The no-slip boundary condition (NSBC) states that there is no relative motion at the fluid-solid interface. It is one of the two pillars in hydrodynamics (the other one being the Navier-Stokes equation). Over the years, NSBC has demonstrated broad applicability, in spite of the fact that there has been no first-principles justification. However, starting about fifty years ago there has been a particularly persistent problem associated with the application of NSBC to the moving contact line in two-phase immiscible flows. The contact line is defined to be the intersection of the fluid-fluid interface with the solid wall. In 1974, it was shown by Dussan and Davis that the application of NSBC leads to a stress singularity for the moving contact line (MCL) problem. This was followed by molecular dynamic (MD) simulations in 1988 showing total slip, not no-slip, for the MCL. And away from the MCL MD simulations have also shown partial slip in the single-phase flow regime. Thus the MCL problem means that the usual continuum hydrodynamics can not accurately model fluids flow on the micro/nano scale. This was sometimes referred to as an example of the “breakdown of continuum.”
Category: Research Highlights
Ultrasound tunneling and focusing through phononic crystals
Tunneling is usually regarded as a quantum mechanical phenomenon. However, more generally it is also a wave phenomenon. In collaboration with Prof. John Page of the University of Manitoba, we have observed tunneling by ultrasound through a phononic crystal made of 0.8 mm diameter tungsten carbide beads, immersed in water. The tunneling phenomenon is characterized by a constant pulse traversing time through the phononic crystal sample, independent of the sample thickness. Therefore one can obtain fairly large group velocities for thick samples, although in such cases the signal amplitude is small. Compared with photon tunneling through photonic crystals, we found the tunnling time to be much larger. In fact, the tunneling time is roughly inversely proportional to the gap width. Thus the much higher frequency photonic bandgap implies a much shorter tunneling time.
Continue reading Ultrasound tunneling and focusing through phononic crystals
Discovery of superconductivity in 4-Angstrom single-walled carbon nanotubes
Following on the success of Zikang Tang in fabricating 4-Angstrom single-walled carbon nanotubes (which are at or close to the theoretical limit of nanotubes’ diameter) and Ning Wang’s direct TEM visualization of these nanotubes, superconductivity has been discovered in these nanotubes. This discovery followed a rather tortuous path, somewhat interesting in its own right. Hence I record it here. The related work was started in 1997-98, when measurement of low temperature electrical transport through the nanotubes, by Jiannong Wang, uncovered a rather sudden disappearance of charge carriers below 12 kelvin. Recognizing the importance of this result, Ping organized efforts to elucidate the underlying cause of this intriguing phenomenon. A casual visit by Steve Louie (UC Berkeley) has brought the attention to a 1995 paper by himself, Marvin Cohen, and their collaborators, predicting superconductivity in carbon nanotubes with increased transition temperature as the diameter decreases. With this jolt, Ping persuaded Xixiang Zhang and his student to measure the Meissner effect. The positive result on the Meissner effect clarified, for Ping at least, the earlier observed phenomenon of the disappearance of the charge carriers (caused by the opening of the superconducting gap at the Fermi level). Continue reading Discovery of superconductivity in 4-Angstrom single-walled carbon nanotubes