UC Irvine

This thesis addresses the experimental results of two different research topics. The first is the experimental work of pressure driven flows in the smallest, single nanotubes ever investigated. The nanotube boundary conditions and slip lengths from argon, nitrogen, water, and helium experiments were analyzed and compared to macroscopic boundary conditions. The second research topic discusses the work on ellipsometric and quartz microbalance measurements of the 2D superfluid phase diagram of ⁴He on alkali substrates. Ellipsometric results of sodium on HOPG provide the first evidence of the existence of the 2D critical point on an intermediate strength substrate.

Pressure driven flows through single nanopores and microtubes were measured with a calibrated mass spectrometer with pressure drops up to 30 Atm. The nanopores were between 30 nm to 600 nm in diameter and etched in mica and PET membranes of several microns thickness. Microtubes several inches long of fused quartz and nickel material were tested with diameters between 1.8 micron and 25 micron. For ⁴He and argon gas we observed the flow transition between the free molecular and continuum regimes at 293 K and 77 K. No discrepancy between the macroscopic theory and the 30 nm nanopore data was found. Because of the exceptionally low viscosity of gaseous helium the laminar-turbulent transition could also be observed within these submicron channels. The small viscosity of ⁴He was too small to dampen inertial effects at a Reynolds number of 2000.

In addition to single phase gas flows, our experimental technique also allows us to investigate flows in which the nano or micro scale pipe is either partially or completely filled with liquids. The position of the intrinsic liquid/vapor interface was important for understanding this type of flow. Strong evaporation and cooling at the liquid-vapor interface can lead to freezing for conventional fluids such as nitrogen and water, which in turn leads to complex intermittent flows. Liquid helium in the normal state is a simpler system because it does not have a triple point and will not solidify at the pressures of our experiments. A systematic study of liquid helium in a 31 nm mica nanopore was done from T_λ to T>T_c. A no slip model accurately represented data if the Laplace pressure and the vapor pressure at the interface were present. The model can also make predictions of the internal location of the liquid/vapor interface as a function of pressure. We also optically investigated the effects of freezing on the liquid/vapor location with water flowing through micron scale capillaries into vacuum. The observations were combined with a numerical modeling which confirmed that external interfaces froze as the result of large evaporation rates and the low thermal conductivity of glass.

In laminar flow of classical fluids, the mass flux is linearly proportional to the pressure drop. Flow of superfluid in a pipe has dramatical different dependence on pressure drop. At low temperatures, the flow rate is almost independent of the pressure drop up to 50 Torr. The temperature dependent critical velocities fluctuated between two states within a 31 nm nanopore At T<1.4 K. A larger, linearly temperature dependent critical velocity was measured with a maximum value of 11 m/s. A thermal nucleation of vortices was predicted to be the source of energy dissipation. The lower second state was temperature independent and caused by the generation of vortices from a pinned site within the nanopore. In the range 1.4 Kλ the velocity exponentially approached the normal viscous state. The fast dissipation rate could be related to the 10⁷ vortex cores scattering from the increasing thermal excitations and generating a complex turbulent state.

The second portion of this thesis presents the experimental results on the 2D superfluid phase diagram of helium on alkali metals. A simultaneous measurement of the total and superfluid film thickness were done with a combination of a photoelastic modulated ellipsometer and a quartz crystal microbalance. Sodium and lithium films were ablated onto the gold electrodes of a QCM at 4 K. The adsorption isotherms of ⁴He were controlled by increasing the chemical potential from vacuum to bulk coexistence. The behavior of helium films are dependent on the strength of the substrate potential. For strong potentials such as gold and graphite the initial layers solidify while for the weaker substrate cesium films do not grow. Lithium and sodium were predicted to be intermediate in strength and for a mobile, helium film to directly grow on its surface. In addition to the superfluid transition a liquid/vapor coexistence region was predicted to also exist directly on an intermediate strength substrate. Our simultaneous QCM and ellipsometer measurements showed no clear evidence for the coexistence of 2D liquid/vapor on sodium or lithium. The gold electrodes which supported the alkali films were suspected of being too rough. We then ablated sodium on atomically smooth HOPG and the ellipsometer measured a discontinuous step at 0.5 K implying a liquid/vapor coexistence which decreased in size until it disappeared at the critical temperature T~0.7 K. This is the first experimental evidence of a 2D critical point on sodium.