Thermophoretic Force on a Small Particle Suspended in a Plasma with a Combined Specular and Diffuse Reflection at the Particle Surface

Additional kinetic-theory analytical results are presented concerning the thermophoretic force acting on a spherical nonmetallic or metallic, nonevaporating or evaporating particle suspended in a plasma for the extreme case of free-molecule regime and thin plasma sheath. A combined specular and diffuse reflection of the atoms incident on or formed in the ion–electron recombination process at the particle surface has been taken into account in this analysis as an extension of the previous paper (Xi Chen, J. Phys. D: Appl. Phys. 30, 826–841, 1997). It has been shown that the specular reflection fraction of gas particles at the surface does not affect the thermophoretic force acting on a nonevaporating, metallic or nonmetallic, spherical particle, but they affect significantly the evaporation-added thermophoretic force. The evaporation-added thermophoretic force decreases linearly with the increase of the specular reflection fraction, and the decreasing rate for a nonmetallic evaporating particle is much greater than that for a metallic one at high plasma temperatures.     

Thermophoretic force on a metallic or nonmetallic particle immersed into a rarefied Plasma

Analytical results of the thermophoretic force on a metallic or nonmetallic spherical particle immersed into a rarefied plasma with a heat flux within the plasma are presented for the extreme case of free-molecule regime and thin plasma sheath. It has been shown that the thermophoresis is predominantly caused by atoms at low plasma temperatures with negligible gas ionization, while it is mainly due to ions and electrons at high plasma temperatures with great degree of ionization. The ion flux incident to a particle is constant on the whole sphere surface, while the electron flux to the metallic sphere is dependent on the -position with slightly greater value at the fore stagnation point. Consequently, there is a small difference between the metallic and nonmetallic spheres in their -distributions of the floating potential on the surface, which causes the thermophoretic force on a nonmetallic sphere to be appreciably greater than that on a metallic sphere at high plasma temperatures. Expressions for the total thermophoretic force on a metallic sphere and its components due to, respectively, atoms, ions, and electrons have been given in a closed form. Calculated results are also presented on the effects of pressure and of electron/heavy-particle temperature ratio. These results can be understood based on the variation of atom, ion, and electron thermal conductivities with the gas pressure, the temperature, and the temperature ratio.     

Drag force acting on an evaporating particle immersed in a rarefied plasma flow

Analytical expressions are presented for the drag force acting on an evaporating or nonevaporating particle immersed in a plasma flow for the extreme case of free-molecule flow regime and thin plasma .sheath. It is shown that the drag force on a spherical particle is proportional to the square of the particle radius and to the relative velocity between the particle and the bulk plasma at low speed ratios. The existence of a relative velocity between the particle and the plasma results in a nonuniform heat flux distribution with its rnaximum value at the frontal stagnation point of tire sphere. This nonuniform distribution of the local heat fux density causes a nonuniforrn distribution of the local evaporated-mass flux and vapor reaction force around the surface of an evaporating particle, and thus induces an additional force on the particle. Consequently, the drag force acting on art evaporating particle is always greater than that on a nonevaporating one. This additional drag force due to particle evaporation is more significant for nonmetallic particles and for particle materials with lower latent heat of evaporation and lower vapor molecular mass. It increases with increasing plasma temperature and with decreasing gas pressure at the high plasma temperatures associated with appreciable gas ionization. The drag ratio increases with increasing electron/heavy-particle temperature ratio at high electron temperatures for a two-temperature plasma.     

Effects of Various Forces on Particle Distribution and Thermal Features of Suspensions Containing Alumina Nanoparticles

The two-phase Euler-Lagrange method has been used in order to investigate the effects of various forces on particle distribution and thermal characteristics of the water-based Al₂O₃ nanofluid flow inside a pipe under uniform wall heat flux. In the Euler-Lagrange approach, the particles are individually tracked in Lagrangian frame, while the fluid is evaluated in Eulerian frame. Brownian, thermophoretic, drag, lift, and virtual mass forces have been considered. Moreover, experimental data from various researchers were used to analyze the results. Concentration distribution is nonuniform at cross section of the pipe which increasing each parameters of Reynolds number, mean concentration and particles size will intensify its nonuniformity. This nonuniformity will make velocity profile flatter. The Brownian force makes the particle distribution more uniform, whereas the thermophoretic force enhances nonuniformity of the particle distribution. The effects of not considering the Brownian and thermophoretic forces on heat transfer are more significant for finer particles and higher concentrations. Furthermore, at lower Reynolds number, the Brownian force incorporates a more significant role especially in farther distances from entrance.      

