Time-dependent Friction Research Articles

The role of memory-dependent friction and solvent viscosity in isomerization kinetics in viscogenic media

Molecular isomerization kinetics in liquid solvent depends on a complex interplay between the solvent friction acting on the molecule, internal dissipation effects (also known as internal friction), the viscosity of the solvent, and the dihedral free energy profile. Due to the absence of accurate techniques to directly evaluate isomerization friction, it has not been possible to explore these relationships in full. By combining extensive molecular dynamics simulations with friction memory-kernel extraction techniques we consider a variety of small, isomerising molecules under a range of different viscogenic conditions and directly evaluate the viscosity dependence of the friction acting on a rotating dihedral. We reveal that the influence of different viscogenic media on isomerization kinetics can be dramatically different, even when measured at the same viscosity. This is due to the dynamic solute-solvent coupling, mediated by time-dependent friction memory kernels. We also show that deviations from the linear dependence of isomerization rates on solvent viscosity, which are often simply attributed to internal friction effects, are due to the simultaneous violation of two fundamental relationships: the Stokes-Einstein relation and the overdamped Kramers prediction for the barrier-crossing rate, both of which require explicit knowledge of friction.

Activation and friction in enzymatic loop opening and closing dynamics

Protein loop dynamics have recently been recognized as central to enzymatic activity, specificity and stability. However, the factors controlling loop opening and closing kinetics have remained elusive. Here, we combine molecular dynamics simulations with string-method determination of complex reaction coordinates to elucidate the molecular mechanism and rate-limiting step for WPD-loop dynamics in the PTP1B enzyme. While protein conformational dynamics is often represented as diffusive motion hindered by solvent viscosity and internal friction, we demonstrate that loop opening and closing is activated. It is governed by torsional rearrangement around a single loop peptide group and by significant friction caused by backbone adjustments, which can dynamically trap the loop. Considering both torsional barrier and time-dependent friction, our calculated rate constants exhibit very good agreement with experimental measurements, reproducing the change in loop opening kinetics between proteins. Furthermore, we demonstrate the applicability of our results to other enzymatic loops, including the M20 DHFR loop, thereby offering prospects for loop engineering potentially leading to enhanced designs.

Brownian motion in a viscous fluid of particles with constant and time-dependent friction

The Brownian motion (BM) of particles in a fluid under the influence of a moving harmonic potential is described analytically. It is assumed that the bath is viscous and particles constituting it experience Stokes' force with friction coefficients that can depend on time. The generalized Langevin equation (GLE) is derived from the equations of motion for the bath and Brownian particles. It has a familiar form, but its memory kernel generalizes the expressions known from the literature even in the case of constant friction. Analytical solutions of the found GLE are obtained for the mean and mean squared displacements of the Brownian particle, assuming the overdamped character of its motion and both the overdamped and underdamped dynamics of bath particles. In the case of constant friction, the model well describes the BM when the external potential does not move so that the system is in equilibrium. The results determined by the time-dependent friction of the bath particles must be specified for concrete fluids. An example of Lennard–Jones atomic liquid is considered with the recently proposed exponential time dependence of the friction coefficient.

Numerical Simulation of Turbulent Flow and Friction Characteristics Through a Loop of Narrow Rectangular Channel Under Rolling Motions

Interaction of prevailing ocean waves and wind with the platforms containing the small modular reactors (SMRs) employed in marine environments may significantly alter the flow and friction characteristics inside these reactors. The present research is focused on the numerical study of the effects of rolling motions on the turbulent flow and frictional characteristics of a three-dimensional closed loop of narrow rectangular channels using Ansys Fluent. The computational results have been corroborated with experimental data present in literature. The results illustrate that flow and friction characteristics fluctuate sinusoidally as the loop undergoes rolling motion. Strong fluctuations were observed in the flow rate and time-dependent friction coefficient with an increase in rolling amplitude or reduction in the rolling period. These variations became more pronounced at low Reynolds numbers and diminished at higher Reynolds numbers. Increasing the fluid viscosity also subsided the rolling effects. The average flow velocity in the loop was found to decrease from 0.27 to 0.15 m/s in various phases of the rolling period. The relative Reynolds number was found to be reduced by 50% under rolling motions for the range of steady-state Reynolds numbers investigated in the present study. The transient friction coefficient was also found to oscillate under rolling motion with the same period as that of excitation. The transient friction coefficient’s oscillations also increased with rolling amplitude or reduction in the rolling period. However, the temporally averaged friction coefficient under rolling motions was found to be equal to the steady-state frictional coefficient in the loop.

