Thermo-Osmotic Flow in Thin Films

We report on the first microscale observation of the velocity field imposed by a nonuniform heat content along the solid-liquid boundary. We determine both radial and vertical velocity components of this thermo-osmotic flow field by tracking single tracer nanoparticles. The measured flow profiles are compared to an approximate analytical theory and to numerical calculations. From the measured slip velocity we deduce the thermo-osmotic coefficient for both bare glass and Pluronic F-127 covered surfaces. The value for Pluronic F-127 agrees well with Soret data for polyethylene glycol, whereas that for glass differs from literature values and indicates the complex boundary layer thermodynamics of glass-water interfaces.

Figure 1

Schematic view of the boundary layer at an interface with nonuniform temperature. (a) Thermo-osmotic velocity profile close to a charged solid boundary with an excess enthalpy within an interaction length $\lambda$; for $z>\lambda$ the velocity saturates at $v_s$. (b) The same for a Pluronic-coated surface. (c) Streamlines in the liquid film resulting from slip velocities at the upper and lower boundaries, reconstructed by numerical calculations and the experimental results for the Pluronic F-127 coated surface.

Figure 2

(a) Principal design of the experiment. The fluid is contained between two glass cover slides in a sandwich structure with a gap of about $5\mu \mathrm{m}$. A $R=125\mathrm{nm}$ AuNP is immobilized at the top surface and used as the heat source. A focused laser beam ($\lambda =532\mathrm{nm}$) heats the particle. $R=75\mathrm{nm}$ AuNPs were used to measure the velocity field. (b) Temperature map around the heated AuNP in cylindrical coordinates $r$ and $z$. (c) Temperature profile along the upper (black curve) and the lower glass (red curve) surface.

Figure 3

Temperature profile and slip velocity along the upper boundary. The temperature agrees very well with the power law $\propto r^{-2}$. The slip velocity on both glass and Pluronic-coated glass follows this law beyond 2 microns from the heated spot.

Figure 4

(a) Two-dimensional velocity map of the tracer motion at the upper surface. The color indicates the vertical velocity with blue being a flow in the negative $z$ direction away from the heat source and red in the positive $z$ direction. (b) Two-dimensional velocity map of the backflow within the sample. (c) The average radial velocity at the upper surface (red curve) and the backflow (blue curve) as a function of the radial distance from the heat source. Negative velocities represent a flow towards the heat source. The dashed line displays the vertically averaged radial velocity obtained from numerical calculations. In addition, the temperature increment surrounding the heat source is displayed (purple curve). (d) The average change of the tracer intensity and the corresponding vertical velocity in comparison to the numerical calculation.