Effect of convective disturbances induced by g-jitter on the periodic precipitation of lysozyme

Numerical simulations are carried out to investigate the crystallization process of a protein macromolecular substance under two different conditions: pure diffusive regime and microgravity conditions present on space laboratories. The configuration under investigation consists of a protein reactor and a salt chamber separated by an “interface”. The interface is strictly related to the presence of agarose gel in one of the two chambers. Sedimentation and convection under normal gravity conditions are prevented by the use of gel in the protein chamber (pure diffusive regime). Under microgravity conditions periodic time-dependent accelerations (g-jitter) are taken into account. Novel mathematical models are introduced to simulate the complex phenomena related to protein nucleation and further precipitation (or resolution) according to the concentration distribution and in particular to simulate the motion of the crystals due to g-jitter in the microgravity environment. The numerical results show that gellified lysozyme (crystals “locked” on the matrix of agarose gel) precipitates to produce “spaced deposits”. The crystal formation results modulated in time and in space (Liesegang patterns), due to the non-linear interplay among transport, crystal nucleation and growth. The propagation of the nucleation front is characterized by a wavelike behaviour. In microgravity conditions (without gel), g-jitter effects act modifying the phenomena with respect to the on ground gellified configuration. The role played by the direction of the applied sinusoidal acceleration with respect to the imposed concentration gradient (parallel or perpendicular) is investigated. It has a strong influence on the dynamic behaviour of the depletion zones and on the spatial distribution of the crystals. Accordingly the possibility to obtain better crystals for diffraction analyses is discussed.     

Vibration-induced particle drift in a fluid cell under microgravity

A theoretical investigation into the effect of small vibrations on the behaviour of a small particle contained in a fluid cell under microgravity is presented. Diffusion-controlled material processing such as protein crystal growth can be adversely affected by small vibrations called g-jitter, if a relative motion is induced between the particle and surrounding fluid. When a fluid cell containing a small particle such as a protein crystal is vibrated parallel to the wall nearest to the particle, the particle oscillates with a certain amplitude and a hydrodynamic force in the direction normal to the wall is induced. Theoretical models based on an inviscid fluid assumption are used to predict the particle amplitude variation and drifting motion. Due to an external vibration such as g-jitter, the oscillating particle is predicted to drift towards the wall and the particle oscillation amplitude to decrease slightly as the distance between the particle and wall is reduced. The reduction in particle ampitude also depends on the particle-to-fluid density ratio. The particle drift towards the nearest wall acclerates due to an increasing attraction force, and the drifting speed increases with both the vibration frequency and particle diameter. Even for small protein crystals with a density close to that of the fluid, the time required to drift from the center of the fluid cell to the wall is predicted to be much shorter than the growth time.     

Droplet Deformation and 2-D/3-D Marangoni Flow Phenomena in Droplets Levitated by Electric Fields

An integrated numerical model is presented for free surface phenomena and Marangoni fluid flows in electrically levitated droplets under both terrestrial and microgravity conditions. The model development is based on the boundary element solution of the Maxwell equations simplified for electrostatic levitation applications and the free surface deformation that is primarily caused from the surface Maxwell stresses resulting from the applied electric fields. The electric and free surface model is further integrated with a finite element model for the surface-tension-induced fluid flows in the levitated droplets. Both 2-D and 3-D fluid flow structures may be developed in the electrically levitated droplets depending on the applied laser heating sources. The integrated model is applied to study the electric field distribution, free surface deformation, and 2-D and 3-D internal fluid flow structures in normal and microgravity for single, symmetric two-beam, four-beam, and six-beam laser heating arrangements. Among these arrangements, the six-beam arrangement with equal heating intensity gives the smallest temperature difference and the smallest maximum velocity.     

Bubble Motion near a Wall Under Microgravity: Existence of Attractive and Repulsive Forces

A numerical simulation for a bubble motion near a wall under microgravity, relevant to material processing such as crystal growth in space, is presented based on a mass conservation level set algorithm to predict the bubble behavior affected by the near wall. The simulation for the wall effect on the bubble driven by an external acceleration parallel with the near wall referred to as g-jitter confirms for the first time the existence of the wall attractive force to the bubble near the wall under certain conditions such as the initial distance between the bubble and the wall, density and viscosity ratios between the bubble and surrounding liquid under microgravity. The wall effect mechanism is explained, and the results show that the wall attractive force increases with the increasing of density ratio. Moreover, the simulation for the wall repulsive effect on the bubble near the wall under microgravity has been carried out as well.     

