Thermophoretic Drift Research Articles

Thermophoretic motion of a charged single colloidal particle.

We calculate the thermophoretic drift of a charged single colloidal particle with hydrodynamically slipping surface immersed in an electrolyte solution in response to a small temperature gradient. Here we rely on a linearized hydrodynamic approach for the fluid flow and the motion of the electrolyte ions while keeping the full nonlinearity of the Poisson-Boltzmann equationof the unperturbed system to account for possible large surface charging. The partial differential equationsare transformed into a coupled set of ordinary differential equationsin linear response. Numerical solutions are elaborated for parameter regimes of small and large Debye shielding and different hydrodynamic boundary conditions encoded in a varying slip length. Our results are in good agreement with predictions from recent theoretical work and successfully describe experimental observations on thermophoresis of DNA. We also compare our numerical results with experimental data on polystyrene beads.

Can the Thermophoretic Mobility of Uncharged Colloids Be Predicted?

The thermophoretic motion of nonionic colloids in an inhomogeneous temperature field is due to the solvent-colloid dispersion interactions. The latter form an attractive near-particle "gravity" field that leads to sinking of the colder solvent layers toward a colloid. The spatial extension of this microconvective motion is comparable to the size of the colloids, which prove to be small enough to observe their own regular thermophoretic drift to the cold. The Boussinesq equations of convection are augmented by the boundary conditions at the characteristic molecular distance dividing the immovable and motile solvent layers. For organic liquids, this distance proves to be a property of pure solvent. The thermophoretic mobilities are found for colloids with and without surfacted layers. They are determined by the bulk properties of substances and the Hamaker constant of the solvent-solute interactions. The mobilities weakly (logarithmically) depend on the size of colloids and tend to a universal value in the limiting case of strongly asymmetrical mixtures. This is the first report that shows a prediction of the thermophoretic velocities of uncharged colloids. The relation between the thermophoretic mobility of colloids and the Hamaker constant of the solute-solvent interactions enables an experimental determination of the latter quantity from thermophoresis data.

Brownian Particle Thermal Drift Caused by Hydrodynamic Fluctuations.

We have studied the thermophoretic drift of a Brownian particle within the framework of the theory of fluctuating hydrodynamics of Landau and Lifshitz. The stochastic motion of a dispersed particle results from the fluctuating part of the stress tensor of the liquid. In the presence of a temperature gradient, the mean volume force acting on the liquid assumes a finite value due to non-vanishing quadratic terms in the fluctuations, which originate from the temperature dependence of the viscosity. An analytical expression is derived for the drift velocity and compared to experimental results.

Thermophoretic tweezers for single nanoparticle manipulation.

We present the trapping and manipulation of a single nano-object in an aqueous medium by optically induced temporally varying temperature gradients. By real-time object tracking and control of the position of the heating laser focus, we can precisely employ thermophoretic drift to oppose the random diffusive motion. As a result, a nano-object is confined in a micrometer-sized trap. Numerical modeling gives a quantitative prediction of the effect. Traps can be dynamically created and relocated, which we demonstrate by the controlled independent manipulation of two nanoparticles.

Optical thermogeneration induced enhanced evaporation kinetics in pendant nanofluid droplets

Optofluidic manipulation using lasers and colloidal systems have immense applications in microscale thermofluidic devices. The present study analyses the effect of laser as an external optical source in modulating the evaporation characteristics of pendent nanofluid microdroplets (which are free from substrate effects) so as to capture the physics behind the interfacial mass transport. The study analyses the effect of the power of laser, nature and concentration of the particle on evaporation rate of the complex fluids. Evidence of internal circulation was observed with Particle Image Velocimetry (PIV) technique in colloidal systems which together with the volumetric heat generation due to laser irradiation can be attributed to be the cause behind the enhanced evaporation rate. The nanoparticles are observed to efficiently convert the energy of radiant photons to heat while water is observed to show poor evaporative performance under laser irradiation. Theoretical analysis of the evaporation rate with the classical diffusion driven evaporation model is found to fall short in predicting the evaporation rate in colloidal systems, even in the absence of laser irradiation. Thermal Marangoni and Rayleigh numbers are calculated from the theoretical examination and are found not potent enough to induce the circulation in such systems which could improve evaporation. Hence the observed weak internal circulation can be attributed to the solutal Marangoni arising out of the local concentration gradients of nanoparticles in the droplet and the enhanced Thermophoretic drift and Brownian dynamics of the nanoparticles. Also the enhancement in the diffusion coefficient and its strong dependence with the particle concentration is also contributing to the enhancement in enhanced evaporation rate in nanocolloidal systems. The augmentation in the evaporative process under laser radiation is found to be governed majorly by the optical heat generation with weak solutal Marangoni and a scaling model is able to accurately predict the experimental observations. The present findings could have implications in modulation of thermofluidic and species transport phenomena in microscale devices.

