Thermophoretic Velocity Research Articles

Light-induced self-thermophoresis of Janus spheroidal nanoparticles.

A theoretical framework is provided for determining the self-thermophoretic velocity of a light irradiated spheroidal Janus nanoparticle consisting of symmetric dielectric and perfectly conducting semi-spheroids. The analysis is based on solving the linearized Joule heating problem due to uniform laser irradiance and on explicitly determining the temperature fields inside and outside the particle. We employ the thermoelectric (Peltier- Seebeck) methodology to find the surface self - induced temperature gradient and the related slip velocity which determines the autonomous phoretic (self - propulsion) mobility of the Janus particle. Simplified explicit expressions for the self - thermophoretic velocities of spheroidal (prolate and oblate) Janus particles in terms of their aspect ratios are found and few practical limiting cases (i.e., sphere, disk and needle) are also discussed.

Thermophoretic force on nonspherical particles in the free-molecule regime.

The present paper is devoted to studying the thermophoresis of a nonspherical convex particle suspended in a gas with nonuniform temperature distribution in the free-molecule regime. Based on the gas kinetic theory and the assumption of a rigid-body collision for the gas-particle interaction, analytical expressions for the thermophoretic forces are obtained for several typical nonspherical bodies, including cylinders, spheroids, needles, disks, and cuboids. The orientation dependences of the thermophoretic forces and thermophoretic velocities are evaluated based on these expressions. It is found that the influence of the pitching effect of the nonspheres can be significant. The expressions for the orientation-averaged thermophoretic forces are also obtained under the assumption of a uniform particle orientation distribution.

Numerical modelling of thermophoresis in water-alumina nanofluid under pool boiling conditions

The Soret-effect or thermo-diffusion in liquids has been a subject of long-standing consideration for research. Numerical modelling of thermophoresis in water-alumina nanofluid subjected to sub-cooled pool boiling conditions is attempted in this paper. Pool boiling experiments are conducted using water-alumina nanofluid for different heater input conditions (50 °C–90 °C). Computational fluid dynamics (CFD) code ANSYS Fluent is used further to analyse thermophoresis in water-alumina nanofluid. 2-D steady pressure-based implicit solver with Gauss-Seidel iterative procedure is used to discretize and numerically solve the mathematical model. Pressure-correction in the numerical procedure is done using SIMPLE (Semi-implicit Method for Pressure Linked Equation) technique. Flow boiling models for micro-sized particles are revised to outfit pool boiling conditions of nanofluid. Results of temperature from the numerical model were found to have a worthy-match with measured temperature values of the experiments. Uncertainty analysis is carried out for the random variation of temperature measurements in experiments. Thermophoretic parameters, Peclet numbers (rotational/translational) and time-scale equations for diffusion are used to analyse minute particle motion due to advection/diffusion nano-scale heat transfer. Results of thermophoretic velocity reveal a diminishing effect of particle motion near heater surface with amplified heater inputs. Results of Peclet numbers (translational/rotational) reveal the significant role of very small nano particle motion on heat diffusion in nanofluids. Combined results of Peclet number and time-scale equations reveal the strengths of advection and diffusion mechanisms in the nano-scale heat transfer process.

Thermophoresis of a spherical particle in a microtube

A theoretical study is presented for the axially symmetric thermophoresis of a spherical particle in a microtube filled with a gaseous medium. The uniformly applied temperature gradient is tangential to the tube wall, which is either prescribed with the linear temperature distribution or well insulated. The Knudsen number is small and the fluid motion is characterized by a continuum flow with temperature jump, thermal creep, and frictional slip at the solid surfaces. The general solution to the thermal and aerodynamic governing equations is presented in both spherical and cylindrical coordinates, and the boundary conditions at the particle surface are enforced by a collocation technique. The collocation solutions for the particle's thermophoretic velocity, which are in good agreement with the asymptotic formula resulting from the method of reflections, are obtained for different particle, tube wall, and fluid characteristics. A tube wall prescribed with the far-field temperature distribution and an insulated tube wall influence the thermophoresis of the particle differently. The mobility of a particle confined by a tube wall without thermal creep is a decreasing function of the particle-to-tube radius ratio. When the thermal creep coefficients of the particle and of the tube wall are comparable, the thermoosmotic fluid flow caused by the wall strongly dominates the particle movement and can simply reverse its direction. In general, the influence of the confining tube on thermophoresis is significant.