Tribology test design for friction measurements with application to oral medicines

In recent years tribology tests have been used to measure friction properties of oral consumables such as semi-solid foods and medicines. The tests aim to simulate thin-film mastication conditions and are intended to correlate with mouth feel or food texture properties. In this paper a new approach is proposed to better simulate shear conditions, fluid supply and friction data capture associated with mastication and swallowing. Two primary changes are suggested: these are the reduction of the inlet influence on lubricant film properties and the ability to measure transient and time-dependent friction. The new test was used to measure friction for a range of oral medicines including a viscous solution (cough syrup) and particulate suspensions (paediatric, calcium carbonate) in combination with an artificial saliva (mucin solution), The tongue-palate was replicated by a PCX glass lens loaded and reciprocating against a textured silicone surface. A short stroke length, comparable to the Hertzian diameter of the contact, was used so the contact operated in a partially replenished lubrication condition. This ensured the film in the contact region has the same composition as the bulk fluid. Friction was measured continuously during reciprocation for up to 5 cycles (comparable to mastication time) and data was sampled at 100 Hz to capture transient friction. Tests were run with and without a mucin layer present. The results showed that tests performed after 20 min adsorption of an artificial saliva solution reduced the friction coefficient from μ = 1 to μ = 0.2–0.3. Tests with the paracetamol suspensions, which contain hard particles, recorded transient friction spikes which were not recorded for the softer calcium carbonate suspensions. Key conclusions for the design of pertinent simulation tests are that the film properties in the oral cavity are not determined by the inlet as for classical lubrication. The (bulk) oral sample is captured in the tongue-palate contact and not continually replenished. When sheared it will exhibit time (transient, longer-term) and speed dependent friction responses which contribute to sensory and texture perception.

Comment on "Brownian motion with time-dependent friction and single-particle dynamics in liquids".

Recently, Lad, Patel, and Pratap [Phys. Rev. E 105, 064107 (2022)10.1103/PhysRevE.105.064107] revisited a microscopic theory of molecular motion in liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)10.1103/PhysRev.176.239]. They argued that the friction coefficient for a Brownian particle in a liquid should exponentially depend on time and derived an equation of motion for the particle's velocity autocorrelation function (VAF). The equation was solved numerically and fitted to the results of molecular dynamics simulations on different liquids. We show that this solution, obtained under the condition of zero derivative of the VAF at time t=0, is physically incorrect at long times. This is evidenced by our exact analytical solution for the VAF, not found by Lad etal., and numerically, by using the same method as in the commented work.

Reply to "Comment on 'Brownian motion with time-dependent friction and single-particle dynamics in liquids' ".

In this reply, we respond to the comments by Lisý and Tóthová (LT) on our recent work [Phys. Rev. E 105, 064107 (2022)10.1103/PhysRevE.105.064107], where we have extended the microscopic theory of molecular motion in atomic liquids that was originally proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)10.1103/PhysRev.176.239]. Contrary to our conclusion of nonavailability of a physically tractable analytical solution of the equation of motion involving dynamic friction, LT have attempted to obtain an analytical solution giving the velocity autocorrelation function in liquids. We show that the analytical solution of the equation of motion derived by LT is incomplete and not an appropriate solution for the description of atomic dynamics in liquids. It is demonstrated that the generalized statements made by LT regarding the equation of motion giving incorrect results are unjustified in the absence of substantial proofs. Also, until and unless proven otherwise, we do not find any reason for the reconsideration of the theory as suggested by LT.

Comparison of Friction Parametrization from Dynamics and Material Properties for a Coarse-Grained Polymer Melt.

