown that these factors strongly affect the droplet lift-off mechanism. The influence of surrounding gas density and viscosity on the droplet behaviour is investigated systematically. It is found that the role of the ambient fluid becomes prominent during the recoiling and the lift-off phase of the jumping droplet. Finally, we demonstrate the applicability of wettability-induced droplet jumping in microfluidic devices where efficient transport of droplet is essential.

Three dimensional computations on successive droplet impingement on a solid surface are reported. A high-density ratio based lattice Boltzmann model is employed for the present two phase computations and a geometric-based contact angle formulation is used to model the moving contact line. The focus of the present work is on the impact behaviour and the interaction dynamics between the impinging droplets with an initial gap. The effects of trailing drop velocity, surface wettability, drop viscosity and surface tension on the time-dependent dynamics are investigated during the impingement process. Two different transient interaction modes are observed for different velocity ratios. With increase in advancing contact angle, it is observed that primary spreading increases in the case of in-phase mode of collision. Effect of eccentricity, through the offset between the droplets, is found to result in an asymmetric evolution of droplet morphologies. Passive particle tracers are seeded inside the droplets to visualize mixing process as a time sequence of closely interacting droplets during the impact with a solid surface.

A liquid drop impacting on a solid substrate is simulated to evaluate the effect of inhomogeneities in the wetting characteristics of the surface. A high density ratio multiphase solver based on phase-field lattice Boltzmann formulation has been employed. Influence of receding contact angle and wettability gradient is investigated to analyse the coupled dynamics of the impacting droplet on the solid surface. Simulations indicate that the receding contact angle is a key wetting parameter to determine the final physical outcome of the impact process. Interplay between tangential velocity component and receding contact angle results in interesting dynamical behaviours in the evolution of the droplet shape for oblique impact scenarios. Substrate inhomogeneities in the form of wettability gradient is found to induce a directional behaviour to the motion of the impacting droplet. The droplet motion is characterised by intense recoiling along the upstream part of the droplet, followed by secondary spreading of the downstream contact line.

We present a numerical study on the dynamic behaviour of two droplets impinging simultaneously onto a liquid film. A high density ratio based lattice Boltzmann method is employed for the present two-phase computations. Formation of a central uprising jet is observed due to the collision and coalescence of in between rims caused by the impacting droplets. Effect of separation gap between the droplets, film thickness, viscosity and gas density on the crown structure and jet behaviour are systematically studied. The influence of a moving wall with a liquid film on the jet behaviour is further investigated. It is shown that for a larger separation gap between the droplets, a delay in formation of central jet is observed while the spread length increases. For the thin films, the central jet height increases with the increase in film thickness, however a reversal in this behaviour is observed for the thicker films. The rate of increase of jet height and spread length is found to decrease with increase in gas density. Effect of wall velocity is found to enhance the upstream jet, while it suppresses the central and the downstream jets.

The steady flow around and through a porous circular cylinder was studied numerically. The effects of the two important parameters, the Reynolds and Darcy numbers, on the flow were investigated in details. The recirculating wake existing downstream of the cylinder is found to either penetrate into or be completely detached from the cylinder. It is also found that, contrary to that of the solid cylinder, the recirculating wake develops downstream of or within the porous cylinder, but not from the surface of it. These new findings provide additional evidence to Leal’s conclusion (Leal LG. Vorticity transport and wake structure for bluff bodies at finite Reynolds number. Phys Fluids A 1989;1:124) that the appearance of recirculating wakes at finite Reynolds number is due to vorticity accumulation, but not a result of the same physical phenomena associated with separation in boundary layers in adverse pressure gradients. Also presented in the current study are the variation of the critical Reynolds number for the onset of a recirculating wake as a function of Darcy number and the variation of a newly defined parameter, the penetration depth, as a function of the Reynolds number and Darcy number.

A two-dimensional flow model, incorporating mass transport, has been developed to simulate a microchannel enzyme reactor with a porous wall. A two-domain approach based on the finite volume method was implemented. Two parameters are defined to characterize the mass transports in the fluid and porous regions: the porous Damkohler number and the fluid Damkohler number. For reactions close to first-order type (enzyme reactor), the concentration results are found to be well correlated by the use of a reaction–convection distance parameter which incorporates the effects of axial distance, substrate consumption and convection. The reactor efficiency reduces with reaction–convection distance parameter because of reduced reaction (or flux) due to the lower concentration. Increased fluid convection improves the efficiency but it is limited by the diffusion in the fluid region. The correlated results can find applications for the design of enzyme reactors with a porous wall.