Thermally “<italic>Smart</italic>” Characteristics of Nanofluids in Parallel Microchannel Systems to Mitigate Hot Spots in MEMS

Mitigation of “hot spots” in microelectromechanical systems (MEMS) employing in situ microchannel systems requires a comprehensive picture of the maldistribution of the working fluid and uniformity of cooling within the same. In this paper, detailed simulations employing parallel microchannel systems with specialized manifold-channel configurations, i.e., U, I, and Z, have been performed. Eulerian–Lagrangian discrete phase model (DPM) and effective property model with water and alumina–water nanofluid as working fluids have been employed. The distributions of the dispersed particulate phase and continuous phase have been observed to be, in general, different from the flow distribution, and this has been found to be strongly dependent on the flow configuration. Accordingly, detailed discussions on the mechanisms governing such particle distribution patterns have been proposed. Particle maldistribution has been conclusively shown to be influenced by various migration and diffusive phenomena, such as Stokesian drag, Brownian motion, thermophoretic drift, and so on. To understand the uniformity of cooling within the device, which is of importance in real-time scenario, an appropriate figure of merit has been proposed. It has been observed that uniformity of cooling improved using nanofluid as working fluid as well as enhanced relative cooling in hot zones, providing evidence of the “smart” nature of such dispersions. To further quantify this smart effect, real-time mimicking hot-spot scenarios have been computationally probed with nanofluid as the coolant. A silicon-based microchip emitting nonuniform heat flux (gathered from real-time monitoring of an Intel Core i7–4770 3.40-GHz quad-core processor) under various processor load conditions has been studied, and the evidence of enhanced cooling of hot spots has been obtained from DPM analysis. This paper sheds insight on-the behavior of nonhomogeneous dispersions in complex flow domains and the caliber of nanofluids in cooling MEMS more uniformly and “smarter” than base fluids.

Particle and thermohydraulic maldistribution of nanofluids in parallel microchannel systems

A deep understanding of fluidic maldistribution in microscale multichannel devices is necessary to achieve optimized flow and heat transfer characteristics. A detailed computational study has been performed using an Eulerian–Lagrangian twin-phase model to determine the concentration and thermohydraulic maldistributions of nanofluids in parallel microchannel systems. The study reveals that nanofluids cannot be treated as homogeneous single-phase fluids in such complex flow situations, and effective property models drastically fail to predict the performance parameters. To comprehend the distribution of the particulate phase, a novel concentration maldistribution factor has been proposed. It has been observed that the distribution of particles does not entirely follow the fluid flow pattern, leading to thermal performance that deviates from those predicted by homogeneous models. Particle maldistribution has been conclusively shown to be due to various migration and diffusive phenomena such as Stokesian drag, Brownian motion and thermophoretic drift. The implications of particle distribution on the cooling performance have been illustrated, and smart fluid effects (reduced magnitude of maximum temperature in critical zones) have been observed for nanofluids. A comprehensive mathematical model to predict the enhanced cooling performance in such flow geometries has been proposed. The article clearly highlights the effectiveness of discrete phase approach in modeling nanofluid thermohydraulics and sheds insight on the specialized behavior of nanofluids in complex flow domains.

Lean Methane-Air Flames Propagating Upward in Vertical Tubes

ABSTRACTThe upward propagation of a lean methane-air flame in a vertical tube is investigated. The shape and the velocity of the flame front are extracted from video records, and the velocity of the flow induced by the flame is measured with particle image velocimetry (PIV) using alumina particles to seed the gas. The thermophoretic drift of these particles relative to the gas is shown to cause an error in the PIV measurements in the transport region of the flame, where the temperature gradient is large. An iterative correction of the measured velocity is proposed that uses simplified, quasiunidimensional energy and species conservation equations to compute an approximation to the profile of gas temperature across the flame in terms of the profile of gas velocity. The correction is tested using synthetic velocity fields and applied along the axis of the tube. The results of the quasiunidimensional model also show that a conduction-radiation balance is approached in a region of low velocity that develops behind the flame front when the flammability limit is approached. Radiation losses from the combustion products in this region then become important and may cause the extinction of the flame.