In this work, we extend an approach to coarse-grained (CG) modeling for polymer melts in which the conservative potential is parametrized using the iterative Boltzmann inversion (IBI) method and the accelerated dynamics inherent to IBI are corrected using the dissipative Langevin thermostat with a single tunable friction parameter (J. Chem. Phys. 2021, 154, 084114). Diffusive measures from picoseconds to nanoseconds are used to determine the Langevin friction factor to apply to the CG model to recover all-atom (AA) dynamics; the resulting friction factors are then compared for consistency. Here, we additionally parametrize the CG dynamics using a material property, the zero-shear viscosity, which we measure using the Green-Kubo (GK) method. Two materials are studied, squalane as a function of temperature and the same polystyrene oligomers previously studied as a function of chain length. For squalane, the friction derived from the long-time diffusive measures and the viscosity all strongly increase with decreasing temperature, showing an Arrhenius-like dependence, and remain consistent with each other over the entire temperature range. In contrast, the friction required for the picosecond diffusive measurement, the Debye-Waller factor, is somewhat lower than the friction from long-time measures and relatively insensitive to temperature. A time-dependent friction would be required to exactly reproduce the AA measurements during the caging transition connecting these two extremes over the entire timespan at this level of coarse-graining. For the polystyrene oligomers for which we previously characterized the diffusive friction, the viscosity-parametrized frictions are consistent with the diffusive measures for the smallest chain length. However, for the longer chains, we find different trends based on measurement method with friction derived from rotational diffusion remaining nearly constant, friction derived from translational diffusion showing a modestly increasing trend, and viscosity-derived friction showing a modest decreasing trend. This seems to indicate that there is some sensitivity of the friction measurement method for systems with increased relaxation times and that in particular, the unsteady dynamics of the individual parametrization schemes plays a role in this. Increased difficulty in applying the GK method with increasing relaxation time of the longer chain systems is also discussed. Overall, we find that when the material is in a high-temperature melt state and the viscosity measurement is reliable, the friction parametrization from the diffusive friction measures is consistent and the lower cost diffusive parametrization is a reliable means for modeling viscosity. Our data give insight into the time-dependent friction one might compute using a non-Markovian approach to enable the recovery of AA dynamics over a wider range of time scales than can be computed using a single friction.

Fast protein folding is governed by memory-dependent friction

When described by a low-dimensional reaction coordinate, the folding rates of most proteins are determined by a subtle interplay between free-energy barriers, which separate folded and unfolded states, and friction. While it is commonplace to extract free-energy profiles from molecular trajectories, a direct evaluation of friction is far more elusive and typically relies on fits of measured reaction rates to memoryless reaction-rate theories. Here, using memory-kernel extraction methods founded on a generalized Langevin equation (GLE) formalism, we directly calculate the time-dependent friction acting on the fraction of native contacts reaction coordinate Q, evaluated for eight fast-folding proteins, taken from a published set of large-scale molecular dynamics protein simulations. Our results reveal that, across the diverse range of proteins represented in this dataset, friction is more influential than free-energy barriers in determining protein folding rates. We also show that proteins fold in a regime where the finite decay time of friction significantly reduces the folding times, in some instances by as much as a factor of 10, compared to predictions based on memoryless friction.

Generalized Langevin equation for solute dynamics in fluids with time-dependent friction

The generalized Langevin equation (GLE) for a Brownian particle (BP) in a bath under the influence of a moving external harmonic potential is derived. It is assumed that the friction coefficients of the bath particles depend on time. The found GLE has the usual form but its memory kernel is a generalization of the expression known as a Prony series used to approximate a number of memory functions from the literature. Analytical solutions are obtained for the mean and mean squared displacements assuming the overdamped character of motion of the BP.

Experiments and Prediction of Hold Time-Dependent Static Friction of a Wet Granular Layer

Experiments and Prediction of Hold Time-Dependent Static Friction of a Wet Granular Layer

Applying position and time dependent nusselt number and friction factor into 1D model to improve regenerator design for solid-state caloric cooling cycles

Active caloric regenerative cycles have recently attracted much attention as a promising cooling technology that can potentially replace the vapor compression cycle based on its high efficiency and eco-friendly characteristics. The use of modeling is necessary in optimizing the active caloric regenerative cycle due to the system’s complex structure and numerous parameters that need to be taken into account. The cycle uses oscillatory flow to efficiently exchange heat between the caloric material and the heat transfer fluid and to generate a desired temperature gradient in the regenerator. When the oscillatory flow is used, hydrodynamically and thermally developing regions occur all over the regenerator when the direction of the fluid flow changes.To the best of the authors’ knowledge, no previous research has considered the oscillatory developing regions in a 1D model. Therefore, this study incorporated the developing regions generated by the oscillatory flow as well as the entrance developing regions into a regenerator model for the first time. Based on the modeling results, the influence of the oscillatory developing regions and the average Nusselt number increase with higher cycle frequency. Additionally, the new 1D model produces average Nusselt number similar to the 2D model with a maximum error of 4 %. Considering that the 2D model requires very high computational cost to solve the transient condition of the caloric cycle, the advanced 1D model can accurately assess the performance of the caloric cycle and provide a detailed analysis of heat transfer phenomena and fluid dynamics in the regenerator at modest computational cost.The parallel plate type, optimized using the new model, has a hydraulic diameter of 0.1 mm. However, maintaining such a small space between the plates can be challenging from an application standpoint. Therefore, this study proposes the use of a wide rectangular microchannel matrix as the regenerator. The rectangular microchannel matrix, with an aspect ratio of 30, produces a coefficient of performance of 5.65, which is comparable to the parallel plate matrix. Consequently, the wide rectangular microchannel matrix can achieve both high Nusselt number and structural stability simultaneously.