Numerical Modeling of Thermophoresis and Diffusiophoresis in Water-Alumina Nano Fluids

Analysis of major heat transfer mechanisms in nanofluids specifically, thermophoresis and diffusiophoresis under pool boiling condition is attempted in this paper. Basic approach of the study tries to correlate thermophoresis in nanofluids to the behavior of rigid particles in gases. Ultimate objective of the study is to elucidate the thermophoresis/diffusiophoresis mechanism in nanofluids using thermophoretic velocity and viscosity of nanofluids. Thermophoretic velocity of water-alumina nanofluid analyzed in this study is assumed to be inversely proportional to fluid viscosity. Experiments and Computational Fluid Dynamics (CFD) tool are used for analyzing the effects of thermophoresis and diffusiophoresis on the heat transfer enhancement process. The numerical model considered for the study is a (2-D) rectangular container with the dimensions of the experimental set-up and a stainless steel heater inside it. Energy equation constituent of ANSYS Fluent is solved using a pressure based implicit solver and appropriate boundary conditions to obtain the temperature distribution pattern of the model. SIMPLE is used as the pressure correction method with Gauss-Siedel iterative method. Numerical simulation results for temperature distribution are validated using experimental readings. Thermophoretic velocity outputs derived from numerical simulation show significant movement of nanoparticles very close to realistic values. However, numerical results of viscosity, specific heat and diffusion coefficient of nanofluids were found to deviate from the results of the experiments. The dependency effect of these parameters needs further attention.

Dry and Direct Deposition of Aerosol-Synthesized Single-Walled Carbon Nanotubes by Thermophoresis.

Single-walled carbon nanotubes (SWCNTs) show great potential as an active material in electronic and photonic devices, but their applicability is currently limited by shortcomings in existing deposition methods. SWCNTs can be dispersed from liquid solutions; however, their poor solubility requires the use of surfactants and ultrasonication, causing defects and degradation in device performance. Likewise, the high temperatures required by their chemical vapor deposition growth limit substrates on which SWCNTs can be directly grown. Here, we present a systematic study of the direct deposition of pristine, aerosol-synthesized SWCNTs by thermophoresis. The density of the deposited nanotube film can be continuously adjusted from individual, separated nanotubes to multilayer thin films by changing the deposition time. Depending on the lateral flow inside the thermophoretic precipitator, the angular distribution of the deposited SWCNT film can be changed from uniform to nonuniform. Because the substrate is kept at nearly ambient temperature, deposition can be thus carried out on practically any flat substrate with high efficiencies close to unity. The thermophoretic terminal velocity of SWCNTs, determined by aerosol loss measurements, is found to be approximately one-third of the usual prediction in the free molecular regime and shows a weak dependence on the nanotube diameter. As a demonstration of the applicability of our technique, we have used thermophoretic deposition in the fabrication of carbon nanotube thin-film transistors with uniform electrical properties and a high, over 99.5%, yield.

Thermophoretic force on nanocylinders in the free molecule regime.

We theoretically investigate the thermophoresis of nanocylinders in the free molecule regime, wherein the nonrigid-body effect is taken into account. The analytical formulas of the thermophoretic forces on cylinders suspended in both simple gases and binary gas mixtures are derived for the two limiting collision models, i.e., specular and diffuse scatterings, based on the gas kinetic theory. In the limit of the rigid-body collision, the expressions can be reduced to the theoretical results of Garcia-Ybarra and Rosner [AIChE J. 35, 139 (1989)10.1002/aic.690350115]. The thermophoretic velocities of the nanocylinders (including carbon nanotubes and long-chain n-alkanes) have been evaluated and it is found that the influence of the nonrigid-body effect on thermophoresis is significant for the case of small cylinder radius and low temperatures.

