Thermophoretic Velocity Research Articles

Performance study of a disk-to-disk thermal precipitator

In this study, the performance of a thermal precipitator of the disk-to-disk type was investigated experimentally and numerically. The prototype precipitator was basically two disks separated via a circular Teflon® spacer. The temperatures of the two disks (one at elevated temperature and the other at room temperature) were individually controlled by a silicone heating element and running water at room temperature. Monodisperse particles of sodium chloride and fluorescein sodium were used to investigate the particle collection efficiency of the precipitator when operated under various aerosol flowrates and temperature gradients. Our experimental data showed that the particle collection efficiency of the precipitator remained approximately constant for test particles with diameters smaller than 300nm and noticeably decreased as the particle diameter increased beyond 300nm. A numerical model was developed and showed that the calculated particle collection efficiency was in reasonable agreement with experiment observations. Finally, a simple model was developed to estimate the particle collection efficiency of a typical disk-to-disk thermal precipitator. The model indicated that the particle collection efficiency of a disk-to-disk precipitator is a function of cold-disk deposition area, the average thermophoretic velocity, and the aerosol flowrate. This model may be useful in the future design of a thermal precipitator with the similar configurations.

Thermophoresis of an Aerosol Sphere with Chemical Reactions

The thermophoretic motion of a spherical aerosol particle undergoing a chemical reaction in a uniformly prescribed temperature gradient is studied theoretically in the quasisteady limit of negligible Peclet and Reynolds numbers. The chemical reaction taking place within the particle can be either endothermic or exothermic. The Knudsen number is assumed to be small (of the order 0.1) so that the fluid flow is described by a model with a thermal slip, a temperature jump, and a frictional slip at the surface of the particle. The energy and momentum equations governing the system are solved analytically, and explicit expressions for the thermophoretic velocity of the particle are obtained. Results of the effect of the chemical reaction inside the particle on its thermophoresis are presented for various distributions of the composition-dependent factor or heat generation parameter of the chemical reaction as well as the relative thermal and surface properties of the aerosol sphere. When the composition-depende...

Thermophoresis particle deposition on unsteady two-dimensional forced convective heat and mass transfer flow along a wedge with variable viscosity and variable Prandtl number

In this paper, the effects of thermophoresis particle deposition on an unsteady two dimensional forced convective heat and mass transfer flow past a wedge taking into account the variation of fluid viscosity and fluid Prandtl number with temperature are studied. The local similarity equations are derived and solved numerically using Nachtsheim–Swigert shooting iteration technique along with the sixth order Runge–Kutta integration scheme. Comparisons with previously published work are performed, and the results are found to be in excellent agreement. Results for the non-dimensional velocity, temperature, concentration, Prandtl number and thermophoretic velocity are displayed graphically whereas thermophoretic deposition velocity is shown in the tabulated form for various values of the pertinent parameters. The obtained numerical results show that in modeling the thermal boundary-layer flow with a temperature-dependent viscosity, consideration of the Prandtl number as a constant within the boundary layer produces unrealistic results, and therefore, it must be treated as a variable rather than a constant within the boundary layer. The results also show that the thermophoretic particle deposition velocity decreases as the thermophoretic coefficient increases.

Thermophoresis particle deposition in natural convection over inclined surfaces in porous media

The present paper is focused on the analysis of heat and mass transfer in boundary-layer free convection over an inclined flat plate embedded in a fluid saturated porous medium in the presence of thermophoresis. The governing equations are transformed into a set of coupled differential equations, which are solved numerically using the local non-similarity method. A comparison between the results given by this method and the local similarity method is also presented. For various values of the problem parameters, graphs of thermophoretic wall velocity, Nusselt number and concentration profiles in the boundary layer are presented. Variation of the dimensional thermophoretic wall velocity along the plate for different angles of inclination are presented in a physical relevant case.

Nanoparticle transport and deposition in boundary layer of stagnation-point premixed flames

Nanoporous TiO2 thin films are deposited directly onto substrates by a one-step stagnation flame synthesis with organometallic precursors. The deposition mechanism in the stagnation-point boundary layer is intensively studied. For the first time, the radial profile of nanoparticle deposition flux is measured using a novel method of concentric collecting rings, which exhibits similar trend with the heat flux profile of stagnation-point flows. Then, we develop the mathematical model of nanoparticle transport and deposition in the stagnation-point boundary layer for further clarifying experimental results, especially the effects of substrate temperatures and in-situ produced particle sizes. Both thermophoresis in an inner part of boundary layer and thermal compression/expansion of the gas phase are found to play important roles in determining the deposition flux. The contribution of Brownian diffusion, determined by a thermophoretic Peclet number, is inappreciable compared to thermophoresis until particle diameter is as small as 2nm. The results in this work support a conclusion of size-independence of the thermophoretic velocity, implying that the rigid-body collision assumption of Waldmann's formula is not accurate for small particles especially less than 10nm. This study can be generally applied to other deposition techniques of thin films.