Exploiting Optical Asymmetry for Controlled Guiding of Particles with Light

Conventional methods of manipulating particles with light, such as optical tweezers and optical tractor beams, rely on beam-shaping to realize complex electromagnetic field profiles and are thus sensitive to scattering. Here, we show that, by introducing tailored optical asymmetry in the particle, we can realize a novel guiding method that is controllable by the frequency of light, without regard to the direction or the shape of the light beam. With detailed stochastic simulations, we demonstrate guiding of a two-faced nanoparticle where the optically induced thermophoretic drift serves as the propulsion mechanism. Exploiting the difference in resonant absorption spectra of the two materials, we create a bidirectional local thermal gradient that is externally switchable. This is advantageous because the frequency of a light beam, unlike its shape or coherence, is preserved even in strongly scattering environments. Since this approach is insensitive to scattering and applicable to many particles at once, a...

Thermophoretically modified aerosol Brownian coagulation

A theory of aerosol coagulation rates resulting from continuum-regime brownian coagulation in the presence of size-dependent particle thermophoresis is developed and explored here. We are motivated by a wide variety of applications in which particle brownian coagulation occurs in a nonisothermal gas where differential thermophoretic drift contributes to, but does not dominate, the encounter frequency between suspended spherical particles (e.g., mist droplets) of different sizes. We employ a Smoluchowski-like population-balance to demonstrate the relative roles of brownian diffusion and thermophoresis in shaping the short and long time (asymptotic or "coagulation-aged") mist-droplet size distribution (DSD) function. To carry out these combined-mechanism DSD-evolution calculations we developed a rational "coupled" coagulation rate constant (allowing for simultaneous brownian diffusion and relative thermophoretic drift) rather than simply adding the relevant individual coagulation "kernels." Dimensionless criteria are provided to facilitate precluding other coagulation mechanisms not considered here (such as simultaneous sedimentation or Marangoni-flow-induced mist-droplet phoresis) and potential complications not included in the present model [as finite-rate coalescence, initial departures from the continuum (Stokes drag-) limit, and even dense (nonideal) vapor effects].

An Optical Conveyor for Molecules

We optically trap molecules in free solution, which allows to accumulate 5-base DNA to a hundredfold excess within seconds [1]. The concentration of the trapped DNA scales exponentially with length, reaching trapping potential depths of 14kT for 50 bases. This novel way to trap molecules could be used to enhance diffusion-limited surface reactions, redirect cellular signaling, observe individual biomolecules over a prolonged time or separate small molecules in solution by their diffusion constant.The mechanism is based on the microscale analog of a conveyor belt: a bidirectional flow, driven optically by the recently shown thermo-viscous fluid pump [2,3], is combined with a perpendicular thermophoretic molecule drift. Arranged in a toroidal geometry, no microfluidics, electrodes or surface modifications are required. As a result, the trap can be dynamically relocated.[1] Weinert and Braun, Nano Letters, accepted[2] Weinert, Kraus, Franosch and Braun, PRL 100, 164501 (2008)[3] Weinert and Braun, JAP 104, 104701 (2008)View Large Image | View Hi-Res Image | Download PowerPoint Slide

An Optical Conveyor for Molecules

Trapping single ions under vacuum allows for precise spectroscopy in atomic physics. The confinement of biological molecules in bulk water is hindered by the lack of comparably strong forces. Molecules have been immobilized to surfaces, however often with detrimental effects on their function. Here, we optically trap molecules by creating the microscale analogue of a conveyor belt: a bidirectional flow is combined with a perpendicular thermophoretic molecule drift. Arranged in a toroidal geometry, the conveyor accumulates a hundredfold excess of 5-base DNA within seconds. The concentrations of the trapped DNA scale exponentially with length, reaching trapping potential depths of 14 kT for 50 bases. The mechanism does not require microfluidics, electrodes, or surface modifications. As a result, the trap can be dynamically relocated. The optical conveyor can be used to enhance diffusion-limited surface reactions, redirect cellular signaling, observe individual biomolecules over a prolonged time, or approach single-molecule chemistry in bulk water.

Optothermal Molecule Trapping by Opposing Fluid Flow with Thermophoretic Drift

Thermophoresis moves molecules along temperature gradients, typically from hot to cold. We superpose fluid flow with thermophoretic molecule flow under well-defined microfluidic conditions, imaged by fluorescence microscopy. DNA is trapped and accumulated 16-fold in regions where both flows oppose each other. Strong 800-fold accumulation is expected, however, with slow trapping kinetics. The experiment is equally described by a three-dimensional and one-dimensional analytical model. As an application, we show how a radially converging temperature field confines short DNA into a 10 microm small spot.

