We study the rolling and sliding motion of droplets on a corrugated substrate by Molecular Dynamics simulations. Droplets are driven by an external body force (gravity) and we investigate the velocity profile and dissipation mechanisms in the steady state. The cylindrical geometry allows us to consider a large range of droplet sizes. The velocity of small droplets with a large contact angle is dominated by the friction at the substrate and the velocity of the center of mass scales like the square root of the droplet size. For large droplets or small contact angles, however, viscous dissipation of the flow inside the volume of the droplet dictates the center of mass velocity that scales linearly with the size. We derive a simple analytical description predicting the dependence of the center of mass velocity on droplet size and the slip length at the substrate. In the limit of vanishing droplet velocity we quantitatively compare our simulation results to the predictions and good agreement without adjustable parameters is found.

Using Couette and Poiseuille flows, we extract the temperature dependence of the slip length, delta, from molecular dynamics simulations of a coarse-grained polymer model in contact with an attractive surface. delta is dictated by the ratio of bulk viscosity and surface mobility. At weakly attractive surfaces, lubrication layers form; delta is large and increases upon cooling. Close to the glass transition temperature Tg, very large slip lengths are observed. At a more attractive surface, a sticky surface layer is built up, giving rise to small slip lengths. Upon cooling, delta decreases at high temperatures, passes through a minimum, and grows for T-->Tg. At strongly attractive surfaces, the Navier-slip condition fails to describe Couette and Poiseuille flows simultaneously. The simulations are corroborated by a schematic, two-layer model suggesting that the observations do not depend on details of the computational model.

In this work we develop theoretical and numerical methods of calculation of a dynamic friction coefficient. The theoretical method is based on an adiabatic approximation which allows us to express the dynamic friction coefficient in terms of the time integral of the autocorrelation function of the force between both sliding objects. The motion of the objects and the autocorrelation function can be numerically calculated by molecular-dynamics simulations. We have successfully applied these methods to the evaluation of the dynamic friction coefficient of the relative motion of two concentric carbon nanotubes. The dynamic friction coefficient is shown to increase with the temperature.PACS numbers: 61.48.+c, 62.20.Qp Thanks to recent developments in nanotechnology, the hope is high to build mechanical devices on the scale of the nanometer. For this purpose, it is important to determine the mechanical properties and, especially, the friction forces in such nanodevices. In this work, we are going to focus on systems of carbon nanotubes. Our particular interest is for a system that Cumings and Zettl [1] observed experimentally with a TEM. They fixed an edge of a multiwalled nanotube to a surface and opened the other edge, they then extracted inner layers from the core for several nanometers and released them. They observed a full retraction of the inner layers and furthermore, they could conclude that the multiwalled nanotubes are self cleaning since amorphous carbon due to the opening of the edge are inside the tube and also do not have any wear, structural change or fatigue after several extraction and retraction processes. This experiment suggest us that the multiwalled nanotubes can be promising systems for future nanometric mechanical parts such as springs, gears or even motors.A short time after the work of Cumings and Zettl, Zheng and Jiang [3] estimated the frequency of the oscillations in this system to be of the order of GHz. This result is also very interesting since in the macroscopic world moving parts with such frequencies does not exist at the present time. But as in the macroscopic world moving parts have friction forces which hinder the motion and dissipate energy. We hence have to know the importance of these forces before conceiving such devices. Our work will thus focus on, firstly methods of calculation of the friction and secondly an application of these theories to the multiwalled nanotubes.The plan of the paper will be as follows, we are first going to introduce the theoretical framework for the description of the mechanics of nanotubes. We will then solve the classical equations of motion and calculate the dynamic friction coefficient by molecular-dynamics simulation and by the autocorrelation-function method developed by Jarzynski, Berry and Robbins [8,9].We have depicted in Fig. 1 two sliding nanotubes. R is the distance between the centers of mass of each nanotube. The Hamiltonian of the system of two nanotubes is given bywhere T 1 and T 2 are respectively the total kinetic energies of th...

We report a study of the rotational dynamics in double-walled nanotubes using molecular dynamics simulations and a simple analytical model that reproduces the observations very well. We show that the dynamic friction is linear in the angular velocity for a wide range of values. The molecular dynamics simulations show that for large enough systems the relaxation time takes a constant value depending only on the interlayer spacing and temperature. Moreover, the friction force increases linearly with contact area and the relaxation time decreases with the temperature with a power law of exponent -1.53+/-0.04.

We report on a study of the translational sliding motion and dynamic friction in systems of double-walled carbon nanotubes using molecular dynamics simulations combined with theoretical analysis. The sliding motion is described by a one-dimensional analytical model which includes the van der Waals force between the nanotubes, a dynamic friction force, and a small Langevin-type fluctuating force. The dynamic friction force is shown to be linear in the velocity over a large domain of initial conditions in armchair-armchair, zigzagarmchair, and zigzag-zigzag double-walled nanotubes. Beyond this domain, evidence is obtained for nonlinear effects which increase friction. In armchair-armchair systems, the dynamic friction is observed to be nonlinearly enhanced by the excitation of internal modes. In the linear domain, the coefficient of proportionality between the dynamic friction force and the velocity is shown to be given by Kirkwood's formula in terms of the force autocorrelation function.