Zero-temperature phase diagram of the second layer of 4^{\bf 4}He adsorbed on graphene

The phase diagram at zero temperature of $^4$He adsorbed on an helium incommensurate triangular solid on top of a single graphene sheet has been obtained using the diffusion Monte Carlo method. We have found that, in accordance with previous experimental and simulation results for graphite, the ground state of $^4$He on this setup is a liquid that, upon compression, transforms into a triangular solid. To define the stability limits of both liquid and solid phases, we considered not only the adsorption energies of the atoms located on the second layer but the average energy of the atoms in both layers. Our results show that the lower density limit for a stable liquid in the second layer is 0.163 $\pm$ 0.005 \AA$^{-2}$ and that the lower limit for the existence of an incommensurate solid on the second layer is 0.186 $\pm$ 0.003 \AA$^{-2}$. Both values are in overall agreement with the results of torsional oscillator experiments and heat capacity measurements on graphite. The 4/7 and 7/12 registered solids are found to be metastable with respect to triangular incommensurate arrangements of the same density.Comment: 7 pages, accepted for publication in Phys. Rev.

Liquid and solid phases of 3He on graphite

Recent heat-capacity experiments show quite unambiguously the existence of a liquid $^3$He phase adsorbed on graphite. This liquid is stable at an extremely low density, possibly one of the lowest found in Nature. Previous theoretical calculations of the same system, and in strictly two dimensions, agree with the result that this liquid phase is not stable and the system is in the gas phase. We calculated the phase diagram of normal $^3$He adsorbed on graphite at $T=0$ using quantum Monte Carlo methods. Considering a fully corrugated substrate we observe that at densities lower that 0.006 \AA$^{-2}$ the system is a very dilute gas, that at that density is in equilibrium with a liquid of density 0.014 \AA$^{-2}$. Our prediction matches very well the recent experimental findings on the same system. On the contrary, when a flat substrate is considered, no gas-liquid coexistence is found, in agreement with previous calculations. We also report results on the different solid structures, and the corresponding phase transitions that appear at higher densities.Comment: 5 page

4He adsorbed outside a single carbon nanotube

The phase diagrams of $^4$He adsorbed on the external surfaces of single armchair carbon nanotubes with radii in the range 3.42 -- 10.85 \AA \ are calculated using the diffusion Monte Carlo method. For nanotubes narrower than a (10,10) one, the ground state is an incommensurate solid similar to the one found for H$_2$ on the same substrates. For wider nanotubes, the phase with the minimum energy per particle is a liquid layer. Curved $\sqrt 3 \times \sqrt 3$ registered solids similar to the ones found on graphene and graphite were unstable for all the tubes considered.Comment: 6 pages, accepted for publication in Phys. Rev.

Isotopic effects of hydrogen adsorption in carbon nanotubes

We present diffusion Monte Carlo calculations of D$_2$ adsorbed inside a narrow carbon nanotube. The 1D D$_2$ equation of state is reported, and the one-dimensional character of the adsorbed D$_2$ is analyzed. The isotopic dependence of the constitutive properties of the quantum fluid are studied by comparing D$_2$ and H$_2$. Quantum effects due to their different masses are observed both in the energetic and the structural properties. The influence of the interatomic potential in one-dimensional systems is also studied by comparing the properties of D$_2$ and $^4$He which have nearly the same mass but a sizeably different potential. The physics of molecular hydrogen adsorbed in the interstitial channels of a bundle of nanotubes is analyzed by means of both a diffusion Monte Carlo calculation and an approximate mean field method.Comment: 17 pages, revtex, 9 ps figures, to be appear in Phys. Rev.

