The simple procedure of the calculation of diffusion coefficient for adsorption on spherical and cylindrical adsorbent particles--experimental verification

A recently proposed simplified procedure for calculating the effective diffusion coefficient (D(e)) for adsorption on spherical and cylindrical adsorbent particles is now experimentally verified for adsorption systems: paracetamol-activated carbon. Adsorption kinetics was measured on nine carbons; for seven of them, measurements were taken at three temperatures. Since for adsorption on spherical adsorbent particles the approximate methods of D(e) calculation are already available in literature, only two systems have been studied, and the results of the new procedure are compared with those calculated from previously published methods. However, for cylinders the proposed method is the first simplification of this kind available in literature, thus, we focus our attention on the comparison of the results of the analytical approach with the simplified approaches for the systems where an adsorbent possesses cylindrically shaped granules. It is shown that for adsorption on spherical as well as on cylindrical adsorbent granules the proposed simplification leads to satisfactory results that, taking into account an experimental error, are practically the same as those obtained from exact time-consuming and mathematically advanced numerical fitting procedure. It is also shown that, for the studied carbons, the surface diffusion process dominates, and this explains the recently obtained correlation between the effective diffusion coefficient and the enthalpy of carbon immersion in water.     

Slip flow in graphene nanochannels

We investigate the hydrodynamic boundary condition for simple nanofluidic systems such as argon and methane flowing in graphene nanochannels using equilibrium molecular dynamics simulations (EMD) in conjunction with our recently proposed method [J. S. Hansen, B. D. Todd, and P. J. Daivis, Phys. Rev. E 84, 016313 (2011)]. We first calculate the fluid-graphene interfacial friction coefficient, from which we can predict the slip length and the average velocity of the first fluid layer close to the wall (referred to as the slip velocity). Using direct nonequilibrium molecular dynamics simulations (NEMD) we then calculate the slip length and slip velocity from the streaming velocity profiles in Poiseuille and Couette flows. The slip lengths and slip velocities from the NEMD simulations are found to be in excellent agreement with our EMD predictions. Our EMD method therefore enables one to directly calculate this intrinsic friction coefficient between fluid and solid and the slip length for a given fluid and solid, which is otherwise tedious to calculate using direct NEMD simulations at low pressure gradients or shear rates. The advantages of the EMD method over the NEMD method to calculate the slip lengths/flow rates for nanofluidic systems are discussed, and we finally examine the dynamic behaviour of slip due to an externally applied field and shear rate.     

Direct measurement of the binding force between microfabricated particles and a planar surface in aqueous solution by force-sensing piezoresistive cantilevers

We propose a force measurement method for evaluating the binding force between microscale flat surfaces in an aqueous solution. Using force-sensing piezoresistive cantilevers with sub-nanonewton force resolution, we have directly measured binding forces between SiO2-SiO2 microcontacts, which were created by gravity-driven random collision between microfabricated SiO2 cylindrical particles and a planar SiO2 substrate in a HCl solution. First, to examine our method we measured the pH dependence of the binding force. The binding forces were 12 and 5.8 nN at pH 1.0 and 2.0, respectively. As the pH increased, the binding force decreased and became zero at pH greater than 3.0. We confirmed that the bindings were based on the van der Waals' (VDW) force at pH 2.0 or less whereas a repulsive double-layer force acted between the surfaces at pH 3.0 or more. Second, the binding forces were categorized into a friction force or an adhesion force between the particles and the substrate. In the measurement, the friction force between the particle and the substrate was measured in the case when the particle slid on the substrate. On the contrary, the adhesion force was measured when the particle came off the substrate. Whether the particle slid or came off depended on the aspect ratio of the particle. We fabricated cylindrical particles with an aspect ratio of 0.03-2.0 and distinguished the friction force from the adhesion force by changing the aspect ratio of the particles. As a result, the friction force per unit contact area between SiO2-SiO2 flat surfaces was found to be 330 pN/microm2 +/- 20% when we used particles with a low aspect ratio (<0.1), and the adhesion force per unit contact area was 90 pN/microm2 +/- 20% for particles with a high aspect ratio (>0.4). For fluidic self-assembly that utilizes microscale surface contact in a liquid, our measurement method is an effective tool for studying and developing systems.     

