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.
Abstract. The properties of polymer liquids on hard and soft substrates are investigated by molecular dynamics simulation of a coarse-grained bead-spring model and dynamic single-chain-in-mean-field (SCMF) simulations of a soft, coarse-grained polymer model. Hard, corrugated substrates are modelled by an FCC LennardJones solid while polymer brushes are investigated as a prototypical example of a soft, deformable surface. From the molecular simulation we extract the coarse-grained parameters that characterise the equilibrium and flow properties of the liquid in contact with the substrate: the surface and interface tensions, and the parameters of the hydrodynamic boundary condition. The so-determined parameters enter a continuum description like the Stokes equation or the lubrication approximation.At high temperatures the Navier slip condition provides an appropriate description of the flow past hard, corrugated surfaces. The position, x b , where the hydrodynamic boundary condition is to be enforced, agrees with the location of the liquid-solid interface and the slip length can be consistently identified by comparing planar shear flow and parabolic, pressure-driven flow. If the surface become strongly attractive or the surface is coated with a brush, the Navier slip condition will fail to consistently describe the flow at the boundary. This failure can be traced back to a boundary layer with an effective, higher viscosity.The solvent flow past a polymer brush induces a cyclic, tumbling motion of the tethered chain molecules. The collective motion gives rise to an inversion of the flow in the vicinity of the grafting surfaces and leads to strong, non-Gaussian fluctuations of the molecular orientations in the flow. Both, molecular dynamics as well as dynamic SCMF simulations, provide evidence that the flow past a polymer brush cannot be described by Brinkmann's equation.The hydrodynamic boundary condition is an important parameter for predicting the motion of polymer droplets on a surface under the influence of an external force. The steady state velocity is dictated by a balance between the power that is provided by the external force and the dissipation. If there is slippage at the liquid-solid interface, the friction at the solid-liquid interface and the viscous dissipation of the flow inside the drop will be the dominant dissipation mechanisms; dissipation at the three-phase contact line appears to be less important on a hard surface.On a soft, deformable substrate like a polymer brush, we observe a lifting up ofFlow past hard and soft surfaces 2 the three-phase contact line. Controlling the grafting density and the incompatibility between the brush and the polymer liquid we can independently tune the softness of the surface and the contact angle and thereby identify the parameters to maximise the deformation at the three-phase contact.
The authors propose a new method, the Helfand-moment method, to compute the shear viscosity by equilibrium molecular dynamics in periodic systems. In this method, the shear viscosity is written as an Einstein-type relation in terms of the variance of the so-called Helfand moment. This quantity is modified in order to satisfy systems with periodic boundary conditions usually considered in molecular dynamics. They calculate the shear viscosity in the Lennard-Jones fluid near the triple point thanks to this new technique. They show that the results of the Helfand-moment method are in excellent agreement with the results of the standard Green-Kubo method.
Tailoring surface interactions or grafting of polymers onto surfaces is a versatile tool for controlling wettability, lubrication, adhesion and interactions between surfaces. Using molecular dynamics of a coarse-grained, bead-spring model and dynamic single-chain-in-mean-field simulations, we investigate how structural changes near the surface affect the flow of a polymer melt over the surface and how these changes can be parameterized by a hydrodynamic boundary condition. We study the temperature dependence of the near-surface flow of a polymer melt at a corrugated, attractive surface. At weakly attractive surfaces, lubrication layers form, the slip length is large and increases upon cooling. Close to the glass transition temperature, very large slip lengths are observed. At a more attractive surface, a ‘sticky surface layer’ is build up, giving rise to a small slip length. Upon cooling, the slip length decreases at high temperatures, passes through a minimum and increases upon approaching the glass transition temperature. At strongly attractive surfaces, the Navier slip condition fails to describe Couette and Poiseuille flows simultaneously. A similar failure of the Navier slip condition is observed for the flow of a polymer melt over a brush comprised of identical molecules. The wetting and flow properties of this surface are rather complex. Most notably, the cyclic motion of the grafted molecules gives rise to a reversal of the flow direction at the grafting surface. The failure of the Navier slip condition in both cases can be rationalized within a schematic, two-layer model, which demonstrates that the Navier slip condition fails to simultaneously describe Poiseuille and Couette flow if the fluid at the surface exhibits a higher viscosity than the bulk.
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