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.

Results of the DCMIX1 experiment on measurement of Soret coefficients in ternary mixtures of hydrocarbons under microgravity conditions on the ISS.

The Soret coefficients of a set of ternary systems of 1,2,3,4-tetrahydronaphthalene (THN), isobutylbenzene (IBB), and n-dodecane (nC12) at 298.15 K were measured under microgravity condition aboard the International Space Station in the frame of the DCMIX1 experiment. The present work includes a comprehensive study of possible data processing sequences for the interpretation of interferometric Soret experiments in ternary systems. Several data processing methodologies are discussed. A significant concentration dependence of the Soret coefficients is observed. In the present study, we have obtained large and positive values for THN and negative ones for IBB in all investigated systems. A linear relation between the Soret coefficients of two components is derived for each system and allows validating experimentally the coefficients measured in other experiments.

Dynamic analysis of the light scattered by the non-equilibrium fluctuations of a ternary mixture of polystyrene-toluene-n-hexane.

Dynamic analysis of the light scattered by non-equilibrium fluctuations in a thermodiffusion experiment has been performed on a sample of polystyrene-toluene-n -hexane, at 0.9-49.55-49.55% mass fraction. Time decays of the non-equilibrium fluctuations have been obtained revealing the accurate detectability of three modes. The slowest mode has been attributed to the mass diffusion of the polymer into the binary solvent; the intermediate one to mass diffusion of the two molecular components of the solvent; finally, the fastest one has been attributed to the thermal diffusivity of the overall mixture. The two eigenvalues of the mass diffusion matrix have been evaluated with accuracy in the order of 1%. Neglecting cross-diffusion effects we obtain a simplified expression for the relative amplitude of the two mass diffusion modes, allowing a parameterized determination of polystyrene and toluene Soret coefficients in the ternary mixture. We suggest that a two wavelength shadowgraph experiment is needed for a complete determination of all the coefficients.

The NEUF-DIX space project - Non-EquilibriUm Fluctuations during DIffusion in compleX liquids.

Diffusion and thermal diffusion processes in a liquid mixture are accompanied by long-range non-equilibrium fluctuations, whose amplitude is orders of magnitude larger than that of equilibrium fluctuations. The mean-square amplitude of the non-equilibrium fluctuations presents a scale-free power law behavior q-4 as a function of the wave vector q, but the divergence of the amplitude of the fluctuations at small wave vectors is prevented by the presence of gravity. In microgravity conditions the non-equilibrium fluctuations are fully developed and span all the available length scales up to the macroscopic size of the systems in the direction parallel to the applied gradient. Available theoretical models are based on linearized hydrodynamics and provide an adequate description of the statics and dynamics of the fluctuations in the presence of small temperature/concentration gradients and under stationary or quasi-stationary conditions. We describe a project aimed at the investigation of Non-EquilibriUm Fluctuations during DIffusion in compleX liquids (NEUF-DIX). The focus of the project is on the investigation in micro-gravity conditions of the non-equilibrium fluctuations in complex liquids, trying to tackle several challenging problems that emerged during the latest years, such as the theoretical predictions of Casimir-like forces induced by non-equilibrium fluctuations; the understanding of the non-equilibrium fluctuations in multi-component mixtures including a polymer, both in relation to the transport coefficients and to their behavior close to a glass transition; the understanding of the non-equilibrium fluctuations in concentrated colloidal suspensions, a problem closely related with the detection of Casimir forces; and the investigation of the development of fluctuations during transient diffusion. We envision to parallel these experiments with state-of-the-art multi-scale simulations.

Thermophoretically induced large-scale deformations around microscopic heat centers.

Selectively heating a microscopic colloidal particle embedded in a soft elastic matrix is a situation of high practical relevance. For instance, during hyperthermic cancer treatment, cell tissue surrounding heated magnetic colloidal particles is destroyed. Experiments on soft elastic polymeric matrices suggest a very long-ranged, non-decaying radial component of the thermophoretically induced displacement fields around the microscopic heat centers. We theoretically confirm this conjecture using a macroscopic hydrodynamic two-fluid description. Both thermophoretic and elastic effects are included in this theory. Indeed, we find that the elasticity of the environment can cause the experimentally observed large-scale radial displacements in the embedding matrix. Additional experiments confirm the central role of elasticity. Finally, a linearly decaying radial component of the displacement field in the experiments is attributed to the finite size of the experimental sample. Similar results are obtained from our theoretical analysis under modified boundary conditions.

Thermophoresis of polymers: nondraining vs draining coil.

Present theories for the thermophoretic mobility of polymers in dilute solution without long-ranged electrostatic interaction are based on a draining coil model with short-ranged segment-solvent interaction. We show that the characteristic thermophoretic interaction decays as r(-2) with the distance from the chain segment, which is of much longer range than the underlying rapidly decaying binary van der Waals interaction (∝ r(-6)). As a consequence, thermophoresis on the monomer level is governed by volume forces, resulting in hydrodynamic coupling between the chain segments. The inner parts of the nondraining coil do not actively participate in thermophoresis. The flow lines penetrate only into a thin surface layer of the coil and cause tangential stresses along the surface of the entire coil, not the individual segments. This model is motivated by recent experimental findings for thermoresponsive polymers and core-shell particles, and it explains the well-known molar mass independent thermophoretic mobility of polymers in dilute solution.

Optical funneling and trapping of gold colloids in convergent laser beams.

The simultaneous trapping of a large number of sedimenting Au colloids by optical radiation forces has been studied in detail. The particles are collected by a convergent laser beam and compressed against gravity and osmotic pressure at the upper window of the cell, thereby forming a dense colloidal gas. A minimum critical laser power is required to transport colloids into the trap. In contrast to conventional optical tweezers, the trap cannot be described by a 3D potential. Once the trap is sufficiently filled, the laser power can be reduced below the critical value, thereby stabilizing the trap population. Some characteristic properties of the trap, like the critical laser power and the transit time, are readily understood from a simple deterministic model. A detailed description that is capable of quantitatively accounting for the time dependence of the trap population, the finite leak rate at low power levels, or hysteresis effects requires the incorporation of fluctuations by means of a proper Langevin equation. Multiple independent traps are realized by time multiplexing of the laser beam, which allows for splitting up, independent manipulation, and subsequent recombination of a trapped colloidal cloud.