On particle-layering effect in wall-bounded Dissipative Particle Dynamics Sergey Litvinov, Marco Ellero, Xiangyu Hu, Nikolaus A. Adams Lehrstuhl f¨ ur Aerodynamik, Technische Universit¨ at M¨ unchen, 85747 Garching, Germany Dissipative Particle Dynamics (DPD) is a mesoscopic simulation method that describes “clusters” of molecules as a single numerical particle. DPD is a very effective method but it introduces numerical artifacts through the coarse-graining procedure, such as particle ordering in the near-wall region. These artifacts can result in non-physical phenomena during a simulation of a polymer tethered to the wall undergoing shear flow: polymer sticking and over-extension for higher shear rates. In this letter we report that a version of DPD with a so-called solidification boundary formulation and conservative-force interactions based on the equation of state allows to reduce number density-fluctuations in near-wall region significantly. PACS numbers: 83.10.Pp, 83.10.Rs, 36.20.-r I. INTRODUCTION Layering of liquids near a solid surface is a very well known phenomena in nanofluids and it has been inten- sively studied experimentally and numerically [1]. The effect is associated to large fluctuations arising in the molecular number density which are ultimately due to a structure induced in the liquid by the presence of the solid wall. The strong inhomogeneities of nanofluids caused by layering effects produce phenomena that are not ob- served in the continuum, as for example depletion layers, modified transport coefficients (e.g. viscosity) and slip flow [2, 3]. It has been often shown that the amount of layering observed in Molecular-Dynamics simulations of confined fluids depends strongly on the type of wall as well as on the wall-liquid microscopic interaction pa- rameters, and decreases rapidly as the distance from the surface exceeds typically a few molecule sizes [4] . At larger distances the number density becomes almost con- stant and the fluid behaves like a continuum. Although this phenomena is to be expected on the molecular level, it must be seen as an artifact on larger scales [5]. Recently, numerical methods operating on a coarse- grained level have been developed which try to achieve larger spatio-temporal scales by reducing the number of atomistic degrees of freedom. An important method in this class is Dissipative Particle Dynamics (DPD). DPD is a relatively new mesoscopic method [6] that uses La- grangian discretization elements (particles) to represent a cluster of molecules rather than individual fluid con- stituents, allowing for the simulation of complex sys- tems at length and time scales inaccessible to Molecular- Dynamics (MD) methods. DPD captures important properties of the microscopic flow but it is known to pro- duce numerical artifacts and anomalous behaviour under specific situations. For example the implementation of no-slip boundary conditions in DPD remains a challenge. Unlike MD, the soft potential used in DPD does not pre- vent particle penetration into the solid boundaries, hence some effort must be made to enforce them correctly. Ap- proaches based on increased density of wall particles or increased interaction strength between fluid and wall par- ticles have been proposed in the past, leading, however, to depletion of particles and layering effects [7]. As sug- gested above, although the presence of wall-induced lay- ering is physically reasonable at atomistic distances from the solid wall, it should not ocurr at the typical scales of the DPD particles which are orders of magnitude larger. It should be noted that layering is frequently observed for many particle-based techniques, such as for exam- ple the continuum Smoothed Particle Hydrodynamics (SPH) method [8]. In this method, however, particle layering does not produce inaccurate results as long as the macroscopic mass fluid density is kept constant and the fluid flow properties (e.g. velocity, pressure fields) are concerned. In spite of this, there are several phys- ical situations in which, rather than the local hydrody- namic properties, the exact Lagrangian dynamics of a single fluid particle is the central focus of the investiga- tion. In such cases the artificial ordering exhibited by coarse-grained particle methods introduces spurious ef- fects which must be avoided. Some attempts to remedy these problems involve, for example, reflection of parti- cles near the wall [9], adaptive models for wall-particle in- teractions [7, 10], extension of the phase-field approach to DPD [11] and the multi-body DPD method [12]. In [13] the authors considered several type of boundary condi- tions combined with a bounce-back reflection rule and found that boundary conditions based on frozen wall particles after a pre-processing stage were able to elim- inate the number density fluctuations in the near-wall region. Duong-Hong and co-authors [14] implemented a two-layer frozen-particle structure as a boundary condi- tion and reported a reduction of number density fluctu- ations. Nevertheless, a bounce-back of penetrating par- ticles was still required. The objective of this paper is to present a new method to solve simultaneously the wall penetration and the unphysical particle-layering problems in coarse-grained DPD simulations. This is achieved by replacing the clas- sical expression for the conservative force by a new one involving an equation of state (described in detail [15]). Additionally, instead of using frozen particles on a lattice to model a solid wall, boundary particles are solidified after achieving thermal equilibrium, producing a final