Edward Smith

Pressure dependence of confined liquid behavior subjected to boundary-driven shear

Non-equilibrium molecular dynamics simulations of boundary-driven sheared Lennard-Jones liquids at variable pressure up to 5 GPa (for argon) reveal a rich out-of-equilibrium phase behavior with a strong degree of shear localization. At the lowest apparent shear rate considered (wall speed ~1 m s(-1)) the confined region is an homogeneously sheared solid (S) with no slip at the walls. This transforms at higher shear rates to a non-flowing plug with slip at the walls, referred to as the plug slip (PS) state. At higher shear rate a central localized (CL) state formed in which the shear gradient was localized in the center of the film, with the rest of the confined sample in a crystalline state commensurate with the wall lattice. The central zone liquidlike region increased in width with shear rate. A continuous rounded temperature profile across the whole system reflects strong dynamical coupling between the wall and confined region. The temperature rise in the confined film is consistent with the Brinkman number. The transition from the PS to CL states typically occurred at a wall speed near where the shear stress approached a critical value of ~3% of the shear modulus, and also near the peak in the traction coefficient, μ. The peak traction coefficient values computed, ~0.12-0.14 at 1000 MPa agree with those found for traction fluids and occur when the confined liquid is in the PS and CL states. At low wall speeds slip can occur at one wall and stick at the other. Poorly wetting liquids manifest long-lived asymmetries in the confined liquid properties across the system, and a shift in solid-liquid phase co-existence to higher shear rates. A non-equilibrium phase diagram based on these results is proposed. The good agreement of the tribological response of the Lennard-Jones fluid with that of more complicated molecular systems suggests that a corresponding states scaling of the tribological behavior could apply.

The equivalence between volume averaging and method of planes definitions of the pressure tensor at a plane.

It is shown analytically that the method of planes (MOP) [Todd, Evans, and Daivis, Phys. Rev. E 52, 1627 (1995)] and volume averaging (VA) [Cormier, Rickman, and Delph, J. Appl. Phys. 89, 99 (2001)] formulas for the local pressure tensor, P(α, y)(y), where α ≡ x, y, or z, are mathematically identical. In the case of VA, the sampling volume is taken to be an infinitely thin parallelepiped, with an infinite lateral extent. This limit is shown to yield the MOP expression. The treatment is extended to include the condition of mechanical equilibrium resulting from an imposed force field. This analytical development is followed by numerical simulations. The equivalence of these two methods is demonstrated in the context of non-equilibrium molecular dynamics (NEMD) simulations of boundary-driven shear flow. A wall of tethered atoms is constrained to impose a normal load and a velocity profile on the entrained central layer. The VA formula can be used to compute all components of P(αβ)(y), which offers an advantage in calculating, for example, P(xx)(y) for nano-scale pressure-driven flows in the x-direction, where deviations from the classical Poiseuille flow solution can occur.

The method of planes pressure tensor for a spherical subvolume

Various formulas for the local pressure tensor based on a spherical subvolume of radius, R, are considered. An extension of the Method of Planes (MOP) formula of Todd et al. [Phys. Rev. E 52, 1627 (1995)] for a spherical geometry is derived using the recently proposed Control Volume formulation [E. R. Smith, D. M. Heyes, D. Dini, and T. A. Zaki, Phys. Rev. E 85, 056705 (2012)]. The MOP formula for the purely radial component of the pressure tensor is shown to be mathematically identical to the Radial Irving-Kirkwood formula. Novel offdiagonal elements which are important for momentum conservation emerge naturally from this treatment. The local pressure tensor formulas for a plane are shown to be the large radius limits of those for spherical surfaces. The radial-dependence of the pressure tensor computed by Molecular Dynamics simulation is reported for virtual spheres in a model bulk liquid where the sphere is positioned randomly or whose center is also that of a molecule in the liquid. The probability distributions of angles relating to pairs of atoms which cross the surface of the sphere, and the center of the sphere, are presented as a function of R. The variance in the shear stress calculated from the spherical Volume Averaging method is shown to converge slowly to the limiting values with increasing radius, and to be a strong function of the number of molecules in the simulation cell.

A localized momentum constraint for non-equilibrium molecular dynamics simulations

A method which controls momentum evolution in a sub-region within a molecular dynamics simulation is derived from Gausss principle of least constraint. The technique for localization is founded on the equations by Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)] expressed in a weak form according to the control volume (CV) procedure derived by Smith et al. [Phys. Rev. E. 85, 056705 (2012)]. A term for the advection of molecules appears in the derived constraint and is shown to be essential in order to exactly control the time evolution of momentum in the subvolume. The numerical procedure converges the total momentum in the CV to the target value to within machine precision in an iterative manner. The localized momentum constraint can prescribe essentially arbitrary flow fields in non-equilibrium molecular dynamics simulations. The methodology also forms a rigorous mathematical framework for introducing coupling constraints at the boundary between continuum and discrete systems. This functionality is demonstrated with a boundary-driven flow test case.

Equilibrium fluctuations of liquid state static properties in a subvolume by molecular dynamics.