Numerical simulations have been performed for the flow past and through a porous square cylinder over a wide range of Reynolds numbers (1 ⩽ Re ⩽ 50) and Darcy numbers (10−6 ⩽ Da ⩽ 10−1). It is found that the recirculating wake existing downstream of the cylinder is completely detached from the body under a certain range of parameters. The size and the location of the wake mainly depend on Re and Da. Specially, the wake may initially increase but then decrease in size with an increase in Re, and eventually disappear when the Reynolds number is sufficiently large. The variation of the critical Reynolds number for the onset of recirculating wake as a function of Darcy number is summarized. The results also show that in the range of Da investigated, different from that of the solid cylinder, the recirculating wake is initially developed downstream of the porous cylinder, but not on the surface of it.

In this paper, a hybrid method is proposed to study the flow-induced deformation of three-dimensional capsules. The capsules consist of Newtonian liquid drops enclosed by thin elastic membranes. In the proposed approach, the front-tracking method is coupled with the lattice Boltzmann method. The fluids inside and outside the capsule is treated as one fluid with varying physical properties, and is modeled by the lattice Boltzmann equation. The capsule membrane is explicitly tracked by the membrane nodes that are advected by the flow. The multi-block strategy of the lattice Boltzmann method is employed to refine the mesh near the capsule, which greatly increase the accuracy and efficiency of the three-dimensional computation. The capsule membrane is discretized into unstructured flat triangular elements, and a finite element model is incorporated to account for the membrane mechanics. With the present method, the transient deformation of initially spherical capsules with membrane following Neo-Hookean constitutive laws is simulated in shear flow, under various dimensionless shear rates and ratios of internal to surrounding liquid viscosities. The present results, including the Taylor shape parameter, the capsule inclination angle and the tank-treading frequency, agree well with previously published numerical results.

The transient deformation of two-dimensional non-circular and three-dimensional non-spherical capsules in simple shear flow is studied numerically, using the hybrid immersed boundary and multi-block lattice Boltzmann method recently proposed by the present authors. The capsules are modeled as Newtonian liquid drops enclosed by elastic membranes; the liquids inside and outside the capsule have the same physical properties. The present results show important different behaviors between two-dimensional and three-dimensional capsules in shear flow. For two-dimensional non-circular capsules without considering the membrane bending rigidity, or considering the bending with the minimum bending-energy configurations (shapes at which the bending-energy has a global minimum) being uniform-curvature shapes, the capsules will always achieve the steady tank treading motion (a capsule deforms to a steady shape with a steady inclination and the membrane rotates around the liquid inside). However, for three-dimensional non-spherical capsules without membrane bending rigidity, such a steady mode does not exist; with the shear rate decreasing, the three-dimensional capsules’ motion changes from swinging mode (a capsule undergoes periodic shape deformation and inclination oscillation while its membrane is rotating around the liquid inside) to flipping mode. The deformation of two-dimensional capsules, with their initial non-circular shapes taken as the minimum bending-energy configurations, is also considered. It is quite interesting to find such two-dimensional capsules behave qualitatively similar to three-dimensional capsules: there is a swinging-to-flipping transition induced by lowering the shear rate.

The effect of cell density on the fluid dynamics and oxygen transport in a micro-bioreactor with a tissue engineering scaffold was investigated. Variations of the permeability and porosity of the scaffold with cell density were estimated by a simple model. Based on the permeability and the porosity obtained, the flow and oxygen transport in a micro-bioreactor were simulated numerically. It was found that the flow rate passing through the scaffold is reduced with an increase in cell density. The oxygen concentration within the scaffold also decreases with an increase in cell density, due to lower oxygen convection caused by lower porous flow rate and higher oxygen consumption. The results suggest that, for high cell density culture, the oxygen concentration within the scaffold may be overestimated if the cell density effect is neglected.

The transient deformation of cylindrical liquid-filled capsules with elastic membranes is studied in simple shear flow at small and moderate Reynolds numbers. The aim of the study is to investigate the inertia effect on the deformation of elastic capsules and the flow structure around them. The simulation is based on a hybrid method which introduces the immersed boundary concept in the framework of the multi-block lattice Boltzmann model. The deformation of capsules with circular and elliptical resting shapes is studied; the membrane constitutive model is Hooke’s law. However, the present model can be implemented to capsules with arbitrary resting configurations and constitutive laws. The simulation results show that inertia has important effect on the transient deformation process, steady configuration and tank treading frequency of a capsule in simple shear flow; Inertia also significantly affects the flow structure and vorticity field around and inside a capsule.