Modeling of aerosol dynamics along a vertical flat plate

This study evaluates aerosol dynamics along an isothermal vertical flat plate. Various transport and removal mechanisms of aerosol dynamics, including fluid convection, Brownian motion, thermophoretic drift, and coagulation of aerosols, are simulated. The SIMPLE method is applied to solve the momentum, energy, and aerosol concentration equations. The main scheme is based on a boundary layer type solution of sectional aerosol simulation that uses flow fields provided a computational dynamics code. This study evaluates the aerosol concentration distribution within the concentration boundary layer and investigates the effect of coagulation on the deposition velocity along a vertical isothermal flat plate.

Mass transport mechanisms during excimer laser nitriding of aluminum

Surface layers of aluminum nitride were formed by irradiating pure aluminum substrates in nitrogen atmosphere with a pulsed excimer laser. The beam was focused on the sample placed inside a chamber filled with nitrogen gas. The irradiation was carried out at various laser fluences, nitrogen gas pressures, and numbers of pulses in order to investigate the influence of each parameter on the nitrogen incorporation and the mass transport mechanisms. X-ray diffraction showed the formation of polycrystalline AlN phase with the wurtzite structure, and the analysis of the nitrogen depth profiles by means of resonant nuclear reaction Analysis revealed a monotonic increase of the nitrogen concentration with the ambient gas pressure and the number of laser shots. It has been found that the laser fluence directly determines the temperature of the substrate and strongly changes the transport mechanism. The thermal simulations and the experimental evidence show that for fluences higher than 3 J/cm 2 the temperature of the substrate exceeds 2900 K. This value is higher than the dissociation temperature (∼2400 K) and close to the melting point (∼3070 K) of AlN, which can therefore dissociate or melt. The atomic nitrogen can rapidly diffuse to greater depths in the liquid Al matrix or it can degas (outgas) through the surface of the sample, leading to the formation of rather homogeneous concentration profiles. For fluences lower than 3 J/cm 2 the temperature of the substrate is not sufficient to destroy the nitride phase and the AIN grains can move inside the molten Al. In this case, the material transport can be attributed to Brownian motion and thermophoretic drift, which in turn are correlated with the chemical and thermal gradient, respectively.

Particle deposition on a rotating disk in application to vapor axial deposition (VAD) process

Vapor axial deposition (VAD), one of the optical waveguide preform fabrication processes, is performed by deposition of silica particles that are synthesized by combustion of raw chemical materials. In this study, flow field in a VAD process is assumed to be a forced uniform flow perpendicularly impinging on a rotating disk. A set of exact solutions for velocity and temperature distributions are developed by employing a similarity variable obtained from force balance on a control volume near the disk. The solutions depend on the rotating velocity of the disk and the forced flow velocity toward the disk. The solutions are then incorporated into the particle dynamics/transport equation. The particles are approximated to be in a lognormal size distribution. A moment model is used in order to predict distributions of particle number density and size simultaneously. Deposition of the particles on the disk is examined, considering convection, diffusion, thermophoresis, and coagulation with variations of the forced flow velocity and the disk rotating velocity. The deposition rate and the deposition efficiency directly increase as the flow velocity increases, resulting from that the increase of the forced flow velocity causes thinner thermal and diffusion boundary layer thicknesses and, thus, causes the increase of thermophoretic drift and Brownian diffusion of the particles toward the disk. However, the increase of the disk rotating velocity does not result in the direct increase of the deposition rate and the deposition efficiency. Slower flow velocity causes extension of the time scale for coagulation and thus, yields larger mean particle size and its geometric standard deviation at the deposition surface. In the case of coagulation starting farther from the deposition surface, coagulation effects increase, resulting in the increase of the particle size and the decrease of the deposition rate at the surface.

