Fig. 2.

Distance- (a, b) and orientation- (c, d) dependence of translational and (mean) angular swim speed. The Janus particle’s swim speed u, (a), and mean angular speed ${\overline{\Omega }}_z$ (averaged over initial orientations $\gamma$) (b) both decay like $r^{-2}$ (dash-dotted line) in the distance r from the heat source, as expected from Fourier’s law of heat diffusion. Upper and lower branch in panel (b) correspond to clockwise and counterclockwise rotation, respectively. The orientational dependence of the swim speed in panel (c), measured at a distance $r=1.25\mathrm{\mu }\text{m}$ from the heat source, conforms with the theoretical fit ${\left(u_x^2,+,u_y^2\right)}^{1/2}$ with $u_{x,y}$ obtained from Eqs. (4), (5) using numerically determined temperature profiles (see Fig. 3). (d). To resolve the orientation-dependence of the angular velocity ${\Omega }_z$, data in the interval $r=1$–$4\mathrm{\mu }\text{m}$ was pooled. The theoretical fit (solid curve) was obtained from Eq. (6), again using the numerically determined temperature profiles. The least-square fits in (c, d) yield ${\mu }_{\mathrm{ps}}=2.88\mathrm{\mu }{\text{m}}^2/\text{sK}$ and ${\mu }_{\mathrm{au}}=1.82\mathrm{\mu }{\text{m}}^2/\text{sK}$ for the mobilities. The alternative fits shown in panel d) follow from Eq. (9) with ${\Omega }_{1,2}$ as independent fit parameters (dashed) and ${\Omega }_z={\Omega }_{0}sin\gamma$ [30], with ${\Omega }_0$ as fit parameter (dotted), and yield ${\Omega }_0={17.4}^{\circ }/\text{s}$, ${\Omega }_1={17.2}^{\circ }/\text{s}$, ${\Omega }_2={-3.25}^{\circ }/\text{s}$. The error bars in all panels have been estimated from the standard deviation of the mean values