Influence of nonliner convection and thermophoresis on heat and mass transfer from a rotating cone to fluid flow in porous medium

In this paper, we study the effects of thermophoresis and non-linear convection on mixed convective flow of viscous incompressible rotating fluid due to rapidly rotating cone in a porous medium, whose surface temperature and concentration are higher than the temperature and concentration of its surrounding fluid. The governing equations for the conservation of mass, momentum, energy, and concentration are transformed, using similarity transformations and the solutions are obtained by employing shooting method that uses Runge-Kutta method and Newton-Raphson method. A comparison of the present results with previously published work for special cases shows a good agreement. The effects of temperature and concentration, ratio of angular velocities, relative temperature difference parameter, thermophoretic coefficients on velocity, temperature, and concentration profiles as well as tangential and circumferential skin friction coefficients, Nusselt number, and Sherwood number results are discussed in detail. The results indicate that the temperature is more influential compared to concentration. Also, the wall thermophoretic deposition velocity changes according to different values of pertinent parameter. Applications of the study arise in aerosol technology, space technology, astrophysics, and geophysics, which related to temperature-concentration-dependent density.

In situ laser diagnostics of nanoparticle transport across stagnation plane in a counterflow flame

The transport of nanoparticles in the boundary layer is closely related to particle mixing or deposition. We present an in situ imaging of TiO2 particle volume fraction near gas stagnation plane in a counterflow flame by recently developed phase-selective laser-induced breakdown spectroscopy technique. The concentration boundary layer is well resolved with a spatial resolution of 10μm. Together with a numerical analysis of particle transport equation, the roles of convection, diffusion and thermophoresis are discussed. The calculated profile of particle volume fraction agrees well with experimental measurements, which indicates that current model of nanoparticle transport is capable to quantitatively predict the concentration profile in boundary layers. Further study shows that altering thermophoretic velocity shifts the concentration boundary layer but does not change the shape of concentration profile. The decaying slope is mainly controlled by diffusion process that is dependent on particle size.

Development for Thermophoresis Experimental Under Microgravity Condition

In the temperature field, a small particle will move towards the lower temperature side. This phenomenon is called thermophoresis, which influences the movement of soot particles in exhaust gas from combustors. It is important to understand the behavior of soot particles in the combustion field for emission control. The main problem for measuring the thermophoretic velocity is the natural convection. The velocity of such natural convection is usually comparable to the thermophoretic velocity and cannot be measured directly. To avoid this problem, experiments should be conducted under microgravity conditions. . In the present work, device has been developed for conducting experiments repeatedly under a microgravity environment in a very short period time, i.e. 0.3 s, by means of the free-fall method, to accumulate data of the thermophoretic velocity. Experiments have been conducted to measure the movement of particles in the microgravity environment with and without temperature gradient. For the former experiment, it is seen that the particles has almost no movement in the horizontal and the vertical directions. Results confirmed that there is negligible effect of blowing and gravitational on the particles movement. For the later one, experiments have been done in a surrounding of a pure gas of argon. The thermophoretic velocity is measured at 313±2 K for various pressure conditions from 20 kPa to 100 kPa. The thermophoretic velocity for each particle is individually measured, and the mean value and its 95% confidence interval for each experimental condition are statistically obtained. Result from experiments are compared with the theory and satisfactorily agreement is found for tested gas.

Transpiration and Thermophoresis Effects on Non-Darcy Convective Flow Past a Rotating Cone with Thermal Radiation

In this article, mathematical model is developed for transport phenomena in an incompressible viscous fluid regime adjacent to a rotating vertical cone with thermal radiation and transpiration effects. The governing equations for the pertinent geometry are non-dimensionalized by employing specified transformations. A set of resultant equations are solved by numerical method. The solutions of this model are carried out under physical realistic boundary conditions to compute velocities, temperature and concentration functions distributions. The results are compared with previously available existing results. The excellent agreement has been found. The effect of thermal radiation, transpiration (surface injection/suction) and Forchheimer parameters, thermophoretic coefficient and relative temperature difference parameter on flow characteristics is illustrated graphically. It is observed that substantial influence has been exerted on flow characteristics, heat transfer rate (Nusselt number) and mass transfer rate (Sherwood number) for various values of transpiration parameter. The wall thermophoretic velocity changes according to the variation of physical parameters.

Thermophoresis of confined colloids in the near-contact limit

The thermophoretic velocity of a colloidal sphere towards a solid boundary due to an imposed temperature gradient perpendicular to that wall is found by a systematic approach to be reduced from the corresponding value in the bulk by a factor $3(h/a)[\mathrm{ln}(a/h)+0.1087]$, in the limit where the particle-wall separation distance h is small compared with particle radius a. This corrects a previous result of $3(h/a)[\mathrm{ln}(a/h)-2.25$ produced by an $a\phantom{\rule{0}{0ex}}d$ $h\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}c$ procedure.