Particle deposition on a rotating disk in application to vapor deposition process (VAD)

Vapor Axial Deposition (VAD), one of optical fiber preform fabrication processes, is performed by deposition of submicron-size silica particles that are synthesized by combustion of raw chemical materials. In this study, flow field is assumed to be a forced uniform flow perpendicularly impinging on a rotating disk. Similarity solutions obtained in our previous study are utilized to solve the particle transport equation. The particles are approximated to be in a polydisperse state that satisfies a lognormal size distribution. A moment model is used in order to predict distributions of particle number density and size simultaneously. Deposition of the particles on the disk is examined considering convection, Brownian diffusion, thermophoresis, and coagulation with variations of the forced flow velocity and the disk rotating velocity. The deposition rate and the efficiency directly increase as the flow velocity increases, resulting from that the increase of the forced flow velocity causes thinner thermal and diffusion boundary layer thicknesses and thus causes the increase of thermophoretic drift and Brownian diffusion of the particles toward the disk. However, the increase of the disk rotating speed does not result in the direct increase of the deposition rate and the deposition efficiency. Slower flow velocity causes extension of the time scale for coagulation and thus yields larger mean particle size and its geometric standard deviation at the deposition surface. In the case of coagulation starting farther from the deposition surface, coagulation effects increases, resulting in the increase of the particle size and the decrease of the deposition rate at the surface.

Electric field enhanced deposition in flame-synthesized materials manufacturing

Theoretical and experimental studies of electric field enhanced deposition of flame-synthesized silica onto a disk target were carried out in relation to applications in optical waveguide preform manufacturing. The deposition method utilized an imposed electric field to induce a charge on the particle and cause electrophoretic drift in addition to thermophoretic drift towards the deposition target. An analytical model utilizing an axisymmetric, viscous stagnation-point flow analysis was developed. From the model calculations, the overall thermophoretic deposition rate (mass/time) onto the target was found to be proportional to the target size to the power of 3 2 . In the presence of an applied electric field the model calculation results showed that for a constant particle density and a constant particle charge the overall deposition rate increased as the strength of the applied electric field increased. The results also showed that for a constant particle density and a constant applied potential the deposition rate increased as the degree of particle charging increased. To confirm the analytical results, experiments were carried out. After preliminary experiments to establish optimal conditions for deposition measurements, silica deposition rates onto targets were measured both in the absence and in the presence of applied electric fields. The experimental results for thermophoretic deposition were found to be within 12% with respect to the deposition rates predicted by the model. When a potential of −1.6 kV was applied to the 9 cm target, for particle average charge of 2.78 e ( e: electronic charge) the deposition rate (0.28 g min −1) was increased by approximately 35% compared to the thermophoretic deposition rate (0.2 g min −1). Related to the deposition measurements, interesting aspects of silica charging mechanisms were discussed.

Characterization of a vapor axial deposition (VAD) flame impinging on a disk for a study o felectric field enhanced deposition

Methane-oxygen-nitrogen flames produced in a vapor axial deposition (VAD) burner and impinging on a disk were characterized with application to the problem of increasing particle deposition (transport) rate by an electric field applied between the disk (powdered) and an inserted ring (grounded). Two-dimensional temperature and electric potential distributions in flames were measured using a B-type thermocouple and an electrostatic probe, respectively. The temperature measurements demonstrate that the concentric tube burner design is effective because it allows thermophoretic focusing of the particle distribution within the flame, thus leading to higher deposition rates. The potential measurements show that that the electrical boundary layer (Debye sheath) appears adjacent to the powered electrode and grows in thickness as the strength of the applied potential increases. For the experimental conditions studied, the probe data show that the sheath extends outside of the thermal boundary layer at a large applied potential; this is expected to increase the effective capture area for particle deposition, depending on the particle-charging mechanisms associated with the polarity of the applied potential. The probe data imply that even for a sheath of thickness smaller than the themal boundary layer thickness the additional electrophoretic effect superimposed on the thermophoresis effect also increases the particle capture area for deposition. Sample calculations of particle drift velocities were carried out based on the probe results. For an electric field of 1 kV/mm the electrophoretic drift velocity becomes higher than the thermophoretic drift velocity when the number of charge carriers attached to a particle exceeds 4.

Effects of heat transfer on the dynamics and transport of small particles suspended in gases

Cases discussed in the article of recent studies include thermophoretic drift of spherical particles in a gas through which energy is diffusing, photophoretic drift of radiation-absorbing suspended spheres, phoresis and apparent Brownian diffusivity of asymmetric particles, including spheres with nonuniform accomodation coefficient and unequal primary particle size aggregates, scavenging of fine particles by evaporating droplets, and coagulation rate of unequal temperature spherical particles. General expressions for the relevant particle drift velocities, coagulation rate constants, or effective particle diffusivities are used to carry out illustrative calculations for multiphase systems of current and future engineering interest, including fine particle synthesis/materials processing, and combustion gas cleaning