Observation of Slip Flow in Thermophoresis

Two differing theories aim to describe fluidic thermophoresis, the movement of particles along a temperature gradient. While thermodynamic approaches rely on local equilibrium, hydrodynamic descriptions assume a quasi-slip-flow boundary condition at the particle’s surface. Evidence for slip flow is presented for the case of thermal gradients exceeding $(a{S}_T{)}^{-1}$ with particle radius $a$ and Soret coefficient $S_T$. Thermophoretic slip flow at spheres near a surface attracts or repels tracer particles perpendicular to the thermal gradient. Moreover, particles mutually attract and form colloidal crystals. Fluid dynamic slip explains the latter quantitatively.

Figure 1

The slip flow induced by a temperature gradient across particles with a diameter of $10\mu \mathrm{m}$ attracts or repels tracer particles of diameter $0.5\mu \mathrm{m}$. The direction of the flow depends on the sign of the Soret coefficient of the large particle. (a) Polystyrene beads with $S_T>0$ attract the tracer particles. (b) Silica spheres with $S_T<0$ repel them. (c),(d) Schematic side view of the flow induced accumulation (depletion) of the tracer particles.

Figure 2

Thermophoretic crystallization. (a) In a strong temperature gradient, particles move ballistically to the cold surface (side view). The persisting slip flow is deflected by the surface and leads to mutual hydrodynamic attraction. (b) Temperature profile. (c) Colloidal crystals of $1\mu \mathrm{m}$ polystyrene particles on a cold surface for positive Soret coefficients (view from the top after 20 s of heating). Inset: Before temperature application. (d) Crystals form equally well for a contact heated chamber without laser irradiation ($2\mu \mathrm{m}$ particles). (e) At a fixed temperature gradient of $0.28\mathrm{K}/\mu \mathrm{m}$, crystallization strongly depends on the Soret coefficient, following the threshold condition of Eq. (1). See supplemental material [34].

Figure 3

Particle attraction from thermophoretic slip flow. (a),(b) The distance distribution of a single particle pair is measured by particle tracking. The effective pseudo pair potential $\Delta V(d)$ was determined using Boltzmann statistics (open circles). (c) The three-dimensional flow around the particles was calculated using finite elements. A projection of the flow lines is shown in gray; the thermal gradient is color coded and given in units of the free solution temperature gradient $\nabla T_0$. The calculated pair potential is plotted as a solid line in (b).