The effect of sintering time on the tribological properties of automotive brake pads

In this study, the effect of sintering temperature on the physical, chemical and tribological effects of sintered automotive friction materials was investigated. Using the powder metallurgy method, 3 different samples were produced with the codes A1, A6 and A11. Mixing, pressing and sintering processes were applied respectively as production steps. Mixing time is 90 minutes, speed is 15 rpm. The pressing pressure is 250 MPa and the duration is 1 min. The sintering temperature was 800 °C and the sintering time was 1, 6 and 11 hours, respectively. The sintering process was carried out in the sintering mold using Argon gas. As the sintering time increased, it was observed that there was an increase in the time-dependent friction coefficients of the samples. Increasing the sintering time also increased the density of the samples. As the sintering time increased, the gap in the sample decreased, as it provided better bonding of the dustsers.

Numerical analysis of time-dependent negative skin friction on pile in soft soils

The generation of negative skin friction (NSF) induces the additional axial force on the pile, which exerts a detrimental load rather than a beneficial one. However, the effect of soil creep on the long-term development of NSF has remained poorly understood. The study uses numerical analysis to investigate this effect. First, an elasto-viscoplastic model with an enhanced time integration algorithm is successfully implemented into a finite element code. Next, the two-dimensional axisymmetric pile-soil interaction model is established and properly calibrated with a known field case. Finally, parametric studies are conducted to examine different degrees of creep effect on the variation in NSF and neutral plane (NP) within the primary and secondary consolidation periods. According to the findings, a high creep coefficient of the soil results in an increase in NSF and descending trend of the NP. The creep induced delay of NSF is observed attributed to the increase in excess pore pressure during the early stage of consolidation. The NP position varies drastically at the commencement of consolidation when taking creep into consideration. Lastly, the study proposes an exponential prediction model to reflect the time dependence of the location of the NP.

Riemann problems for the 2-D pressureless gas dynamics with external forces

Abstract This paper is concerned with the pressureless gas dynamics with a space-dependent gravity or a time-dependent friction in two dimensions. The basic Riemann problems with two pieces of constant initial data are considered. By the characteristic analysis, the Riemann problems are constructively solved by two kinds of solutions: vacuum solution and delta-shock solution, which describe the phenomena of cavitation and concentration, respectively. Especially, the generalized Rankine–Hugoniot relations for delta-shock waves are clarified and applied to the Riemann problems.

Investigation of the time-dependent friction behavior of polyacrylamide hydrogels

Hydrogels have attracted enormous frictional investigation owing to their great potential in hydration lubrication. Researchers have revealed that the lubrication behavior of hydrogel depends on a number of parameters such as contact area, sliding velocity, and solution condition. However, less effort has been devoted to understanding the time-dependent friction behavior of polymeric hydrogels. In this work, the time-dependent behavior of hydrogel friction was systematically investigated through three typical polyacrylamide hydrogels (PAM, PAM-PEI, and PAM-PAA) on a rheometer. Interestingly, the friction coefficients (μ) of the hydrogels varied with time, and two distinct regimes (viz., the friction-decrease regime and friction-constant/increase regime) were observed. In the friction-decrease regime, all the friction coefficients for the three PAM-based hydrogels dramatically decreased (e.g. μ decreased from ∼ 0.107 to ∼ 0.034 for PAM, μ decreased from ∼ 0.059 to ∼ 0.021 for PAM-PAA). The decrease of friction coefficients can be explained by frictional relaxation mechanism, where the deformation of polymers in the shear direction and the desorption of polymer chains from solid surface play dominant roles. Tribological results show that the increase in friction is determined by the charge behavior and polymer network of the PAM-based hydrogels. Besides, shear velocity and pH of the solution also significantly affected the friction behavior of hydrogels on the glass substrate. The understanding of the time-dependent friction behavior of PAM hydrogels provides insights to develop water-based lubricants with engineering applications.