Amontonian frictional behaviour of nanostructured surfaces

With nanotextured surfaces and interfaces increasingly being encountered in technological and biomedical applications, there is a need for a better understanding of frictional properties involving such surfaces. Here we report friction measurements of several nanostructured surfaces using an Atomic Force Microscope (AFM). These nanostructured surfaces provide well defined model systems on which we have tested the applicability of Amontons' laws of friction. Our results show that Amontonian behaviour is observed with each of the surfaces studied. However, no correlation has been found between measured friction and various surface roughness parameters such as average surface roughness (R(a)) and root mean squared (rms) roughness. Instead, we propose that the friction coefficient may be decomposed into two contributions, i.e., μ = μ(0) + μ(g), with the intrinsic friction coefficient μ(0) accounting for the chemical nature of the surfaces and the geometric friction coefficient μ(g) for the presence of nanotextures. We have found a possible correlation between μ(g) and the average local slope of the surface nanotextures.     

Precise multipole method for calculating many-body hydrodynamic interactions in a microchannel

We introduce a novel and precise method for computing many-body hydrodynamic interactions in a cylindrical microchannel. The method is generic in the sense that we can easily change the radius and the character of particles (hard spheres, droplets, permeable spheres, etc.). These features are not available in any of the existing methods. Comparison with the available results validates our method. In particular we obtain excellent agreement with the analytically known expression for the single particle friction coefficient. Additionally we observe negative hydrodynamic coupling for finite particles which are consistent with the recently reported effect for point particles. As an example we compute the velocities of polymeric chains of particles in parabolic flow and compare them to unbounded space. The method will be helpful in the understanding of physical and physicochemical processes in a wide range of bio-, geophysical, and microfluidic systems.     

Transport phenomena in an agitated vessel with an eccentrically located impeller

The paper presents results of an experimental analysis of the transport phenomena at the vicinity of the wall of an unbaffled agitated vessel with an eccentrically located impeller. Distributions of the transport coefficients were experimentally studied using an electrochemical method within the turbulent regime of the Newtonian liquid flow. Measurements were carried out in an agitated vessel with the inner diameter T = 0.3 m. Liquid height in the vessel was equal to the inner diameter, H = T. The agitated vessel was equipped with a Rushton or a Smith turbine or an A 315 impeller. Eccentricity of the impeller shaft was varied from 0 to 0.53. Local values of the dimensionless shear rate, shear stress, dynamic velocity and friction coefficient were integrated numerically for the whole surface area of the cylindrical wall of the vessel. Averaged values of these quantities were correlated with the impeller eccentricity and modified Reynolds number. The proposed Eqs. (5)–(8), with the coefficients given in Table 2, have no equivalent in open literature concerning this subject. Distributions of the shear rate, γ/n, and friction coefficient, f, at the vicinity of the cylindrical wall of the unbaffled vessel equipped with eccentric Rushton or Smith turbine or A 315 impeller are very uneven and they depend significantly on the impeller eccentricity, e/R. Maximum local values of these variables are located on the wall section closest to the impeller blades. From among the tested impellers, the greatest effects of the impeller eccentricity, e/R, and the liquid turbulence (described by the modified Reynolds number Re _P,M) on the averaged dimensionless shear rate (γ/n)_m and friction coefficient, f _m, are found for the radial-flow Rushton turbine located eccentrically in an unbaffled agitated vessel.     

Simulations of nanotribology with realistic probe tip models

We present the results of massively parallel molecular dynamics simulations aimed at understanding the nanotribological properties of alkylsilane self-assembled monolayers (SAMs) on amorphous silica. In contrast to studies with opposing flat plates, as found in the bulk of the simulation literature, we use a model system with a realistic AFM tip (radius of curvature ranging from 3 to 30 nm) in contact with a SAM-coated silica substrate. We compare the differences in response between systems in which chains are fully physisorbed, fully chemisorbed, and systems with a mixture of the two. Our results demonstrate that the ubiquitous JKR and DMT models do not accurately describe the contact mechanics of these systems. In shear simulations, we find that the chain length has minimal effects on both the friction force and coefficient. The tip radius affects the friction force only (i.e., the coefficient is unchanged) by a constant shift in magnitude due to the increase in pull-off force with increasing radius. We also find that at extremely low loads, on the order of 10 nN, shearing from the tip causes damage to the physisorbed monolayers by removal of molecules.     