Investigation of the Velocity Field and Nanoparticle Concentration Distribution of Nanofluid Using Lagrangian-Eulerian Approach

In this study, we use the Lagrangian-Eulerian approach to determine the concentration distribution and velocity of nanoparticles are investigated in nanofluid. Furthermore, the velocity of the fluid phase affected by the particle movement is examined. Moreover, the effects of Brownian, thermophoretic, gravitational,, and drag forces on particles and fluid velocity and nanoparticle distribution are studied, as are the effects of Reynolds number on the concentration distribution.According to the results of this study, particles are not uniformly distributed, rather, they areconcentrated more in the vicinity of the centerline of the pipe than the wall; the cause of this lack of uniform distribution is due to Brownian and thermophoretic forces. In addition, the results of this study show that the effects of Brownian forces on nanoparticle distribution and velocity field is stronger than that of other forces including thermophoretic ones.     

Thermophoretic force acting on an evaporating particle suspended in a rarefied plasma

Analytical results of the thermophoretic force on an evaporating spherical particle immersed in a rarefied plasma with a large temperature gradient are presented for the extreme case of free-molecule regime and thin plasma sheath. It has been shown that the existence of a temperature gradient in the plasma causes a nonuniform distribution of the local heat flux density on the sphere surface with its maximum value at the fore-stagnation point of the sphere, although the total heal flux to the whole particle is independent of the temperature gradient existing in the plasma. This nonuniform-distribution of the local heat flux density causes a nonuniform distribution of the. local evaporated-mass flux and related reaction force around the surface of an evaporating particle, and thus causes an additional force on the particle. Calculated results show that the thermophoretic force on an evaporating particle may substantially exceed that on a nonevaporating one, especially for the case of a metallic particle (with infinite electric conductivity). The effect of evaporation on the thermophoretic force is more pronounced as the evaporation latent heat of the particle material is comparatively low and as high plasma temperatures are involved.     

An experimental study of the drag force on a sphere exposed to an argon thermal plasma flow

Experimental data are presented concerning the drag force on a stationary phere exposed to an argon plasma flow with temperatures about 10⁴ K and velocities about 10² m/s. A novel probe construction has been employed in the drag measurements in order to exclude the effect of the supporting wire on the sphere drag data. By using the new probe construction with a compensating wire, drag forces on an individual steel sphere in the plasma flow have been measured and compared with those obtained by using the probe construction ernployed by a few previous authors. Experimental results show that the measured drag forces are always less than their counterparts obtained from the standard sphere-drag curve under isothermal flow conditions with the same Reynolds numbers based on the oncoming plasma properties. The drag force on a sphere increases only slightly with the increasing surface temperature of the sphere before it melts. Appreciable diference was found between the experimental data and the predicted results of the available expressions for drag on a sphere exposed to a thermal plasma flow. Further research effort is required to build a more suitable drag correlation.     

Inertial separation in a contraction-expansion array microchannel

We report a contraction-expansion array (CEA) microchannel that allows inertial size separation by a force balance between inertial lift and Dean drag forces in fluid regimes in which inertial fluid effects become significant. An abrupt change of the cross-sectional area of the channel curves fluid streams and produces a similar effect compared to Dean flows in a curved microchannel of constant cross-section, thereby inducing Dean drag forces acting on particles. In addition, the particles are influenced by inertial lift forces throughout the contraction regions. These two forces act in opposite directions each other throughout the CEA microchannel, and their force balancing determines whether the particles cross the channel, following Dean flows. Here we describe the physics and design of the CEA microfluidic device, and demonstrate complete separation of microparticles (polystyrene beads of 4 and 10 μm in diameter) and efficient exchange of the carrier medium while retaining 10 μm beads.     