Micromechanics of rock damage and its recovery in cyclic loading conditions

SUMMARY Under compressive stress, rock ‘damage’ in the form of tensile microcracks is coupled to internal slip on microscopic interfaces, such as pre-existing cracks and grain boundaries. In order to characterize the contribution of slip to the overall damage process, we conduct triaxial cyclic loading experiments on Westerly granite, and monitor volumetric strain and elastic wave velocity and anisotropy. Cyclic loading tests show large hysteresis in axial stress–strain behaviour that can be explained entirely by slip. Elastic wave velocity variations are observed only past a yield point, and show hysteresis with incomplete reversibility upon unloading. Irrecoverable volumetric strain and elastic wave velocity drop and anisotropy increase with increasing maximum stress, are amplified during hydrostatic decompression, and decrease logarithmically with time during hydrostatic hold periods after deformation cycles. The mechanical data and change in elastic properties are used to determine the proportion of mechanical work required to generate tensile cracks, which increases as the rock approaches failure but remains small, up to around 10 per cent of the net dissipated work per cycle. The pre-rupture deformation behaviour of rocks is qualitatively compatible with the mechanics of wing cracks. While tensile cracks are the source of large changes in rock physical properties, they are not systematically associated with significant energy dissipation and their aperture and growth is primarily controlled by friction, which exerts a dominant control on rock rheology in the brittle regime. Time-dependent friction along pre-existing shear interfaces explains how tensile cracks can close under static conditions and produce recovery of elastic wave velocities over time.

Non-Markovian dynamics of black hole phase transition

We provide a comprehensive study on the non-Markovian dynamics of the black hole phase transitions based on the underlying free energy landscape. By assuming that the transition processes between different black hole states are stochastic, the non-Markovian dynamics of the black hole phase transition is governed by the generalized Langevin equation with the time-dependent friction that represents the memory effect from the effective thermal bath when the timescale of the system is comparable or shorter than the timescale of the effective thermal bath. We consider the first passage problem associated with the black hole phase transitions and derive the analytical expressions of the mean first passage time in the weak, intermediate, and large friction regimes. As the concrete examples, we study the effects of three types of time dependent friction kernel (delta function friction, exponentially decayed friction, and oscillatory friction) on the dynamics of Hawking-Page phase transition and the small/large RNAdS black hole phase transition. we found that there is a kinetic turnover point for each type of friction kernel when the friction strength varies. For the exponentially decayed friction kernel, it is shown that the non-Markovian effect slows down the phase transition dynamics in the weak friction regime and speeds up the transition process in the strong friction regime. For the oscillating decayed friction kernel, we found kinetic resonances when the oscillating frequency of the effective thermal bath is equal to the oscillating frequency of the black hole state in the initial potential well on the free energy landscape.

Dynamics of a colloidal particle coupled to a Gaussian field: from a confinement-dependent to a non-linear memory

The effective dynamics of a colloidal particle immersed in a complex medium is often described in terms of an overdamped linear Langevin equation for its velocity with a memory kernel which determines the effective (time-dependent) friction and the correlations of fluctuations. Recently, it has been shown in experiments and numerical simulations that this memory may depend on the possible optical confinement the particle is subject to, suggesting that this description does not capture faithfully the actual dynamics of the colloid, even at equilibrium. Here, we propose a different approach in which we model the medium as a Gaussian field linearly coupled to the colloid. The resulting effective evolution equation of the colloidal particle features a non-linear memory term which extends previous models and which explains qualitatively the experimental and numerical evidence in the presence of confinement. This non-linear term is related to the correlations of the effective noise via a novel fluctuation-dissipation relation which we derive.

Brownian motion with time-dependent friction and single-particle dynamics in liquids.

A microscopic theory of molecular motion in classical monatomic liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)10.1103/PhysRev.176.239], is revisited and extended to incorporate the dynamic friction in the Brownian description of the atomic diffusion in a mean-time-dependent harmonic force field. A modified, non-Markovian Langevin equation is utilized to derive an equation of motion for the velocity autocorrelation function with time-dependent friction coefficient. Numerical solution of the equation gives an excellent account of the velocity autocorrelation function in Lennard-Jones liquids, liquid alkali, and transition metals over a broad range of density and temperature. Derivation of the equation of motion leads to a self-consistent expression for the time dependence of friction coefficient. Our results demonstrate that the nature of time dependence of the friction coefficient changes dramatically with the liquid density. At low and moderate densities, the dynamic friction decays exponentially whereas it increases exponentially at high liquid densities. Our findings provide an opportunity for a different outlook of the Brownian description of atomic dynamics in liquids.