Visualization study of thermal counterflow of superfluid helium in the proximity of the heat source by using solid deuterium hydride particles

Steady-state thermal counterflow of superfluid ${}^4\mathrm{He}$ (He II) is experimentally investigated in a channel of square cross section, with a planar heater placed at its bottom. We focus on the flow region close to the heat source, which has received little attention to date. Relatively small particles of solid deuterium hydride, having a density comparable to that of He II, are suspended in the liquid and their flow-induced dynamics is studied by using the particle tracking velocimetry technique. The comparison with results obtained in similar conditions with solid deuterium particles, which are about 1.4 times denser than He II, confirms that, in the heater proximity, the mean distance between quantized vortices, representing the characteristic length scale of the flow, appears to be about one order of magnitude smaller than that expected in the bulk, at the same temperature and applied heat flux. Additionally, we find that the lighter particles seem to experience a slightly denser vortex tangle, supporting therefore the view that heavy particles tend to stay trapped on quantized vortices for longer times than light ones. In the range of investigated parameters, the heavier particles consequently appear to be more suitable to probe the occurrence of vortex reconnections, deemed to be crucial in explaining energy dissipation mechanisms in quantum flows.

Figure 1

Flatness of the $(u-u_m)/u_{\text{s.d.}}$ distribution as a function of the scale ratio $R$ [Eq. (4)], where $u_m$ and $u_{\text{s.d.}}$ indicate the mean value and the standard deviation of the instantaneous dimensional velocity $u$ in the horizontal direction, respectively $(u$ is positive if directed from the left to the right of the field of view); at least ${10}^5$ velocities are taken into account for each $R$. Circles denote counterflow data obtained in the bulk; closed and open symbols indicate data obtained in the heater proximity with deuterium and deuterium hydride particles, respectively; see Table 1 for the experimental conditions (the data sets are labeled accordingly in the figure; the temperature of the heater proximity cases is specified in each panel; the bulk data were obtained at 1.77 K). The magenta line shows the flatness of the Gaussian distribution.

Figure 2

Flatness of the $(u-u_m)/u_{\text{s.d.}}$ distribution as a function of the scale ratio $R$ [Eq. (4)]. The symbols have the same meaning as in Fig. 1 (see also Table 1). Note that, compared to Fig. 1, different scales are used here to highlight the data obtained in the heater proximity.

Figure 3

Flatness of the $(u-u_m)/u_{\text{s.d.}}$ distribution as a function of the effective scale ratio $R_1=cR$ [Eq. (6)]. Relevant $c$ values are shown in parentheses following the data set symbols, which are as in Fig. 1 (see also Table 1).

Figure 4

Flatness of the $(u-u_m)/u_{\text{s.d.}}$ distribution as a function of the effective scale ratio $R_1=cR$ [Eq. (6)]. Relevant $c$ values are shown in parentheses following the data set symbols, which are as in Fig. 1 (see also Table 1). Note that, compared to Fig. 3, different scales are used here to highlight the data obtained in the heater proximity.