Semi-analytical modeling of non-premixed counterflow combustion of metal dust

In this study, a semi-analytical model is developed for non-premixed combustion of metal dusts in counterflow configuration. Combustion domain is divided into three separate zones, each of which possesses corresponding mass and energy conservation equations as well as boundary and jump conditions. Metal dust, assumed to be aluminum, undergoes an Arrhenius-type reaction with oxidizer, when it is heated enough to reach the ignition temperature. Dimensionless forms of conservation equations are derived and utilized to elucidate the combustion characteristics. The effects of oxidizer Lewis number and fuel mass concentration on the flame position and temperature are discussed thoroughly. In addition, temperature distribution of the whole domain is calculated by numerically solving the system of partial differential equations. In order to track particles through combustion domain, Lagrangian equations of motion are solved either mathematically or numerically, considering thermophoretic, weight, buoyancy and drag forces. The effects of thermophoretic force on the particle path are investigated, and the deviation of particle from carrier neutral gas direction is obtained. The results showed a great agreement with the data reported in the literature highlighting the fact that the presented model is an efficient one to accurately model the non-premixed counterflow combustion of metal dust.

     

Surface Potential of Coal Particles in Coal-Oil Mixture and Control of Settling Stability Under Gravity

This work deals with the problem of settling under gravity for coal-oil mixtures when the concentration of particles is large. The repulsive force necessary to ensure stability of coal particle is vital. The net forces acting on the particle include gravity, buoyancy, viscous drag force, and electrostatic repulsive force. Accordingly, the equation at the terminal velocity at settling is obtained along with a critical surface potential to prevent settling under gravity.     

Dynamic drag force based on iterative density mapping: A new numerical tool for three‐dimensional analysis of particle trajectories in a dielectrophoretic system

Dielectrophoresis is a widely used means of manipulating suspended particles within microfluidic systems. In order to efficiently design such systems for a desired application, various numerical methods exist that enable particle trajectory plotting in two or three dimensions based on the interplay of hydrodynamic and dielectrophoretic forces. While various models are described in the literature, few are capable of modeling interactions between particles as well as their surrounding environment as these interactions are complex, multifaceted, and computationally expensive to the point of being prohibitive when considering a large number of particles. In this paper, we present a numerical model designed to enable spatial analysis of the physical effects exerted upon particles within microfluidic systems employing dielectrophoresis. The model presents a means of approximating the effects of the presence of large numbers of particles through dynamically adjusting hydrodynamic drag force based on particle density, thereby introducing a measure of emulated particle–particle and particle–liquid interactions. This model is referred to as “dynamic drag force based on iterative density mapping.” The resultant numerical model is used to simulate and predict particle trajectory and velocity profiles within a microfluidic system incorporating curved dielectrophoretic microelectrodes. The simulated data are compared favorably with experimental data gathered using microparticle image velocimetry, and is contrasted against simulated data generated using traditional “effective moment Stokes‐drag method,” showing more accurate particle velocity profiles for areas of high particle density.     

On the effect of thermophoretic force,gravitational force,and particle–particle interactions in field-flow fractionation

The theoretical calculations confirmed that the gravitational force cannot be neglected in all field-flow fractionation techniques separating nanometer-sized colloidal particles whenever particle diameter is approximately 200?nm and larger. Particle–particle repulsive interactions, mostly electrostatic repulsions, influence substantially concentration distribution established by any effective field acting across the fractionation channel, as confirmed explicitly for thermophoretic force generated by temperature gradient in microthermal field-flow fractionation. The ionic strength of the carrier liquid causes the screening of the electrostatic double layer around the dispersed particles and thus influences the retention. The attractive particle–particle forces occur when the zeta potential of the particles approaches to 0?mV, the electrostatic repulsions are screened, and the aggregation of the particles is observed. The pH influences differently the size and zeta potential of the plain polystyrene latex particles and of the particles modified on the surface by the groups –COOH and –NH₂. The role of a detergent in carrier liquid is non-negligible, as demonstrated by its presence or absence in carrier liquid.     

Dielectric force and relative motion between two spherical particles in electrophoresis

When two particles close to each other are in electrophoretic motion, each particle is under the influence of the nonuniform electric field generated by the other particle. Two particles may attract or repel each other due to the dielectric force, depending on their positions in the nonuniform electric field. In this work, the dielectric interaction and the subsequent relative motion of the two arbitrarily oriented spherical particles are analyzed. The dielectric force is obtained by integrating the Maxwell stress. The result is valid for arbitrary orientations of the particles under the thin electrical-double-layer assumption. The magnitude of the dielectric force is compared to the so-called inertia-induced force, which shows that the dielectric force is normally much greater than the inertia-induced force. The relative velocity of particles is determined by the force balance between the dielectric force and the Stokes drag. The regions of attraction and repulsion are defined. It is shown that a pair of particles eventually aligns parallel to the externally applied electric field, except in the case where the two particles are initially oriented perpendicular to the electric field. A closed-form analytical solution is obtained for the particle trajectory by using the approximate expression for the dielectric force valid for not-too-closely located particles.     

