The motion of tracer particles in turbulent superfluid $^4$He down to the zero-temperature limit

Abstract

An injection system for polymer particles, with diameters ranging from 1 to 6 $μ$m, has been developed for visualizing flows in superfluid $^4$He at temperatures down to 0.14 K. Using an ultrasound transducer, bursts of particles were launched into a sample of superfluid and allowed to descend under gravity. The particles were imaged using their fluorescence in the presence of a sheet of laser light. We report on the statistical behavior of particles during their descent, including descriptions of a mixture of smooth and erratic trajectories, indicative of the interactions with thermal excitations and quantized vortex lines. Temperature-dependent velocity distributions were measured and analyzed, yielding Gaussian distributions with power law tails persisting into the zero temperature limit. When sampled over increasing length scales, these distributions bifurcated into exponential for the smallest particles and bimodal Gaussian for the largest. We also report observations of long-lived suspensions of small particles at temperatures near 1 K, which appear to be associated with the trapping of large numbers of particles in a turbulent vortex tangle. A method was developed for identifying and quantifying the numbers of particles bound to vortex lines, allowing for a description of the temporal dynamics of their population by an analytical model.

Figures (20)

• Figure 1: Left: Schematic of the experimental cell showing the path of the laser sheet, particle injection system, positions of the cell thermometer and thermal link to the refrigerator. Right: Microscopic view of 6 µ m particles on the transducer surface.
• Figure 2: Schematic of the optical arrangement for admitting light to, and extracting images from the experimental cell.
• Figure 3: Masked image particle tracking example. Left: raw image of a burst of 1-5 µ m particles at 1 K with transducer surface visible at the bottom of the frame. Middle: mask generated from summed frames with detections overlaid. Right: Detections shown over raw image.
• Figure 4: Velocity PDFs for 6 µ m particles (top) and large bursts of 1-5 µ m particles (bottom) for horizontal motion (left), and vertical motion (right).
• Figure 5: Horizontal (top) and vertical (bottom) velocity PDFs for large bursts of 1--5 µ m particles at $0.19{\rm \,K} \leq T \leq 1.2$ K (blue points) fitted with a double-sided Crystal Ball function (red line). Error bars show the standard error on the mean of 10 measurements at each temperature.