The flow environment in the micro-bioreactor with a tissue engineering scaffold was numerically modeled. The finite volume method based on multi-block grid was applied to simulate the coupled flow and oxygen transport in both porous medium and homogenous fluid regions. At porous–fluid interface, a stress jump condition that includes both viscous and inertial effects was imposed. A parametric study was performed to investigate the effects of Reynolds, Darcy, and Damkohler numbers on the flow and oxygen concentration fields inside and outside the scaffold. The minimum oxygen concentration in the scaffold and its location under different conditions were summarized.

Vortex breakdown effects on oxygen concentration distributions in a micro-bioreactor were investigated by a finite volume model. The bioreactor consists of a cylindrical chamber with a rotating bottom wall. The minimum oxygen concentration and volumetric oxygen transfer coefficient were summarized at different Reynolds numbers, Damkohler numbers as well as bioreactor aspect ratios. It was found that vortex breakdown extends the axis region where oxygen concentration is higher. Also vortex breakdown tends to induce a uniform oxygen concentration distribution in the bioreactor. Thus, the occurrence of vortex breakdown is of benefit to animal cell culture. Compared with that in the bioreactor with a rigid lid, vortex breakdown in the bioreactor with free surface may be better for animal cell culture as the bubble has larger size and may occur apart from the axis.

In this paper, the conjugate heat transfer in electronic cooling is numerically simulated with the newly proposed algorithm CLEARER on collocated grid. Because the solid heat source and substrate are isolated from the boundary, special attention is given to deal with the velocity and temperature in the solid region in the full field computation. The influence of openings on the substrate, heat source height and their distribution along the substrate on the maximum temperature and overall Nusselt number is investigated. The numerical results show that the openings on the substrate can enhance the heat transfer as well as increasing the heat source height, meanwhile, by arranging the heat sources coarsely in the front part and densely in the rear part of the substrate, the thermal performance can also be increased. Then the results are analyzed from the viewpoint of field synergy principle, and it is shown that the heat transfer improvement can all be attributed to the better synergy between the velocity field and temperature field, which may offer some guidance in the design of electronic devices.

A hybrid method is proposed to study the transient deformation of liquid filled capsules with elastic membranes under flow. In this method, the immersed boundary concept is introduced into the framework of lattice Boltzmann method, and the multi-block strategy is employed to refine the mesh near the capsule to increase the accuracy and efficiency of computation. A finite element model is incorporated to obtain the forces acting on the membrane nodes of the three-dimensional capsule which is discretized into flat triangular elements. The present method was validated by studying the transient deformation of initially spherical and oblate-spheroidal capsules with various membrane constitutive laws under shear flow; and there were good agreements with previous theory or numerical results. The versatility of the present method was demonstrated by studying the effects of inertia on the deformation of capsules in shear flow; and the inertia effects were found to be significant. The transient deformation of capsules with initially biconcave discoid shape in shear flow was also studied. The unsteady tank-treading motion was observed, in which the capsule undergoes periodic shape deformation and inclination oscillation while its membrane is rotating around the liquid inside. To our knowledge, this motion of three-dimensional biconcave discoid capsules has not been fully recovered by numerical simulation so far.

Microchannel bioreactors have been used in many studies to investigate the fluid microenvironment around cells. In the present study, a three-dimensional numerical model was developed to simulate the fluid flow and mass transfer in a 3D flat-plate rectangular microchannel bioreactor with a monolayer of cells adherent to the bottom. The numerical results of mass transfer were well correlated in terms of two dimensionless parameters: Sherwood number at base (Sh) and effective distance (κ). The generalized results show the mass transfer characteristic in the flat-plate microchannel bioreactors, which may find applications in culturing cells in these bioreactors.

A 3D numerical model was developed to study the flow field and oxygen transport in a micro-bioreactor with a rotating magnetic bar on the bottom to mix the culture medium. The Reynolds number (Re) was kept in the range of 100-716 to ensure laminar environment for animal cell culture. The volumetric oxygen transfer coefficient (k(L)a) was determined from the oxygen concentration distribution. It was found that the effect of the cell consumption on k(L)a could be negligible. A correlation was proposed to predict the liquid-phase oxygen transfer coefficient (k(Lm)) as a function of Re. The overall oxygen transfer coefficient (k(L)) was obtained by the two-resistance model. Another correlation, within an error of 15%, was proposed to estimate the minimum oxygen concentration to avoid cell hypoxia. By combination of the correlations, the maximum cell density, which the present micro-bioreactor could support, was predicted to be in the order of 10(12) cells m(-3). The results are comparable with typical values reported for animal cell growth in mechanically stirred bioreactors.