Thermophoresis effect on heat and mass transfer from a rotating cone in a porous medium with thermal radiation

This work is devoted to study the combined effects of thermal radiation and thermophoresis on heat and mass transfer by mixed convection over a vertical rotating cone in a fluid saturated porous medium. The governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta method and Newton–Raphson method. The numerical results are compared and found to be approximately better than previously published results, Hering and Grosh (ASME J Heat Transf 85:29–34, 1963) and Himasekhar et al. (Int Commun Heat Mass Transf 16:99–106, 1989) as special cases of the present work. The local tangential and azimuthal skin friction coefficients, dimensionless wall thermophoretic velocity, local Nusselt and Sherwood numbers are presented graphically for different values of Darcy number, thermophoretic coefficient, thermal radiation parameter, and discussed to depict interesting features of the solutions.

Thermophoretic motion of large heated aerosol spherical particles

The stationary motion of a large spherical aerosol particle in the external field of a temperature gradient in zero gravity is theoretically described using the Stokes approximation and the assumption that the average temperature of the particle surface differs considerably from the temperature of the surrounding gaseous medium. The gas dynamics equations are solved taking into account the power-law temperature dependence of the molecular transport coefficients (viscosity, thermal conductivity) and the density of the gaseous medium. Numerical estimates show that the dependence of the thermophoretic force and velocity on the average temperature of the particle surface is nonlinear.

Particle behavior simulation considering thermophoretic and drag forces by direct simulation Monte Carlo method

A micro size particle behavior considering thermophoretic and drag forces are simulated by using direct simulation Monte Carlo (DSMC) method. The computation time is too high to compute the micro particle movement by conventional DSMC method because the computation time is proportional to a particle diameter. In this paper, the molecule-particle collision model, which computes the collision between a particle and multi molecules in a collision event, is considered. The momentum transfer to the particle is computed with a collision weight factor, where the collision weight factor means the number of molecules colliding with a particle in a collision event. The large time step is adopted by considering the collision weight factor. Therefore, the computation time becomes fifty thousandth times for micro size particle computation theoretically. We simulate the particle motion considering thermophoretic and drag forces by DSMC-Neutrals (Particle-PLUS neutral module) with above molecule-particle collision model, where DSMC-Neutrals is commercial software adopting DSMC method. The thermophoretic velocity with molecule-particle collision model is verified by comparison with Waldmann's model. Furthermore, it is shown that the DSMC method with molecule-particle collision model reproduces completely the conventional DSMC method. The behavior of a particle, which is polystyrene latex (PSL), is simulated.

Effects of variable fluid properties and thermophoresis on unsteady forced convective boundary layer flow along a permeable stretching/shrinking wedge with variable Prandtl and Schmidt numbers

In this paper, the effects of variable fluid properties and thermophoresis on unsteady forced convective boundary layer flow along a permeable stretching/shrinking wedge are studied numerically. The analysis accounts for temperature dependent viscosity and thermal conductivity. The governing time dependent nonlinear partial differential equations are reduced to a set of nonlinear ordinary differential equations by the similarity transformations. The resulting local similarity equations are solved numerically by Nachtsheim–Swigert shooting iteration technique with sixth order Runge–Kutta integration scheme. Comparison with previously published work is performed and the results are found to be in excellent agreement. Numerical results for the non-dimensional velocity, temperature and concentration profiles as well as the variable Prandtl number and the variable Schmidt number are displayed graphically for several sets of material parameters. The effects of the model parameters on the local skin friction coefficient, the rate of heat and mass transfer, and the thermophoretic particle deposition velocity are also tabulated. The results show that for the flow with variable thermal conductivity, the Prandtl number as well as the Schmidt number varies significantly within the boundary layer. Thus, in any physical model where fluid transport properties are temperature dependent, the Prandtl number and the Schmidt number within the boundary layer should be considered as variables rather than constants.

On the Motion of Carbon Nanotube Clusters near Optical Fiber Tips: Thermophoresis, Radiative Pressure, and Convection Effects.

