Self-Propulsion of Immersed Objects via Natural Convection

Natural convection of a fluid due to a heated or cooled boundary has been studied within a myriad of different contexts due to the prevalence of the phenomenon in environmental and engineered systems. It has, however, hitherto gone unrecognized that boundary-induced natural convection can propel immersed objects. We experimentally investigate the motion of a wedge-shaped object, immersed within a two-layer fluid system, due to a heated surface. The wedge resides at the interface between the two fluid layers of different density, and its concomitant motion provides the first demonstration of the phenomenon of propulsion via boundary-induced natural convection. Established theoretical and numerical models are used to rationalize the propulsion speed by virtue of balancing the propulsion force against the appropriate drag force.

Figure 1

(a) (top to bottom) A sequence of three images of the wedge moving in a two-layer stratification after the heated surface was activated ($\sim 300\mathrm{s}$), the initial cage release is at $t=0\mathrm{s}$. The apparent shape of the wedge is distorted slightly by the vertically varying optical properties of the stratification (top right), and the active heating pad is indicated in red. (lower left) A schematic of the velocity and temperature profiles induced by the heated surface. (b) Displacement (⊳) and speed (□) of the wedge as a function of time.

Figure 2

The experimental PIV velocity field, magnitude (color map), and direction (arrows), in the vicinity of the heated surface of the stationary wedge for a $21\pm 1\mathrm{W}$ battery. The rectangular shaded region within the wedge indicates the heated surface, similarly to Fig. 1, and the dashed gray lines are transects along which experimental data are compared with theory and numerics in Fig. 3.

Figure 3

Comparison of experimental (*) and numerical (∘) data with the analytical model, using $\mathrm{Pr}=9.1$, for the velocity (black, with a maximum near $\eta =1$) and temperature (red, monotonically decreasing from 0.8 to 0) profiles extracted along the four transects indicated in Fig. 2. The intensity of the color (gray or red) for experimental and numerical points is an indication of the transect considered in Fig. 2.

Figure 4

(a) Theoretical ($-$) and numerical calculations (∘) of the propulsion force as a function of heat flux, for the physical parameters listed in the text. (b) Numerical results for the drag on a fixed 3D wedge as a function of the flow velocity $U$; (inset) same data in dimensionless form, i.e., he drag coefficient as a function of the Reynolds number. (c) Propulsion speed as a function of the power input for experiments in water (▫) and sugar water (⊲), linear fits to the experimental data ($--$) and the theoretical prediction ($-$) rescaled by a factor $k=1/5$. (d) Evolution of the rescaled experimental propulsion speed, in $\mathrm{mm}{\mathrm{s}}^{-1}$, as a function of the kinematic viscosity for an effective power input $q=5000\mathrm{W}{\mathrm{m}}^{-2}$.