System property fluctuations increasingly dominate a physical process as the sampling volume decreases. The purpose of this work is to explore how the fluctuation statistics of various thermodynamic properties depend on the sampling volume, using molecular dynamics (MD) simulations. First an examination of various expressions for calculating the bulk pressure of a bulk liquid is made, which includes a decomposition of the virial expression into two terms, one of which is the Method of Planes (MOP) applied to the faces of the cubic simulation cell. Then an analysis is made of the fluctuations of local density, temperature, pressure, and shear stress as a function of sampling volume (SV). Cubic and spherical shaped SVs were used within a spatially homogeneous LJ liquid at a state point along the melting curve. It is shown that the MD-generated probability distribution functions (PDFs) of all of these properties are to a good approximation Gaussian even for SV containing only a few molecules (∼10), with the variances being inversely proportional to the SV volume, Ω. For small subvolumes the shear stress PDF fits better to a Gaussian than the pressure PDF. A new stochastic sampling technique to implement the volume averaging definition of the pressure tensor is presented, which is employed for cubic, spherical, thin cubic, and spherical shell SV. This method is more efficient for less symmetric SV shapes.

Moving Contact Lines: Linking Molecular Dynamics and Continuum-Scale Modeling

Despite decades of research, the modeling of moving contact lines has remained a formidable challenge in fluid dynamics whose resolution will impact numerous industrial, biological, and daily life applications. On the one hand, molecular dynamics (MD) simulation has the ability to provide unique insight into the microscopic details that determine the dynamic behavior of the contact line, which is not possible with either continuum-scale simulations or experiments. On the other hand, continuum-based models provide a link to the macroscopic description of the system. In this Feature Article, we explore the complex range of physical factors, including the presence of surfactants, which governs the contact line motion through MD simulations. We also discuss links between continuum- and molecular-scale modeling and highlight the opportunities for future developments in this area.

The pressure tensor across a liquid-vapour interface

Inhomogeneous fluids exhibit physical properties that are neither uniform nor isotropic. The pressure tensor is a case in point, key to the mechanical description of the interfacial region. Kirkwood and Buff and, later, Irving and Kirkwood, obtained a formal treatment based on the analysis of the pressure across a planar surface [J. G. Kirkwood and F. P. Buff, J. Chem. Phys. 17(3), 338 (1949); J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950)]. We propose a generalisation of Irving and Kirkwoods argument to fluctuating, non-planar surfaces and obtain an expression for the pressure tensor that is not smeared by thermal fluctuations at the molecular scale and corresponding capillary waves [F. P. Buff et al., Phys. Rev. Lett. 15, 621-623 (1965)]. We observe the emergence of surface tension, defined as an excess tangential stress, acting exactly across the dividing surface at the sharpest molecular resolution. The new statistical mechanical expressions extend current treatments to fluctuating inhomogeneous systems far from equilibrium.

Towards the Irving-Kirkwood limit of the mechanical stress tensor

The probability density functions (PDFs) of the local measure of pressure as a function of the sampling volume are computed for a model Lennard-Jones (LJ) fluid using the Method of Planes (MOP) and Volume Averaging (VA) techniques. This builds on the study of Heyes, Dini, and Smith [J. Chem. Phys. 145, 104504 (2016)] which only considered the VA method for larger subvolumes. The focus here is typically on much smaller subvolumes than considered previously, which tend to the Irving-Kirkwood limit where the pressure tensor is defined at a point. The PDFs from the MOP and VA routes are compared for cubic subvolumes, V=ℓ3. Using very high grid-resolution and box-counting analysis, we also show that any measurement of pressure in a molecular system will fail to exactly capture the molecular configuration. This suggests that it is impossible to obtain the pressure in the Irving-Kirkwood limit using the commonly employed grid based averaging techniques. More importantly, below ℓ≈3 in LJ reduced units, the PDFs depart from Gaussian statistics, and for ℓ=1.0, a double peaked PDF is observed in the MOP but not VA pressure distributions. This departure from a Gaussian shape means that the average pressure is not the most representative or common value to arise. In addition to contributing to our understanding of local pressure formulas, this work shows a clear lower limit on the validity of simply taking the average value when coarse graining pressure from molecular (and colloidal) systems.

A Langevin model for fluctuating contact angle behaviour parametrised using molecular dynamics

Molecular dynamics simulations are employed to develop a theoretical model to predict the fluid-solid contact angle as a function of wall-sliding speed incorporating thermal fluctuations. A liquid bridge between counter-sliding walls is studied, with liquid-vapour interface-tracking, to explore the impact of wall-sliding speed on contact angle. The behaviour of the macroscopic contact angle varies linearly over a range of capillary numbers beyond which the liquid bridge pinches off, a behaviour supported by experimental results. Nonetheless, the liquid bridge provides an ideal test case to study molecular scale thermal fluctuations, which are shown to be well described by Gaussian distributions. A Langevin model for contact angle is parametrised to incorporate the mean, fluctuation and auto-correlations over a range of sliding speeds and temperatures. The resulting equations can be used as a proxy for the fully-detailed molecular dynamics simulation allowing them to be integrated within a continuum-scale solver.

Decay studies at the end of the rp-process

The rapid proton-capture process (rp-process) produces proton rich nuclei on the surface of accreting neutron stars. The light curves of type I X-ray bursts are an observable result of the energy produced. In reaction networks, a series of (p, γ) reactions and β-decays proceed along a path close to the proton drip-line culminating, for some bursts, in a Sn—Sb—Te cycle. To address uncertainties in the masses near the proton drip-line, we have observed the β-decay of neutron-deficient Sb isotopes at the National Superconducting Cyclotron Laboratory at Michigan State University. A mixed beam of unstable nuclei was produced at the Coupled Cyclotron Facility and isolated in the A1900 fragment separator. Nuclei were then implanted and decays were observed in the NSCL β-decay end station. We discuss preliminary results on β-decay properties and the search for proton radioactivity.