We analyze the motion of multiwalled carbon nanotubes clusters in water or ethanol upon irradiation with a 975 and 1550 nm laser beam guided by an optical fiber. Upon measuring the velocities of the nanotube clusters in and out of the laser beam cone, we were able to identify thermophoresis, convection and radiation pressure as the main driving forces that determine the equilibrium position of the dispersion at low optical powers: while thermophoresis and convection pull the clusters toward the laser beam axis (negative Soret coefficient), radiation pressure pushes the clusters away from the fiber tip. A theoretical solution for the thermophoretic velocity, which considers interfacial motion and a repulsive potential interaction between the nanotubes and the solvent (hydrophobic interaction), shows that the main mechanism implicated in this type of thermophoresis is the thermal expansion of the fluid, and that the clusters migrate to hotter regions with a characteristic thermal diffusion coefficient D(T) of 9 × 10(-7) cm(2) K(-1) s(-1). We further show that the characteristic length associated with thermophoresis is not that of the nanotube clusters size, O(1) μm, but that corresponding to the microstructure of the clusters, O(1) nm. We finally discuss the role of the formation of gas-liquid interfaces (microbubbles) at high optical powers on the deposition of carbon nanotubes on the optical fiber end faces.

Transient thermophoretic particle deposition on forced convective heat and mass transfer flow due to a rotating disk

Abstract This paper investigates thermophoretic deposition of micron sized particles on unsteady forced convective heat and mass transfer flow due to a rotating disk. Using similarity transformations the governing nonlinear partial differential equations are transformed into a system of ordinary differential equations that are then solved numerically by applying Nachtsheim–Swigert shooting iteration technique along with sixth-order Runge–Kutta integration scheme. The effects of the pertinent parameters on the radial, tangential and axial velocities, temperature and concentration distributions, and axial thermophoretic velocity together with the local skin-friction coefficient, and local Nusselt number are displayed graphically. The inward axial thermophoretic deposition velocity (local Stanton number) is also tabulated. The obtained results show that axial thermophoretic velocity is increased with the increasing values of the thermophoretic coefficient, thermophoresis parameter, rotational parameter as well as unsteadiness parameter. The results also show that inward axial thermophoretic particle deposition velocity decreases with the increase of the Lewis number.

ICONE23-1779 THERMOPHORESIS RESEARCH OF NANOPARTICLES IN LIQUID LEAD-BISMUTH EUTECTIC ALLOY

Thermophoresis theory of solid particles in liquid are selected to research thermophoresis phenomenon in liquid Lead-Bismuth Eutectic (LBE). Thermophoretic velocity of different particles in LBE and stainless steel particles in different fluid are calculated. The results showed that, thermophoretic velocity of particles in LBE increase with the increase of temperature gradient and the decrease of particle radius. And the thermophoretic velocity of stainless steel particles two orders of magnitude lower than the Carbon Nanotubes (CNT) particles, at the same time, it is similar to copper particles in LBE. What's more, the thermophoretic velocity of stainless steel particles in LBE would one order of magnitude lower than that in water and R134a. Of course, it is still faster than that in Engine Oil and Ethyl Glycol two orders of magnitude.

Brownian movement and thermophoresis of nanoparticles in liquids

Abstract Thermophoresis is the realization of the averaged Brownian motion of particles in a fluid, which is subject to a steady temperature gradient. At sufficiently long times, the stronger molecular impulses in the hotter fluid region drive particles towards the colder region, where the molecular impulses are weaker. The effect of the molecular impulses on the particles is described by a stochastic Brownian force. When this force is applied to an ensemble of particles the thermophoretic velocity is the average velocity of the ensemble. In this study the motion of an ensemble of 4000 spherical nanoparticles with the material properties of CNT, aluminum, aluminum oxide, copper and gold was simulated in four base liquids–water, ethyl glycol, engine oil and R134a. The ensemble-averaged results generate the thermophoretic velocity of these particles in the base liquids. It was observed that the computational results agree very well with the few experimental data available for liquids. The computational method is general and may be applied to all heterogeneous systems of nanoparticles in liquids. The numerical results yield very useful information on the process of thermophoresis in liquids as well as values of the thermophoretic coefficients in nanofluids.