Lie group analysis for thermophoretic and radiative augmentation of heat and mass transfer in a Brinkman-Darcy flow over a flat surface with heat generation

A boundary layer analysis is presented to investigate numerically the effects of radiation, thermophoresis and the dimensionless heat generation or absorption on hydromagnetic flow with heat and mass transfer over a flat surface in a porous medium. The boundary layer equations are transformed to non-linear ordinary differential equations using scaling group of transformations and they are solved numerically by using the fourth order Runge-Kutta method with shooting technique for some values of physical parameters. Comparisons with previously published work are performed and the results are found to be in very good agreement. Many results are obtained and a representative set is displayed graphically to illustrate the influence of the various parameters on the dimensionless velocity, temperature and concentration profiles as well as the local skin-friction coefficient, wall heat transfer, particle deposition rate and wall thermophoretic deposition velocity. The results show that the magnetic field induces acceleration of the flow, rather than deceleration (as in classical magnetohydrodynamics (MHD) boundary layer flow) but to reduce temperature and increase concentration of particles in boundary layer. Also, there is a strong dependency of the concentration in the boundary layer on both the Schmidt number and mass transfer parameter.

Water Droplets Behavior in Extinguishing the Methane-Air Counterflow Diffusion Flame

The behavior of fine water droplets was investigated in a methane-air counterflow diffusion flame, specifically when the water droplets were added to the inlet air feed and used to extinguish the diffusion flame. The water droplets studied had a relatively broad size distribution (from 1 to 60 ?m), with the number mean diameter of 15 ?m and Sauter mean diameter of 25 ?m. With an increase in the velocity gradient, the flame approaches towards the stagnation plane and flame thickness decreases. The flame properties, such as flame location and flame thickness are insensitive to the water mass loading. Along the stagnation stream line, the velocity decreases towards a local minimum just before the flame front. In contrast, the velocity increases in the flame zone due to the thermal expansion, and then decreases towards the stagnation point. In the decelerating zone, the droplet mass flux decreases on approach to the flame zone due to a non-equilibrium in velocity of large droplets between liquid and gas phases. Furthermore, as the droplet-laden air approaches the flame front, the flow stream begins to diverge in the counterflow field. Since the small droplets move away from the burner axis, the divergence of the air flow acts to reduce the water droplet mass flux along the stagnation streamline. Large droplets moving faster than the air flow “catch up” to slower ones just before the flame front, and the mass flux of the droplets tends to increase, resulting in the droplets accumulating just before the flame zone. Measurements of the velocities of individual droplets show that large droplets move faster than the small droplets which are in equilibrium (in velocity) between liquid and gas phases. Droplet behavior was found to be controlled by the Stokes number. Equilibrium in velocity is re-established just in front of the flame zone. Closer to the flame front, evaporation occurs and the mass flux of the droplets decreases drastically. On the other hand, thermophoresis acts on extremely small droplets to move them along the steep temperature gradient and these droplets are forced from the high to low temperature regions against the convection velocity. The thermophoretic velocity was estimated in the present study to be compared with the measured convection velocity and it was concluded that the thermophoretic effect is negligibly small over all sizes of droplets.

Thermophoresis of axially and fore-and-aft symmetric aerosol particles

The thermophoretic motion of an aerosol particle of revolution with fore-and-aft symmetry in a uniformly prescribed temperature gradient normal to its axis of revolution is studied theoretically. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model. A method of distribution of a set of spherical singularities along the axis of revolution within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solutions for the temperature and fluid velocity fields. The temperature jump and fluid slip conditions at the particle surface are satisfied by applying a boundary collocation technique to these general solutions to determine the unknown coefficients. The thermophoretic velocity of the particle is calculated with good convergence behavior for various cases, and the agreement between our results and the available analytical solutions is very good. It is found that the normalized thermophoretic velocity of a prolate or oblate spheroid perpendicular to its axis of revolution decreases monotonically with an increase in its axial-to-radial aspect ratio. For most practical cases of a spheroid with a specified aspect ratio, its thermophoretic mobility is not a monotonic function of its relative thermal conductivity. For the general problem of a particle with axial and fore-and-aft symmetry undergoing thermophoresis in a temperature gradient oriented arbitrarily with respect to its axis of revolution, the solution of the particle velocity can be obtained as a superposition of the solution obtained previously for the axisymmetric motion of the particle and the current result.