Micro-wilhelmy and related liquid property measurements using constant-diameter nanoneedle-tipped atomic force microscope probes

The micro-Wilhelmy method is a well-established method of determining surface tension by measuring the force of withdrawing a tens of microns to millimeters in diameter cylindrical wire or fiber from a liquid. A comparison of insertion force to retraction force can also be used to determine the contact angle with the fiber. Given the limited availability of atomic force microscope (AFM) probes that have long constant diameter tips, force-distance (F-D) curves using probes with standard tapered tips have been difficult to relate to surface tension. In this report, constant diameter metal alloy nanowires (referred to as "nanoneedles") between 7.2 and 67 microm in length and 108 and 1006 nm in diameter were grown on AFM probes. F-D and Q damping AFM measurements of wetting and drag forces made with the probes were compared against standard macroscopic models of these forces on slender cylinders to estimate surface tension, contact angle, meniscus height, evaporation rate, and viscosity. The surface tensions for several low molecular weight liquids that were measured with these probes were between -4.2% and +8.3% of standard reported values. Also, the F-D curves show well-defined stair-step events on insertion and retraction from partial wetting liquids, compared to the continuously growing attractive force of standard tapered AFM probe tips. In the AFM used, the stair-step feature in F-D curves was repeatably monitored for at least 0.5 h (depending on the volatility of the liquid), and this feature was then used to evaluate evaporation rates (as low as 0.30 nm/s) through changes in the surface height of the liquid. A nanoneedle with a step change in diameter at a known distance from its end produced two steps in the F-D curve from which the meniscus height was determined. The step features enable meniscus height to be determined from distance between the steps, as an alternative to calculating the height corresponding to the AFM measured values of surface tension and contact angle. All but one of the eight measurements agreed to within 13%. The constant diameter of the nanoneedle also is used to relate viscous damping of the vibrating cantilever to a macroscopic model of Stokes drag on a long cylinder. Expected increases in drag force with insertion depth and viscosity are observed for several glycerol-water solutions. However, an additional damping term (associated with drag of the meniscus on the sidewalls of the nanoneedle) limits the sensitivity of the measurement of drag force for low-viscosity solutions, while low values of Q limit the sensitivity for high-viscosity solutions. Overall, reasonable correspondence is found between the macroscopic models and the measurements with the nanoneedle-tipped probes. Tighter environmental control of the AFM and treatments of needles to give them more ideal surfaces are expected to improve repeatability and make more evident subtle features that currently appear to be present on the F-D and Q damping curves.     

Strong magnetic field effects on solid-liquid and particle-particle interactions during the processing of a conducting liquid containing non-conducting particles

The behavior of micrometer-sized weak magnetic insulating particles migrating in a conductive liquid metal is of broad interest during strong magnetic field processing of materials. In the present paper, we develop a numerical method to investigate the solid-liquid and particle-particle interactions by using a computational fluid dynamics (CFDs) modeling. By applying a strong magnetic field, for example, 10 Tesla, the drag forces of a single spherical particle can be increased up to around 15% at a creeping flow limit. However, magnetic field effects are reduced when the Reynolds number becomes higher. For two identical particles migrating along their centerline in a conductive liquid, both the drag forces and the magnetic interaction will be influenced. Factors such as interparticle distance, Reynolds number and magnetic flux density are investigated. Shielding effects are found from the leading particle, which will subsequently induce a hydrodynamic interaction between two particles. Strong magnetic fields however do not appear to have a significant influence on the shielding effects. In addition, the magnetic interaction forces of magnetic dipole-dipole interaction and induced magneto-hydrodynamic interaction are considered. It can be found that the induced magneto-hydrodynamic interaction force highly depends on the flow field and magnetic flux density. Therefore, the interaction between insulating particles can be controlled by applying a strong magnetic field and modifying the flow field. The present research provides a better understanding of the magnetic field induced interaction during liquid metal processing, and a method of non-metallic particles manipulation for metal/ceramic based materials preparation may be proposed.     