Tribological properties of alkylsilane self-assembled monolayers

In this study, we perform molecular dynamics simulations of adhesive contact and friction between alkylsilane Si(OH)(3)(CX(2))(10)CX(3) and alkoxylsilane Si(OH)(2)(CX(2))(10)CX(3) (where X = H or F) self-assembled monolayers (SAMs) on an amorphous silica substrate. The alkylsilane SAMs are primarily hydrogen-bonded or physisorbed to the surface. The alkoxylsilane SAMs are covalently bonded or chemisorbed to the surface. Previously, we studied the chemisorbed systems. In this work, we study the physisorbed systems and compare the tribological properties with the chemisorbed systems. Furthermore, we examine how water at the interface of the SAMs and substrate affects the tribological properties of the physisorbed systems. When less than a third of a monolayer is present, very little difference in the microscopic friction coefficient mu or shear stresses is observed. For increasing amounts of water, the values of mu and the shear stresses decrease; this effect is somewhat more pronounced for fluorocarbon alkylsilane SAMs than for the hydrocarbon SAMs. The observed decrease in friction is a consequence of a slip plane that occurs in the water as the amount of water is increased. We studied the frictional behavior using relative shear velocities ranging from v = 2 cm/s to 2 m/s. Similar to previously reported results for alkoxylsilane SAMs, the values of the measured stress and mu for the alkylsilane SAM systems decrease monotonically with v.     

Effects of unsaturation on film structure and friction of fatty acids in a model base oil

The normal and friction forces between layers of three fatty acids (stearic, oleic, and linoleic acid) and a rosin acid (dehydroabietic acid) have been measured in n-hexadecane with a surface forces apparatus. Stearic, oleic, and dehydroabietic acid form loose-packed monolayers on mica surfaces when adsorbed from dry n-hexadecane. Linoleic acid forms an additional dimer layer between monolayer-covered surfaces, where it is stabilized by interactions between the double-bond-rich regions of the molecules. The monolayers formed by linoleic and dehydroabietic acid are thinner than the ones formed by stearic and oleic acid, but are not as easily removed from between the mica surfaces when the load or pressure is increased. The friction force increased linearly with load in all systems, and the friction coefficient increased with increasing unsaturation. Linoleic acid showed two regimes of linear friction with increasing load, corresponding to two different film thicknesses. Its friction was sensitive to sliding speed and adsorption time, and the thinner film observed at higher load had a lower friction coefficient. Such features were not observed for stearic and oleic acid, where the monolayers were removed and the friction coefficient changed to that of pure n-hexadecane at a pressure of 3.5 MPa.     

On the friction coefficient of straight-chain aggregates

A methodology to calculate the friction coefficient of an aggregate in the continuum regime is proposed. The friction coefficient and the monomer shielding factors, aggregate-average or individual, are related to the molecule-aggregate collision rate that is obtained from the molecular diffusion equation with an absorbing boundary condition on the aggregate surface. Calculated friction coefficients of straight chains are in very good agreement with previous results, suggesting that the friction coefficients may be accurately calculated from the product of the collision rate and an average momentum transfer, the latter being independent of aggregate morphology. Langevin-dynamics simulations show that the diffusive motion of straight-chain aggregates may be described either by a monomer-dependent or an aggregate-average random force, if the shielding factors are appropriately chosen.     

A method for estimating unperturbed chain dimension from molecular weight dependence of sedimentation and diffusion coefficients

A method (method 2L) has been proposed for evaluation of the unperturbed chain dimension A from the molecular weight dependence of the molecular friction coefficient, derived from sedimentation and diffusion coefficients. This method is widely applicable when the unperturbed chain is non-Gaussian and/or the solvent molecules are semi-permeable through the polymer chain sphere (i.e. the solvent draining effect is not negligible). Literature data for cellulose and amylose derivative solutions have been analysed according to the method proposed here and the A values obtained thus are in good agreement with those by other methods for a non-Gaussian and draining chain.     

Study on friction performance of graphene-based semi-solid grease

The graphene-based semi-solid grease with low friction coefficient was prepared by highly dispersed mixing method.The friction testing result showed that the friction coefficient of the graphene oxidebased semi-solid grease reduced from ca.0.105 of graphite-based one to ca.0.075,approximately 30%decreasing.Further,the graphene-based semi-solid grease shows the more outstandingly lubricating property,and the friction coefficient approximately drops to the range of between 0.04 and 0.06.By comparing with the graphite-based grease,the friction coefficient decreases about 40%–60% and the wear reduced over 50%.     