Self-thermophoresis and thermal self-diffusion in liquids and gases

This paper demonstrates the existence of self-thermophoresis, a phenomenon whereby a virtual thermophoretic force arising from a temperature gradient in a quiescent single-component liquid or gas acts upon an individual molecule of that fluid in much the same manner as a "real" thermophoretic force acts upon a macroscopic, non-Brownian body immersed in that same fluid. In turn, self-thermophoresis acting in concert with Brownian self-diffusion gives rise to the phenomenon of thermal self-diffusion in single-component fluids. The latter furnishes quantitative explanations of both thermophoresis in pure fluids and thermal diffusion in binary mixtures (the latter composed of a dilute solution of a physicochemically inert solute whose molecules are large compared with those of the solvent continuum). Explicitly, the self-thermophoretic theory furnishes a simple expression for both the thermophoretic velocity U of a macroscopic body in a single-component fluid subjected to a temperature gradient ∇T , and the intimately related binary thermal diffusion coefficient D{T} for a two-component colloidal or macromolecular mixture. The predicted expressions U=-D{T}∇T≡-βD{S}∇T and D{T}=βD{S} (with β and D{S} the pure solvent's respective thermal expansion and isothermal self-diffusion coefficients) are each noted to accord reasonably well with experimental data for both liquids and gases. The likely source of systematic deviations of the predicted values of D{T} from these data is discussed. This appears to be the first successful thermodiffusion theory applicable to both liquids and gases, a not insignificant achievement considering that the respective thermal diffusivities and thermophoretic velocities of these two classes of fluids differ by as much as six orders of magnitude.

Effects of thermophoresis on the forced convective laminar flow of a viscous incompressible fluid over a rotating disk

In this paper we investigate the effects of thermophoresis on the forced convective laminar flow of a viscous incompressible fluid due to a rapidly rotating disk whose surface temperature is lower than the temperature of its surrounding fluid. The governing equations of continuity, momentum, energy and concentration are transformed using similarity analysis, and the solutions are obtained through numerical techniques. The results show that if the thermophoretic coefficient increases, thermophoretic velocity increases and it intensifies significantly when the relative temperature difference parameter increases. The results also show that axial particle deposition velocity increases as the thermophoretic coefficient as well as Schmidt number increases.

A new technique to derive particle size distributions and aerosol number concentrations directly from thermophoretic data

The manufacture of many high value-added powders takes place by the decomposition of gaseous precursors in aerosol tube reactors. Historically, process improvements were achieved by making changes on the outside of the reactor and observing what comes out at the end of the pipe. The development of increasingly accurate aerosol dynamics models based on engineering first principles has been limited because models were typically validated on integral properties of ex situ product, instead of particle properties measured at multiple positions inside the reactor. In this study, a model reactor was equipped to capture samples thermophoretically from 15 internal positions. Additional in-line measurements were achieved with a multi-stage inertial impactor and by traditional analysis of ex situ product. Calculations were performed to verify that thermophoresis was the dominant mechanism of particle capture. The thermophoretic samples were analyzed by electron beam microscopy and image analysis to develop particle size distributions at each of the internal positions inside the reactor. An approximation of Talbot's Equation for thermophoretic velocity allowed experimental measurements to be combined with thermophoretic sample data to give predictions of particle number concentration corresponding to the precise sampling locations. The combinations of particle size distributions and number concentrations provide powerful insights on particle nucleation and growth dynamics.

Thermophoretic motion of slightly deformed aerosol spheres

The thermophoretic motion of a slightly deformed aerosol sphere in a uniformly prescribed but arbitrarily oriented temperature gradient is analyzed in the steady limit of negligible Peclet and Reynolds numbers. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the surface of the particle. The energy and momentum equations governing the system are solved asymptotically using a method of perturbed expansions. To the second order in the small parameter characterizing the deformation of the aerosol particle from the spherical shape, the thermal and hydrodynamic problems are formulated for the general case, and explicit expressions for the thermophoretic velocity of the particle are obtained for the special cases of prolate and oblate spheroids. The agreement between our asymptotic results for a thermophoretic spheroid and the relevant exact or numerical solutions in the literature is quite good, even if the particle deformation from the spherical shape is not very small. Depending on the values of the relative thermal and surface properties of the aerosol spheroid, its thermophoretic mobility normalized by the corresponding value for a spherical particle with equal equatorial radius is not necessarily a monotonic function of the aspect ratio of the spheroid.

