Microscale Fluid Flow Induced by Thermoviscous Expansion Along a Traveling Wave

The thermal expansion of a fluid combined with a temperature-dependent viscosity introduces nonlinearities in the Navier-Stokes equations unrelated to the convective momentum current. The couplings generate the possibility for net fluid flow at the microscale controlled by external heating. This novel thermomechanical effect is investigated for a thin fluid chamber by a numerical solution of the Navier-Stokes equations and analytically by a perturbation expansion. A demonstration experiment confirms the basic mechanism and quantitatively validates our theoretical analysis.

Figure 1

Finite-element solution for a temperature wave in the comoving frame. (a) The temperature profile is indicated by the color scale and the arrows refer to the induced velocity flow. (b) The corresponding pressure modulation (color scale) and the solenoidal component of the flow.

Figure 2

Demonstration experiment. (a) A circular thermal wave is created in water by a moving focus of an infrared laser. The temperature is inferred by stroboscopic imaging of a temperature-sensitive fluorescent dye. (b) Peak temperature along the circumference. A sinusoidal fit yields a temperature amplitude of $\delta T_0=3.8\pm 0.5\mathrm{K}$.

Figure 3

Experiment versus theory. (a) The fluid velocity scales quadratically with the amplitude of the thermal wave $\delta T_0$. (b) The speed increases linearly with the velocity $u$ of the thermal wave. Measurements are given as dots, the theory as solid lines with the geometrical prefactor determined in Ref. 13. Error bars are standard errors.