Effect of Viscosity on Vibration-Induced Motion of a Spherical Particle Suspended in a Fluid Cell

Production of protein and semi-conductor crystals with advanced quality and properties is possible under microgravity conditions due to the suppression of convection effects. However, aboard space platforms, g-jitter induced motions of solid particles can cause unsteady convection that may result in degradation of the properties of crystals produced. There are different effects of g-jitter on small particles suspended in a fluid cell which are not fully understood. To investigate these small vibration effects, ground experiments were conducted by suspending a spherical particle with a thin wire in a rectangular fluid cell and subjecting the cell and particle to horizontal vibrations with different frequencies and amplitudes. The fluid viscosity was varied to investigate the attraction or repulsion force induced in the direction normal to the direction of the vibration. The force was found to change from attraction to repulsion with an increase in the fluid viscosity and increase with the increasing vibration frequency and amplitude.     

Comparison on the convective effects in high temperature solution in space and on ground

A space experiment on a mixture of Li₂B₄O₇+KNbO₃ cellular growth in high temperature solution was carried on board of the recoverable satellite in 1996. Numerical simulation of velocity profile and temperature profile in the high temperature solution of a loop-shaped Pt wire heater was made by using the commercial computational code ANSYS. The numerical simulation of two-dimensional model is applied to study the convective effects in space and on ground. The results of numerical modeling are compared with the space and ground experimental data obtained in 1996. It shows that the complicated coupled vortex modes in high temperature solution are found for the crystal growth on the ground and the gravitation has an important influence on the velocity profile and temperature profile in the solution. But in space, when the value of the gravity arrives at a certain value, the simplest flow modes appear and the fluid flow effects have little influence on the instability resulted from the heat transport and mass transport in crystal growth from the melted solution. Meantime, the analysis on the comparison of the crystal growth between space and ground experiments agrees well with that of the numerical simulation. The velocity profile and temperature profile develop to the steady crystal growth with decreasing the gravity level and the convection driven by surface tension is the main factor to form the uniform cellulation.     

Experimental investigation of Marangoni convection and vibration-induced crystal motion during protein crystal growth

The occurrence of Marangoni convection during cytochrome c’ crystal growth and vibration-induced motion of lysozyme crystals were investigated using a High Density Protein Crystal Growth (HDPCG) apparatus. Particle image velocimetry was used to visualize fluid motion, but no particle motion was observed, which suggests that under the experimental conditions used, Marangoni convection is not a significant cause of fluid and crystal motion. When horizontal vibrations of controlled amplitude and frequency were applied to the HDPCG apparatus, lysozyme crystals located on the liquid-vapour interface of the HDPCG cell made significant movements up to 0.5mm in amplitude and velocities reaching 0.06mm/s. These results from the Marangoni convection and horizontal vibration experiments suggest that protein crystal movements observed in past space experiments were most likely caused by g-jitter on the spacecraft rather than Marangoni convection.     

Two‐fluid model with interface sharpening

Two‐fluid models are applicable for simulations of all types of two‐phase flows ranging from separated flows with large characteristic interfacial length scales to highly dispersed flows with very small characteristic interfacial length scales. The main drawback of the two‐fluid model, when used for simulations of stratified flows, is the numerical diffusion of the interface. Stratified flows can be easily and more accurately solved with interface tracking methods; however, these methods are limited to the flows, that do not develop into dispersed types of flows. The present paper describes a new approach, where the advantage of the two‐fluid model is combined with the conservative level set method for interface tracking. The advection step of the volume fraction transport equation is followed by the interface sharpening, which preserves the thickness of the interface during the simulation. The proposed two‐fluid model with interface sharpening was found to be more accurate than the existing two‐fluid models. The mixed flow with both: stratified and dispersed flow, is simulated with the coupled model in this paper. In the coupled model, the dispersed two‐fluid model and two‐fluid model with interface sharpening are used locally, depending on the parameter which recognizes the flow regime. Copyright © 2010 John Wiley & Sons, Ltd.     

Influence of G-jitter on the characteristics of a non-premixed flame: Experimental approach