Effect of particle morphology on thermophoretic velocity of aggregated soot particles

A particle under a temperature gradient experiences a force toward the colder region if a particle is very small. This phenomenon is called thermophoresis, a mass transfer phenomenon induced by the temperature gradient. It is well known that the magnitude of the thermophoretic force depends on the size of particle and the temperature gradient. In addition, the magnitude of the thermophoretic force depends on various factors such as the ambient gas’s kinematic viscosity and thermal conductivity and the morphology of the particle. To understand thermophoresis in detail, the effects of these factors need to be evaluated. In this study, we accurately measured the thermophoretic velocity of aggregated particles in order to understand the effect of particle morphology. We used carbon black particles of well-defined aggregation parameters to systematically understand the effect of morphology. In addition, we introduced a new optical system to measure the velocity and the size of each particle simultaneously. Five different samples of carbon black particles with different aggregation parameters were used to systematically understand the effect of morphology. The measured thermophoretic velocities were almost proportional to ν∇ T/ T. The measured dimensionless thermophoretic velocities, U T /( ν∇ T/ T), were much larger than those expected based on the size of aggregates and rather close to those expected based on the primary particle size even when the size of aggregates are larger than 100 mm. This result infers that thermophoretic velocity of an aggregated particle is governed by the primary particle size. The dimensionless density, the ratio of the bulk density to the true density, which represents the overall packing degree of aggregate, is also found to have a significant effect on the thermophoretic behavior.

Augmentation of thermophoretic deposition in natural convection flow through a parallel plate channel with heat sources

Submicron sized particles suspended in a hot flue gas exposed to a cold wall are driven towards the wall where they finally get deposited. The driving force and velocity acquired by the particles are known as thermophoretic force and thermophoretic velocity respectively. Natural convection through parallel plate channel is considered for analysis in this paper. Two dimensional free convection boundary layer equations are solved using a finite difference marching technique. Incompressible steady flow is considered. Effect of axial laser heating is studied by incorporating heat source term in the energy equation. It is found that the axial laser heating results in enhanced mass deposition rate on the channel wall. Deposition rate is found to be a function of intensity of heating. Results are presented in the form of graphs. Axial heating is useful to enhance smoke particle deposition rate from medium sized wood-fired appliances on account of increasing demand for such appliances throughout the world including developed countries owing to the depleting nature of fossil fuel.

Particle Trajectories and Temperature Histories of TiO<SUB>2</SUB> Nanoparticles Synthesized in Diffusion Flame Reactor

The computational analysis was developed to illustrate the gas temperature and velocity profiles in the oxy-methane diffusion flame reactor during the formation of TiO2 nanoparticles and the collection of the TiO2 nanoparticles by filter. The computational simulation shows that the increase in gas temperature and velocity is significantly affected by the increase in CH4 flow rate. The particle trajectory was calculated by using the model, which concerns the effects of thermophoretic force and gas velocity on the particle movement. The particles starting from different initial positions in radial direction will move in different trajectories. The particles following different trajectories have different temperature histories and also residence times in the gas phase. As the particles start at the initial position of the reactor which is further away from the central axis, they spend longer time in the gas phase and deposit on the higher position of filter. For particles starting at the initial position of the reactor which is further than 0.5 cm from the central axis, they move to deposit on the pyrex tube instead of filter. As the CH4 flow rate increases, the particles move further from the central axis, but it takes a shorter time for the particles to deposit on the filter. The particles synthesized at a higher CH4 flow rate show significantly higher temperature history than those particles synthesized at a lower CH4 flow rate. The temperature histories of particles in diffusion flame reactor can be quite important information to control the properties of TiO2 nanoparticles.