Dynamics of imbibition into a pore with a heterogeneous surface

We use large-scale molecular dynamics simulations to study the dynamics of liquid penetration into a cylindrical pore having a randomly heterogeneous surface comprising areas of differing wettability. Our results confirm that the equilibrium contact angle in the heterogeneous pore is well described by Cassie's law. As in the case of the uniform pore studied previously, the dynamics of penetration can be described by the Lucas-Washburn equation corrected to include the effect of a dynamic contact angle. The dissipation at the three-phase line, which gives rise to the dynamic contact angle, may be characterized in terms of a friction coefficient. Interestingly, the wetting-line friction on the heterogeneous surface also turns out to be a linear function of the fractional concentration of the areas of different wettability, analogous to Cassie's law. These results can be interpreted in terms of an independent random walk mechanism.     

Combining molecular dynamics with Lattice Boltzmann: a hybrid method for the simulation of (charged) colloidal systems

We present a hybrid method for the simulation of colloidal systems that combines molecular dynamics (MD) with the Lattice Boltzmann (LB) scheme. The LB method is used as a model for the solvent in order to take into account the hydrodynamic mass and momentum transport through the solvent. The colloidal particles are propagated via MD and they are coupled to the LB fluid by viscous forces. With respect to the LB fluid, the colloids are represented by uniformly distributed points on a sphere. Each such point [with a velocity V(r) at any off-lattice position r] is interacting with the neighboring eight LB nodes by a frictional force F = xi0(V(r)-u(r)), with xi0 being a friction coefficient and u(r) being the velocity of the fluid at the position r. Thermal fluctuations are introduced in the framework of fluctuating hydrodynamics. This coupling scheme has been proposed recently for polymer systems by Ahlrichs and Dunweg [J. Chem. Phys. 111, 8225 (1999)]. We investigate several properties of a single colloidal particle in a LB fluid, namely, the effective Stokes friction and long-time tails in the autocorrelation functions for the translational and rotational velocity. Moreover, a charged colloidal system is considered consisting of a macroion, counterions, and coions that are coupled to a LB fluid. We study the behavior of the ions in a constant electric field. In particular, an estimate of the effective charge of the macroion is yielded from the number of counterions that move with the macroion in the direction of the electric field.     

Electrophoretic mobility of cylindrical soft particles

 A general theory for the electrophoresis of a cylindrical soft particle (i.e., a cylindrical hard colloidal particle coated with a layer of ion-penetrable polyelectrolytes) in an electrolyte solution in an applied transverse or tangential electric field is proposed. This theory unites two different electrophoresis theories for cylindrical hard particles and for cylindrical polyelectrolytes. That is, the general mobility expression obtained in this paper tends to the mobility expression for a cylindrical hard particle for the case where the polyelectrolyte layer is absent or the frictional coefficient in the poly-electrolyte layer becomes infinity, whereas it tends to that for a cylin-drical polyelectrolyte in the absence of the particle core. Simple approximate analytic mobility expressions are also presented. Received: 29 August 1996 Accepted: 7 November 1996     

A random walk through the dynamics of homogeneous vapor-liquid nucleation

A method of calculating rates of homogeneous vapor-liquid nucleation based on Langevin dynamics of a few relevant degrees of freedom on a free-energy surface is proposed. The surface is obtained here from simulation and from a semi empirical expression. The mass and friction coefficients are derived from atomistic umbrella-sampling molecular-dynamics simulations. The calculated nucleation rate agrees with atomistic simulations for one particular state point of the Lennard-Jones fluid. The present method is about four orders of magnitude more computationally efficient than the direct atomistic simulation of the transmission coefficient.     