Phase diagram of H2 adsorbed on graphene

The phase diagram of the first layer of H$_2$ adsorbed on top of a single graphene sheet has been calculated by means of a series of diffusion Monte Carlo (DMC) simulations. We have found that, as in the case of $^4$He, the ground state of molecular hydrogen is a $\sqrt3 \times \sqrt3$ commensurate structure, followed, upon a pressure increase, by an incommensurate triangular solid. A striped phase of intermediate density was also considered, and found lying on top of the equilibrium curve separating both commensurate and incommensurate solids.Comment: 5 pages, 3 figure

Generation and Breakup of Worthington Jets After Cavity Collapse

Helped by the careful analysis of their experimental data, Worthington (1897) described roughly the mechanism underlying the formation of high-speed jets ejected after the impact of an axisymmetric solid on a liquid-air interface. In this work we combine detailed boundary-integral simulations with analytical modeling to describe the formation and break-up of such Worthington jets in two common physical systems: the impact of a circular disc on a liquid surface and the release of air bubbles from an underwater nozzle. We first show that the jet base dynamics can be predicted for both systems using our earlier model in Gekle, Gordillo, van der Meer and Lohse. Phys. Rev. Lett. 102 (2009). Nevertheless, our main point here is to present a model which allows us to accurately predict the shape of the entire jet. Good agreement with numerics and some experimental data is found. Moreover, we find that, contrarily to the capillary breakup of liquid cylinders in vacuum studied by Rayleigh, the breakup of stretched liquid jets at high values of both Weber and Reynolds numbers is not triggered by the growth of perturbations coming from an external source of noise. Instead, the jet breaks up due to the capillary deceleration of the liquid at the tip which produces a corrugation to the jet shape. This perturbation, which is self-induced by the flow, will grow in time promoted by a capillary mechanism. We are able to predict the exact shape evolution of Worthington jets ejected after the impact of a solid object - including the size of small droplets ejected from the tip due to a surface-tension driven instability - using as the single input parameters the minimum radius of the cavity and the flow field before the jet emerges

4He adsorbed inside (10,10) single walled carbon nanotubes

Diffusion Monte Carlo calculations on the adsorption of $^4$He in open-ended single walled (10,10) nanotubes are presented. We have found a first order phase transition separating a low density liquid phase in which all $^4$He atoms are adsorbed close to the tube wall and a high density arrangement characterized by two helium concentric layers. The energy correction due to the presence of neighboring tubes in a bundle has also been calculated, finding it negligible in the density range considered.Comment: 5 pages, accepted for publication in Phys. Rev.

Splash wave and crown breakup after disc impact on a liquid surface

In this paper we analyze the impact of a circular disc on a free surface using experiments, potential flow numerical simulations and theory. We focus our attention both on the study of the generation and possible breakup of the splash wave created after the impact and on the calculation of the force on the disc. We have experimentally found that drops are only ejected from the rim located at the top part of the splash --giving rise to what is known as the crown splash-- if the impact Weber number exceeds a threshold value \Weber_{crit}\simeq 140. We explain this threshold by defining a local Bond number $Bo_{tip}$ based on the rim deceleration and its radius of curvature, with which we show using both numerical simulations and experiments that a crown splash only occurs when $Bo_{tip}\gtrsim 1$, revealing that the rim disrupts due to a Rayleigh-Taylor instability. Neglecting the effect of air, we show that the flow in the region close to the disc edge possesses a Weber-number-dependent self-similar structure for every Weber number. From this we demonstrate that \Bond_{tip}\propto\Weber, explaining both why the transition to crown splash can be characterized in terms of the impact Weber number and why this transition occurs for $We_{crit}\simeq 140$. Next, including the effect of air, we have developed a theory which predicts the time-varying thickness of the very thin air cushion that is entrapped between the impacting solid and the liquid. Our analysis reveals that gas critically affect the velocity of propagation of the splash wave as well as the time-varying force on the disc, $F_D$. The existence of the air layer also limits the range of times in which the self-similar solution is valid and, accordingly, the maximum deceleration experienced by the liquid rim, what sets the length scale of the splash drops ejected when We>\Weber_{crit}