Dynamic wetting experiments with nitrogen in a quasi-capillary tube

This work investigates the wetting dynamics of cryogenic fluids in inertia-dominated conditions. We experimentally characterize an oscillating gas-liquid interface of liquid nitrogen in a partially filled U-shaped quartz tube. The experiments were carried out in controlled cryogenic conditions, with interface oscillations produced by releasing the liquid column from an unbalanced position and having nitrogen vapor as the only ullage gas. During the experiments, the interface shape was tracked via image processing and used to fit a model from which the contact angle could be accurately determined. The results show that the dynamic contact angle evolution in advancing conditions is linearly linked to the capillary number, with a slope depending on whether the interface moves over a dry or a prewet surface. However, the contact angle remains close to the one at equilibrium in receding conditions. To analyze the relation between contact angle and interface dynamics, we define an equivalent contact angle as the one that would make a spherical interface produce the same capillary pressure drop as the actual interface shape. The evolution of this equivalent contact angle proved to be independent of the evolution of the actual one, suggesting that the interface shape is not influenced by it. Finally, a theoretical analysis of the interface motion using a simplified model shows that viscous forces dominate the damping of the interface for small tube sizes, while gravity and inertial forces dominate the oscillating dynamics of the liquid column for larger tubes.

Figure 1

Schematic of U-tube with dimensions in millimeters. The relevant experimental variables are also shown on the right side of the tube and in the close-up view of the gas-liquid interface.

Figure 2

Schematic of cryostat facility. Pressure sensors are indicated with PT and pressure indicators with PI. Temperature sensors are indicated with TT and level transducers with LT.

Figure 3

Picture of the U-tube and the channel distributor assembly, showing the U-tube together with some of the components shown in the schematic of Fig. 2.

Figure 4

The portion on the left shows the results of interface regression on the data. The portion on the right shows a zoom near the wall, plotting the interface regression together with data and the linear extrapolation from which the contact-line velocity is defined. The model-based measurement yields ${\theta }_D=4.16\pm 0.{51}^{\circ }$.

Figure 5

Summary of the measurements in advancing (left panels) vs receding (right panels) conditions. Panels (a) and (b) show some selected snapshots. Panels (c) and (d) show the corresponding interface detection, and panels (e) and (f) show the time history of the average interface. Panels (g) and (h) plot the dynamic contact angle vs capillary number.

Figure 6

Comparison of the equivalent contact angle computed with Eq. (7) and the measured dynamic contact angle. On the left panel (a) shows the case of Fig. 5, and on the right panel (b) shows the case of Fig. 5.

Figure 7

The left panel (a) shows the comparison of the experiment with the interface prediction obtained solving the 1D-ODE model equation (11). The right panel (b) shows the evolution of the dimensionless terms of Eq. (11).

Figure 8

(a) Square of the l2 norm of each force term in the model equation (11). The plot shows that the capillary pressure drop at the interface has a minor impact also in small experiments because of the rising contribution of viscous forces. (b) Section of the chart (a) for $L^{*}=94$, together with the dimensionless duration of the virtual experiment.