DC-electrokinetic motion of colloidal cylinder(s) in the vicinity of a conducting wall

The boundary effects on DC-electrokinetic behavior of colloidal cylinder(s) in the vicinity of a conducting wall is investigated through a computational model. The contribution of the hydrodynamic drag, gravity, electrokinetic (i.e., electrophoretic and dielectrophoretic), and colloidal forces (i.e., forces due to the electrical double layer and van der Waals interactions) are incorporated in the model. The contribution of electrokinetic and colloidal forces are included by introducing the resulting forces as an external force acting on the particle(s). The colloidal forces are implemented with the prescribed expressions from the literature, and the electrokinetic force is obtained by integrating the corresponding Maxwell stress tensor over the particles' surfaces. The electrokinetic slip-velocity together with the thin electrical double layer assumption is applied on the surfaces. The position and velocity of the particles and the resulting electric and flow fields are obtained and the physical insight for the behavior of the colloidal cylinders are discussed in conjunction with the experimental observations in the literature.     

Influence of particle-particle interactions and particles rotational motion in traveling wave dielectrophoresis

Traveling wave dielectrophoresis provides an interesting method for the controlled movement of microsized particles in suspended mixtures, and as such is a promising tool in microfluidic technology. In this case, the electrostatic force acting on the particles has two components: one due to the spatially varying magnitude of the electric field and the other due to the spatially varying phase. The actual movement of the particle is determined by the combined effect of these two forces and corresponding torques, the viscous drag exerted by the fluid on the particle, and the electrostatic and hydrodynamic particle-particle interactions. This paper presents the first numerical simulations of the motion of particles subjected to all previous forces and torques. Our technique is based on a finite-element scheme in which the particles are moved using a direct simulation scheme respecting the fundamental equations of motion for both the fluid and the solid particles. The fluid-particle motion is resolved by the method of distributed Lagrange multipliers and the electrostatic forces are computed using the point-dipole approximation. Our simulations show that the particle behavior strongly depends on the mismatch of the dielectric properties between the particles and the fluid, and that the particle-particle interaction force as well as particles rotation speeds play crucial roles in the various regimes.     

Creeping motion of an assemblage of composite spheres relative to a fluid

The sedimentation of a homogeneous distribution of spherical composite particles and the fluid flow through a bed of these particles are investigated theoretically. Each composite particle is composed of a spherical solid core and a surrounding porous shell. In the fluid-permeable porous shell, idealized hydrodynamic frictional segments are assumed to distribute uniformly. The effect of interactions among the particles is taken into explicit account by employing a fundamental cell-model representation which is known to provide good predictions for the motion of a swarm of nonporous spheres within a fluid. In the limit of a small Reynolds number, the Stokes and Brinkman equations are solved for the flow field in a unit cell, and the drag force exerted by the fluid on the particle is obtained in a closed form. For a distribution of composite spheres, the normalized mobility of the particles decreases or the particle interactions increase monotonically with a decrease in the permeability of their porous shells. The effect of particle interactions on the creeping motion of composite spheres relative to a fluid can be quite significant in some situations. In the limiting cases, the analytical solutions describing the drag force or mobility for a suspension of composite spheres reduce to those for suspensions of solid spheres and of porous spheres. The hydrodynamic behavior for composite spheres may be approximated by that for permeable spheres when the porous layer is sufficiently thick, depending on the permeability.     

Different elution modes and field programming in gravitational field-flow fractionation. 2. Experimental verification of the range of conditions for flow-rate and carrier liquid density programming

Gravitational field-flow fractionation utilises the Earth's gravitational field as an external force that causes the settlement of particles towards the channel accumulation wall. Hydrodynamic lift forces oppose this action by elevating of particles from the channel accumulation wall. Therefore there are several possibilities to modulate the resulting force field acting on particles in gravitational field-flow fractionation. Regarding the force field programming in gravitational field-flow fractionation, this work focused on two topics: changes of the difference between particle density and carrier liquid density in Brownian and focusing elution modes and influencing of lift forces achieved by changing the flow-rate in focusing elution mode. We have found and described the experimental conditions applicable to force field programming in the case of separations of silica gel particles by gravitational field-flow fractionation. It was shown that the effect of carrier liquid viscosity in the water-methanol system is implemented as an additional factor enhancing the desired effect of carrier liquid density. Some other forces influencing the retention behaviour of the model particles are discussed.