A Dissipative-Particle-Dynamics Model for Simulating Dynamics of Charged Colloid

A mesoscopic colloid model is developed in which a spherical colloid is represented by many interacting sites on its surface. The hydrodynamic interactions with thermal fluctuations are taken accounts in full using Dissipative Particle Dynamics, and the electrostatic interactions are simulated using Particle-Particle-Particle Mesh method. This new model is applied to investigate the electrophoretic mobility of a charged colloid under an external electric field, and the influence of salt concentration and colloid charge are systematically studied. The simulation results show good agreement with predictions from the electrokinetic theory.Comment: 17 pages, 8 figures, submitted to the proceedings of High Performance Computing in Science & Engineering '1

Inertial Coupling Method for particles in an incompressible fluctuating fluid

We develop an inertial coupling method for modeling the dynamics of point-like 'blob' particles immersed in an incompressible fluid, generalizing previous work for compressible fluids. The coupling consistently includes excess (positive or negative) inertia of the particles relative to the displaced fluid, and accounts for thermal fluctuations in the fluid momentum equation. The coupling between the fluid and the blob is based on a no-slip constraint equating the particle velocity with the local average of the fluid velocity, and conserves momentum and energy. We demonstrate that the formulation obeys a fluctuation-dissipation balance, owing to the non-dissipative nature of the no-slip coupling. We develop a spatio-temporal discretization that preserves, as best as possible, these properties of the continuum formulation. In the spatial discretization, the local averaging and spreading operations are accomplished using compact kernels commonly used in immersed boundary methods. We find that the special properties of these kernels make the discrete blob a particle with surprisingly physically-consistent volume, mass, and hydrodynamic properties. We develop a second-order semi-implicit temporal integrator that maintains discrete fluctuation-dissipation balance, and is not limited in stability by viscosity. Furthermore, the temporal scheme requires only constant-coefficient Poisson and Helmholtz linear solvers, enabling a very efficient and simple FFT-based implementation on GPUs. We numerically investigate the performance of the method on several standard test problems...Comment: Contains a number of corrections and an additional Figure 7 (and associated discussion) relative to published versio

Effective slip-length tensor for a flow over weakly slipping stripes

We discuss the flow past a flat heterogeneous solid surface decorated by slipping stripes. The spatially varying slip length, $b(y)$, is assumed to be small compared to the scale of the heterogeneities, $L$, but finite. For such "weakly" slipping surfaces, earlier analyses have predicted that the effective slip length is simply given by the surface-averaged slip length, which implies that the effective slip-length tensor becomes isotropic. Here we show that a different scenario is expected if the local slip length has step-like jumps at the edges of slipping heterogeneities. In this case, the next-to-leading term in an expansion of the effective slip-length tensor in powers of ${max}\,(b(y)/L)$ becomes comparable to the leading-order term, but anisotropic, even at very small $b(y)/L$. This leads to an anisotropy of the effective slip, and to its significant reduction compared to the surface-averaged value. The asymptotic formulae are tested by numerical solutions and are in agreement with results of dissipative particle dynamics simulations.Comment: 11 pages, 4 figures, submitted to Phys. Rev.

Physical mechanisms governing drag reduction in turbulent Taylor-Couette flow with finite-size deformable bubbles

The phenomenon of drag reduction induced by injection of bubbles into a turbulent carrier fluid has been known for a long time; the governing control parameters and underlying physics is however not well understood. In this paper, we use three dimensional numerical simulations to uncover the effect of deformability of bubbles injected in a turbulent Taylor-Couette flow on the overall drag experienced by the system. We consider two different Reynolds numbers for the carrier flow, i.e. $Re_i=5\times 10^3$ and $Re_i=2\times 10^4$; the deformability of the bubbles is controlled through the Weber number which is varied in the range $We=0.01 - 2.0$. Our numerical simulations show that increasing the deformability of bubbles i.e., $We$ leads to an increase in drag reduction. We look at the different physical effects contributing to drag reduction and analyse their individual contributions with increasing bubble deformability. Profiles of local angular velocity flux show that in the presence of bubbles, turbulence is enhanced near the inner cylinder while attenuated in the bulk and near the outer cylinder. We connect the increase in drag reduction to the decrease in dissipation in the wake of highly deformed bubbles near the inner cylinder

Effective slippage on superhydrophobic trapezoidal grooves

We study the effective slippage on superhydrophobic grooves with trapezoidal cross-sections of various geometries (including the limiting cases of triangles and rectangular stripes), by using two complementary approaches. First, dissipative particle dynamics (DPD) simulations of a flow past such surfaces have been performed to validate an expression [E.S.Asmolov and O.I.Vinogradova, J. Fluid Mech. \textbf{706}, 108 (2012)] that relates the eigenvalues of the effective slip-length tensor for one-dimensional textures. Second, we propose theoretical estimates for the effective slip length and calculate it numerically by solving the Stokes equation based on a collocation method. The comparison between the two approaches shows that they are in excellent agreement. Our results demonstrate that the effective slippage depends strongly on the area-averaged slip, the amplitude of the roughness, and on the fraction of solid in contact with the liquid. To interpret these results, we analyze flow singularities near slipping heterogeneities, and demonstrate that they inhibit the effective slip and enhance the anisotropy of the flow. Finally, we propose some guidelines to design optimal one-dimensional superhydrophobic surfaces, motivated by potential applications in microfluidics.Comment: 11 pages, 8 figures, submitted to J. Chem. Phy

The Stokes-Einstein Relation at Moderate Schmidt Number

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently-developed minimally-resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The numerical data is in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.Comment: Submitte

A GPU-accelerated package for simulation of flow in nanoporous source rocks with many-body dissipative particle dynamics

Mesoscopic simulations of hydrocarbon flow in source shales are challenging, in part due to the heterogeneous shale pores with sizes ranging from a few nanometers to a few micrometers. Additionally, the sub-continuum fluid-fluid and fluid-solid interactions in nano- to micro-scale shale pores, which are physically and chemically sophisticated, must be captured. To address those challenges, we present a GPU-accelerated package for simulation of flow in nano- to micro-pore networks with a many-body dissipative particle dynamics (mDPD) mesoscale model. Based on a fully distributed parallel paradigm, the code offloads all intensive workloads on GPUs. Other advancements, such as smart particle packing and no-slip boundary condition in complex pore geometries, are also implemented for the construction and the simulation of the realistic shale pores from 3D nanometer-resolution stack images. Our code is validated for accuracy and compared against the CPU counterpart for speedup. In our benchmark tests, the code delivers nearly perfect strong scaling and weak scaling (with up to 512 million particles) on up to 512 K20X GPUs on Oak Ridge National Laboratory's (ORNL) Titan supercomputer. Moreover, a single-GPU benchmark on ORNL's SummitDev and IBM's AC922 suggests that the host-to-device NVLink can boost performance over PCIe by a remarkable 40\%. Lastly, we demonstrate, through a flow simulation in realistic shale pores, that the CPU counterpart requires 840 Power9 cores to rival the performance delivered by our package with four V100 GPUs on ORNL's Summit architecture. This simulation package enables quick-turnaround and high-throughput mesoscopic numerical simulations for investigating complex flow phenomena in nano- to micro-porous rocks with realistic pore geometries

Molecular transport and flow past hard and soft surfaces: Computer simulation of model systems

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 Lennard-Jones 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.Comment: 41 pages, 13 figure