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 equation of the unperturbed system to account for possible large surface charging. The partial differential equations are transformed into a coupled set of ordinary differential equations in 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.

Thermophoresis beyond Local Thermodynamic Equilibrium.

We measure the thermophoresis of polysterene beads over a wide range of temperature gradients and find a pronounced nonlinear phoretic characteristic. The transition to the nonlinear behavior is marked by a drastic slowing down of thermophoretic motion and is characterized by a Péclet number of order unity as corroborated for different particle sizes and salt concentrations. The data follow a single master curve covering the entire nonlinear regime for all system parameters upon proper rescaling of the temperature gradients with the Péclet number. For low thermal gradients, the thermal drift velocity follows a theoretical linear model relying on the local-equilibrium assumption, while linear theoretical approaches based on hydrodynamic stresses, ignoring fluctuations, predict significantly slower thermophoretic motion for steeper thermal gradients. Our findings suggest that thermophoresis is fluctuation dominated for small gradients and crosses over to a drift-dominated regime for larger Péclet numbers in striking contrast to electrophoresis.

Two-dimensional Brownian motion of anisotropic dimers.

We study the two-dimensional motion of colloidal dimers by single-particle tracking and compare the experimental observations obtained by bright-field microscopy to theoretical predictions for anisotropic diffusion. The comparison is based on the mean-square displacements in the laboratory and particle frame as well as generalizations of the self-intermediate scattering functions, which provide insights into the rotational dynamics of the dimer. The diffusional anisotropy leads to a measurable translational-rotational coupling that becomes most prominent by aligning the coordinate system with the initial orientation of the particles. In particular, we find a splitting of the time-dependent diffusion coefficients parallel and perpendicular to the long axis of the dimer which decays over the orientational relaxation time. Deviations of the self-intermediate scattering functions from pure exponential relaxation are small but can be resolved experimentally. The theoretical predictions and experimental results agree quantitatively.