Thermophoresis of an aerosol spheroid along its axis of revolution

The thermophoretic motion of a spheroidal particle freely suspended in a gaseous medium prescribed with a uniform temperature gradient along the axis of revolution of the particle is studied theoretically in the steady limit of small Peclet and Reynolds numbers. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the particle surface. The general solutions in prolate and oblate spheroidal coordinates can be expressed in infinite-series forms of separation of variables for the temperature distribution and of semiseparation of variables for the stream function. The jump/slip boundary conditions on the particle surface are applied to these general solutions to determine the unknown coefficients of the leading orders, which can be numerical results obtained from a boundary-collocation method or explicit formulas derived analytically. Numerical results for the thermophoretic velocity of the spheroidal particle are obtained in a broad range of its aspect ratio with good convergence behavior for various cases. For the axisymmetric thermophoresis of an aerosol spheroid, prolate, or oblate, with no temperature jump and frictional slip at its surface, our results agree excellently with the analytical solution obtained previously. The agreement between our results and the available numerical solutions obtained by using a singularity method is also very good. For most practical cases of a spheroid with a specified aspect ratio, the thermophoretic mobility of the particle is not a monotonic function of its relative jump/slip coefficients and thermal conductivity. The axisymmetric thermophoretic mobilities of a prolate spheroid and of an oblate spheroid with large aspect ratios can be much greater and smaller, respectively, than that of a sphere with the same equatorial radius.

Effect of thermophoretic particle deposition in non-Newtonian free convection flow over a vertical plate with magnetic field effect

The present contribution deals with the effects of thermophoretic particle deposition on the free convective flow over a vertical flat plate embedded in a non-Newtonian fluid-saturated porous medium in the presence of a magnetic field. The governing partial differential equations are transformed into ordinary differential equations by using special transformations. The resulting similarity equations are solved numerically by an efficient implicit finite-difference method. For various values of the problem parameters, graphs of the profile concentration in the boundary layer and of thermophoretic deposition velocity are presented.

Thermophoresis particle deposition — thermal radiation interaction on mixed convection from vertical surfaces embedded in porous medium

This work deals with thermophoresis particle deposition and thermal radiation interaction on mixed convection heat and mass transfer by steady laminar boundary-layer flow over a nonisothermal vertical flat plate embedded in a fluid-saturated porous medium. The governing partial-differential equations are transformed into nonsimilar form by using a special transformation and then solved numerically by using an implicit finite-difference method. Different results are obtained and displayed graphically to explain the effect of various physical parameters on the wall thermophoretic deposition velocity, Nusselt numbers, and temperature and concentration profiles. It was found that the increasing of radiation parameter or dimensionless temperature ratio heated the fluid and decreased the temperature gradients near the impermeable wall, which increased the local Nusselt numbers and decreased the wall thermophoresis velocities. It was also found that the effect of power indexes of either temperatures or concentration enhances both local Nusselt numbers and wall thermophoresis velocities. Comparison with previously published work in the limits of absent thermophoresis and thermal radiation effects shows excellent agreement.

Suction/injection effects on thermophoresis particle deposition in a non-Darcy porous medium under the influence of Soret, Dufour effects

The effect of suction/injection on thermophoretic particle deposition in free convection on a vertical plate embedded in a fluid saturated non-Darcy porous medium is studied using similarity solution technique. The effect of Soret and Dufour parameters on convective transport, wall thermophoretic deposition velocity, heat transfer and mass transfer is discussed in detail for different values of dispersion parameters, ( Ra γ, Ra ξ ) inertial parameter F and Lewis number Le. The result indicates that in both suction, injection the Soret effect is more influential in increasing the concentration distribution in both aiding as well as opposing buoyancies. Also, it is worth mentioning here that the combined effect of opposing buoyancy and injection will have a more significant effect on the boundary layer thickness. In both the cases, suction as well as injection, magnitude of heat transfer is observed to be more when the second order effects are considered than when they are not. But, mass transfer and the wall thermophoretic deposition velocity V tw becomes less when all effects are considered than when they are not.

Thermophoresis of axisymmetric aerosol particles along their axes of revolution

AbstractThe axisymmetric thermophoretic motion of an aerosol particle of revolution in a uniformly prescribed temperature gradient is studied theoretically. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model. A method of distribution of a set of spherical singularities along the axis of revolution within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solutions for the temperature distribution and fluid velocity field. The jump/slip conditions on the particle surface are satisfied by applying a boundary‐collocation technique to these general solutions. Numerical results for the thermophoretic velocity of the particle are obtained with good convergence behavior for various cases. For the axisymmetric thermophoresis of an aerosol spheroid with no temperature jump and frictional slip at its surface, the agreement between our results and the available analytical solutions is very good. The thermophoretic velocity of a spheroid along its axis of revolution in general increases with an increase in its axial‐to‐radial aspect ratio, but there are exceptions. For most practical cases of a spheroid with a specified aspect ratio, its thermophoretic mobility is not a monotonic function of its relative jump/slip coefficients and thermal conductivity. © 2008 American Institute of Chemical Engineers AIChE J, 2009