A two-dimensional particle image tracking velocimetry (PIV) system has been used to map the velocity vector fields and Reynolds stresses in the immediate downstream vicinity of a porcine bioprosthetic heart valve at the aortic root region in vitro under pulsatile flow conditions. Measurements were performed at five different time steps of the systolic phase of the cardiac cycle. The velocity vector fields and Reynolds stress mappings at different time steps allowed us to chart a time history of the stress levels experienced by fluid particles as they move across the aortic root. This Lagrangian description of the stresses experienced by individual blood cells enabled us to estimate the propensity of shear-induced damage to platelets and red blood cells. Coupled with flow visualization techniques, the hydrodynamic consequences of introducing a porcine bioprosthetic heart valve into the aortic root was examined. Although the PIV measurements may lack the accuracy of single point measuring systems, the overall view of the flow in the aortic root region compensates for the shortcoming.

Particle Image Velocimetry (PIV), capable of providing full-field measurement of velocities and flow stresses, has become an invaluable tool in studying flow behaviour in prosthetic heart valves. This method was used to evaluate the performances of four prosthetic heart valves; a porcine bioprostheses, a caged ball valve, and two single leaflet tilting disc valves with different opening angles. Flow visualization techniques, combined with velocity vector fields and Reynolds stresses mappings in the aortic root obtained from PIV, and pressure measurements were used to give an overall picture of the flow field of the prosthetic heart valves under steady flow conditions. The porcine bioprostheses exhibited the highest pressure loss and Reynolds stresses of all the valves tested. This was mainly due to the reduction in orifice area caused by the valve mounting ring and the valve stents. For the tilting disc valves, a larger opening angle resulted in a smoother flow profile, and thus lower Reynolds stresses and pressure drops. The St. Vincent valve exhibited the lowest pressure drop and Reynolds stresses.

A comparative flow study has been conducted on two configurations of the Fontan operations for congenital heart defects in which the right ventricle is by-passed. The study was made on rigid in vitro models of the atriopulmonary and cavopulmonary connections under steady-flow conditions. It involved using pressure and flow measurements to determine the pressure-drop coefficient, pressure-energy-loss coefficient and total-energy-loss coefficient. The cavopulmonary model was found to have much lower flow losses compared to the atriopulmonary model, especially at flow rates about 5 l min-1.

An experimental investigation has been carried out on a wind-assisted ship propulsion device (WASP), consisting of a cylinder-flap wing with boundary layer suction. Measurements of the pressure distribution, lift and drag have been presented for various angular locations of the suction area and flap. It was found that a lift coefficient of 4.2 is obtained, with suction coefficient of 0.09, when the suction area and flap are symmetrically placed at angular locations of 110° from the relative wind axis; the corresponding lift-drag ratio is 6. Also presented is a polar plot which ascertained that the propulsion force is not significantly affected by small variations (±10°) in the angular position of the flap. However, a corresponding variation in the suction location will significantly affect the propulsion force.

An experimental study was carried out on a cylinder undergoing harmonic oscillation in line with an indident flow at Reynolds numbers of 27×10 3 and 54×10 3 . Measurements were obtained of the ensemble-averaged cyclic pressure distribution, from which the cyclic in-line force was determined. It was found that the cyclic force could be approximated by a simple empirical relation based on a quasi-steady consideration of the flow. The quasi-steady drag coefficient was determined for various amplitude to diamater ratios from 0.4 to 2.4, and for a reduced velocity of up to 200. The base pressure coefficient was found to increase with the oscillation amplitude.

An experimental investigation has been made of the fluid forces acting on a circular cylinder oscillating in line with a uniform flow. The in-line forces were determined from measurements of the ensemble-averaged, cyclic pressure-distribution. The Morison equation, together with the least square method, was then used to evaluate the hydrodynamic coefficients of drag and inertia. Measurements of the drag coefficient are presented for large reduced velocities from 20 to 110, and Keulegan-Carpenter number from 2.5 to 15. It was found that the inertia coefficient at large reduced velocities, up to about 100, could be determined from the Morison equation provided the Keulegan-Carpenter number has a large value of about 15.