The combustion of a flat plate in a boundary layer under microgravity conditions, which was first described by Emmons, is studied using a gas burner. Magnitude of injection and blowing velocities are chosen to be characteristic of pyrolyzing velocity of solid fuels, and of ventilation systems in space stations. These velocities are about 0.1 m/s for oxidiser flow and 0.004m/s for fuel flow. In this configuration, flame layout results from a coupled interaction between oxidiser flow, fuel flow and thermal expansion. Influences of these parameters are studied experimentally by means of flame length and standoff distance measurements using CH* chemiluminescence’s and visible emission of the flame. Flow was also studied with Particle Image Velocimetry (PIV). Inert flows, with and without injection, and reacting flow in a microgravity environment were considered to distinguish aerodynamic from thermal effect. Thermal expansion effects have been shown by means of the acceleration of oxidiser flow. Three-dimensional effects, which are strongly marked for high injection velocities were studied. Three-dimensional tools adaptability to parabolic flights particular conditions were of concern. Flame sensitivity to g-jitters was investigated according to g-jitters frequency and range involved by parabolic flights. It appears that flame location (standoff distance), flame characteristics (length, thickness, brightness) and the aerodynamic field of the low velocity reacting flow are very much affected by the fluctuation of the gravity level or g-jitter. The lower the g-jitter frequency is, the higher the perturbation. Consequently it is difficult to perform relevant experiments for a main flow velocity lower than 0.05m/s. DNS calculations confirm the present observations, but most of the results are presented elsewhere.     

3D numerical simulations of thermodiffusion experiment for a ternary mixture on-board foton

The phenomenon of mass flux in a mixture due to a temperature gradient is known as the Soret effect. Accurate experimental and theoretical models are needed for a better understanding and effective characterisation of situations involving coupled transport processes as in hydrocarbon reservoirs. This requires precise knowledge of the transport coefficients particularly the Fick and Soret diffusion coefficients. We have investigated the effect of residual-g and (very) low-frequency g-jitters encountered on-board spacecraft FOTON on mass-thermo-fluid dynamics in the presence of Soret effect. Results revealed that the diffusion process is slightly affected by the g-jitter on board the FOTON platform, which indicates that FOTON is a good platform to conduct near perfect microgravity environment.     

Effect of a Rotating Magnetic Field on Convection Stability and Crystal Growth in Zero Gravity and on the Ground

A numerical study of the flows arising in a conducting liquid under the action of a rotating magnetic field as well as under its interaction with gravitational and thermocapillary convection has been made. The boundaries of the transition to the oscillating regime of convective flows have been determined. Regions of mixed flows, in which the impurity macrosegregation in crystals grown by the Bridgman and floating-zone methods decrease, have been revealed. It has been shown that regions of flows in which both a smooth increase in the impurity macrosegregation and a change in the form of a clearly defined extremum are observed also exist. The possibilities of mathematical modeling of geophysical problems with the use of a rotating magnetic field are discussed.     

微重力条件下熔体中对流过程的数值模拟

微重力条件下生长优质晶体遇到的最大问题是要控制晶体生长的条件，抑制由于重大的减弱而引起的熔体中的热毛细时流。但是，用实验来解决这些问题费用高，周期也长，而且有时完全用实验来模拟也是很困难的。用数值计算方法来模拟微重力条件下熔体中的对流过程是空间晶体生长研究的一个重要的方向，计算结果对控制空间生长晶体和抑制熔体中的对流有指导意义。对微重力条件下熔体中对流发生、发展的过程进行了数值研究。以有限差分法研究了沿上表面为自由表面的水平区域不同边界条件下的熔体中的对流过程。     

Numerical and experimental investigation of solid particle motion in a fluid cell under microgravity

This research aims at understanding the mechanisms and parameters that affect particle motion induced by g-jitter. Simultaneous experimental (parabolic flights) and numerical work was conducted to study the motion of a spherical particle in a microgravity environment subjected to vibrations in either horizontal or vertical direction. The data from both vertically and horizontally vibrated experiments clearly show that the investigated particle properties, size and density, affect the amplitude of the particle motion. In all experiments the amplitude of the particle motion increased with the density and diameter of the particle in the cell frame of reference. It was also observed that the particles moved at the frequency equal to that of applied vibration. These results are consistent with the preliminary numerical simulation predictions. Numerical simulations also showed that increasing the viscosity of the surrounding fluid would reduce the amplitude of the particle motion.     

Theory and simulation of buoyancy-driven convection around growing protein crystals in microgravity

We present an order-of-magnitude analysis of the Navier-Stokes equations in a time-dependent, incompressible and Boussinesq formulation. The hypothesis employed of two different length scales allows one to determine the different flow regimes on the basis of the geometrical and thermodynamical parameters alone, without solving the Navier-Stokes equations. The order-of-magnitude analysis is then applied to the field of protein crystallization, and to the flow field around a crystal, where the driving forces are solutal buoyancy-driven convection, from density dependence on species concentration, and sedimentation caused by the different densities of the crystal and the protein solution. The main result of this paper is to provide predictions of the conditions in which a crystal is growing in a convective regime, rather than in the ideal diffusive state, even under the typical microgravity conditions of space platforms.     