Directionally negative friction: a method for enhanced sampling of rare event kinetics

A method exploiting the properties of an artificial (nonphysical) Langevin dynamics with a negative frictional coefficient along a suitable manifold and positive friction in the perpendicular directions is presented for the enhanced calculation of time-correlation functions for rare event problems. Exact time-correlation functions that describe the kinetics of the transitions for the all-positive, physical system can be calculated by reweighting the generated trajectories according to stochastic path integral treatment involving a functional weight based on an Onsager-Machlup action functional. The method is tested on a prototypical multidimensional model system featuring the main elements of conformational space characteristic of complex condensed matter systems. Using the present method, accurate estimates of rate constants require at least three order of magnitudes fewer trajectories than regular Langevin dynamics. The method is particularly useful in calculating kinetic properties in the context of multidimensional energy landscapes that are characteristic of complex systems such as proteins and nucleic acids.     

Friction between brush layers of charged and neutral bottle-brush macromolecules. molecular dynamics simulations

Using molecular dynamics simulations, we study the lubricating properties of neutral and charged bottle-brush coatings as a function of the compression and shear stresses and brush grafting density. Our simulations have shown that in charged bottle-brush systems under shear there is a layer with excess counterions located in the middle between brush-bearing surfaces. The main deformation mode of the charged bottle-brush layers is associated with the backbone deformation, resulting in the backbone deformation ratio, α, and shear viscosity, η, being universal functions of the Weissenberg number. In the case of neutral bottle-brush systems, in addition to the backbone deformation there is also side chain deformation. The coupling between backbone and side chain deformation violates universality in the deformation ratio, α, dependence on the Weissenberg number and results in scaling exponents varying with the compression stress and brush grafting density. The existence of different length scales controlling deformation of neutral bottle brushes manifests itself in the shear viscosity, η, dependence on the shear rate, ?γ. Shear viscosity, η, as a function of the shear rate, ?γ, has two plateaus and two shear thinning regimes. The low shear rate plateau and shear thinning regime correspond to the backbone deformation, while the second plateau and shear thinning regime at moderate shear rates are due to side chain deformation. For both systems the value of the friction coefficient increases with increasing shear rate. The values of the friction coefficient for charged bottle-brush systems are about ten times smaller than corresponding values for neutral systems at the same shear rate.     

A new correlation on predicting self- and mutual-diffusion coefficient of Lennard–Jones chain fluid

Based on the Chapman–Enskog theory of diffusion and molecular dynamics simulation data for Lennard–Jones chain (LJC) fluid, a new semi-empirical correlation for calculating the self-diffusion coefficient of LJC fluid is proposed. The new correlation introduces in two correction functions with six fitting parameter to modify the impact of intermolecular repulsive and attractive potential energy on molecular friction coefficient. The new correlation represents the experimental self-diffusion coefficients with an average absolute deviation (AAD) of 3.46% for 23 polyatomic compounds (1102 experimental data points) over wide ranges of temperature and pressure. On this basis, the van der Waals mixing rule is adopted to calculate the mutual-diffusion coefficient of binary LJC fluid. By comparison of calculated results with the experimental data of 12 binary LJC systems over wide range of temperature and composition, the average absolute deviation is 6.98% which verifies the accuracy and the effectiveness of the new correlation.     

Selection of natural fibers based brake friction composites using hybrid ELECTRE-entropy optimization technique

Selecting the best brake friction composite composition amongst a set of natural fibres reinforced composites using hybrid optimization method - ELECTRE (elimination and choice translating priority) II - entropy is discussed in this article. Three sets of natural fibres containing different amounts of banana, hemp, and pineapple reinforced brake friction composites were tested according to IS 2742 (part-4) regulations on a chase friction testing machine. The experimental results have been discussed in terms of seven performance defining attributes such as coefficient of friction, fade, wear, friction stability coefficient, friction recovery, friction fluctuations, and friction variability coefficient. The composite containing 5 wt% pineapple fiber exhibit the highest coefficient of friction, whereas wear performance and friction stability remain highest for 5 wt% hemp fiber based composites. The recovery performance remains highest for the composite containing 15 wt% banana fiber, while fade, friction variability, and fluctuations remain lowest for 10 wt% banana fiber reinforced composites. The tribological results indicate that the inclusion of disparate natural fibers in varying amounts may differently affect the tribological performances and therefore to choose the best brake friction composite satisfying the maximum beneficial criteria hybrid ELECTRE II- entropy optimization technique is used. Brake friction composite containing ~10 wt% banana fibers was ranked first, in meeting the desired performance tribological properties. A comparison of this optimization approach with other multi-criteria decision-making techniques is also made for validating the performance ranking of these composites.