Theory and simulation of buoyancy-driven convection around growing protein crystals in microgravity

We present an order-of-magnitude analysis of the Navier-Stokes equations in a time-dependent, incompressible and Boussinesq formulation. The hypothesis employed of two different length scales allows one to determine the different flow regimes on the basis of the geometrical and thermodynamical parameters alone, without solving the Navier-Stokes equations. The order-of-magnitude analysis is then applied to the field of protein crystallization, and to the flow field around a crystal, where the driving forces are solutal buoyancy-driven convection, from density dependence on species concentration, and sedimentation caused by the different densities of the crystal and the protein solution. The main result of this paper is to provide predictions of the conditions in which a crystal is growing in a convective regime, rather than in the ideal diffusive state, even under the typical microgravity conditions of space platforms.     

Three-dimensional analysis for liquid hydrogen in a cryogenic storage tank with heat pipe–pump system

This paper presents a study on fluid flow and heat transfer of liquid hydrogen in a zero boil-off cryogenic storage tank in a microgravity environment. The storage tank is equipped with an active cooling system consisting of a heat pipe and a pump–nozzle unit. The pump collects cryogen at its inlet and discharges it through its nozzle onto the evaporator section of the heat pipe in order to prevent the cryogen from boiling off due to the heat leaking through the tank wall from the surroundings. A three-dimensional (3-D) finite element model is employed in a set of numerical simulations to solve for velocity and temperature fields of liquid hydrogen in steady state. Complex structures of 3-D velocity and temperature distributions determined from the model are presented. Simulations with an axisymmetric model were also performed for comparison. Parametric study results from both models predict that as the speed of the cryogenic fluid discharged from the nozzle increases, the mean or bulk cryogenic fluid speed increases linearly and the maximum temperature within the cryogenic fluid decreases.     

A numerical simulation study for the Czochralski growth process of Si under magnetic field

The article presents results of the numerical simulations carried out for the transport phenomena occurring during the Czochralski crystal growth process. Due to computational constraints, the simulations were kept limited to axisymmetric geometries. The simulation model gives special attention to the crystal–melt interface and oxygen transport, and treats the crystal–melt interface according to Stefan’s balance, by explicitly moving the grids. Oxygen evaporation at the free surface is expressed by balancing the corresponding fluxes. Marangoni convection due to temperature gradients is also incorporated into the model. The role of an applied axial magnetic field in controlling fluid flow, interface shape, and oxygen levels is studied in detail. The effect of crystal and crucible rotations is also examined under the influence of the magnetic field. Simulation results show that the application of an axial magnetic field leads to flatter interfaces and lower oxygen concentration levels, but makes the oxygen distribution non-uniform at the crystal–melt interface.     

Effect of rotation on surface tension driven flow during protein crystallization

The effect of rotation on surface tension gradient driven flow, also known as Marangoni convective flow, during protein crystallization is modeled and studied computationally under microgravity conditions, where the surface tension gradient force is the main significant driving force. The main parameters are the solutal Marangoni number M_c, representing the surface tension gradient force and the Taylor number Ta representing the rotational effect. The numerical computations for various values of the parameters and low gravity levels indicated nontrivial competing effects, due to surface tension gradient, centrifugal and Coriolis forces on the flow adjacent to the protein crystal interface and the associated solute flux. In particular, for given values of M_c, certain values of Ta were detected where the Sherwood number (Sh), representing the convective solute flux, and the convective flow effects are noticeably reduced. These results can provide conditions under which convective flow transport during the protein crystallization approaches the diffusion limited transport, which is desirable for the production of higher quality protein crystals.     

A fast integral approach for drag force calculation due to oscillatory slip stokes flows

In this paper, we describe an efficient numerical method for modelling oscillatory incompressible slip Stokes flows in three dimensions. The efficiency is achieved by employing an integral approach combined with an accelerated boundary‐element‐method (BEM) solver. First the integral representations for slip flows with two different slip models are formulated. The resulting integral equations are then solved using the BEM combined with the precorrected‐FFT accelerated technique. 3D numerical codes have been developed based on the method described above. These codes are then used to calculate the drag forces on oscillating objects immersed in an unbounded slip flow. Three objects are considered, namely a sphere, a pair of plates and a comb structure. The simulated drag forces on these objects obtained from the two slip models are compared. In the sphere case, the simulated results are also compared with the analytical solutions for both the steady‐state case and the no‐slip oscillatory case and are found to be in good agreement. In addition, qualitative comparison of the simulation results with the experimental results in the plate problem is also presented in this paper. Copyright © 2004 John Wiley & Sons, Ltd.