Fluid particle model

Abstract

We present a mechanistic model for a Newtonian fluid called fluid particle dynamics. By analyzing the concept of "fluid particle" from the point of view of a Voronoi tessellation of a molecular fluid, we propose an heuristic derivation of a dissipative particle dynamics algorithm that incorporates shear forces between dissipative particles. The inclusion of these non-central shear forces requires the consideration of angular velocities of the dissipative particles in order to comply with the conservation of angular momentum. It is shown that the equilibrium statistical mechanics requirement that the linear and angular velocity fields are Gaussian is sufficient to construct the random thermal forces between dissipative particles. The proposed algorithm is very similar in structure to the (isothermal) smoothed particle dynamics algorithm. In this way, this work represents a generalization of smoothed particle dynamics that incorporates consistently thermal fluctuations and exact angular momentum conservation. It contains also the dissipative particle dynamics algorithm as a special case. Finally, the kinetic theory of the dissipative particles is derived and explicit expressions of the transport coefficients of the fluid in terms of model parameters are obtained. This allows to discuss resolution issues for the model.

Lattice Boltzmann Simulations of Soft Matter Systems

“…DPD can be extended to thermalize the perpendicular component of the interparticle velocity as well, thereby allowing more control over the transport properties of the model [49,57].…”

“…Dissipative Particle Dynamics, which has become quite popular in the soft-matter community [44][45][46][47][48][49][50][51][52][53][54][55][56], was developed to address the computational limitations of MD. A very soft interparticle potential, representing coarse-grained aggregates of molecules, enables a large time step to be used.…”

Everything you always wanted to know about SDPD⋆ (⋆but were afraid to ask)

“…In order to have better representations of the friction forces and angular momentum conservation, the fluid particle model (FPM) was introduced in Refs. [50] and [51]. SDPD can be regarded as the final outcome of these endeavors, grouping all the partial solutions to the above problems.…”

A mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method

“…The dimension of the particle mass matrix M A is 3n a × 3n a . The minimum of the residual corresponds to the following relationship: (10) where M is the FE mass matrix, with dimensions 3N × 3N, expressed as (11) Since the basic assumption of the mesoscale discretization relies on the Voronoi tesselation of space, the matrix M represents the finite element consistent mass matrix M, i.e., (12) where ρ is the fluid density, V is the element volume, and N(ξ 1 , ξ 2 , ξ 3 ) is the matrix of interpolation functions of order 3N × 3N, evaluated at material points continuously distributed within the finite element. From the relation (10) we obtain (13) Substituting (13) into (5) and then into (4), we obtain the fine scale velocity correction v′ as (14) expressed in terms of the fine scale (mesoscale) velocity v. This equation can be written as (15) where (16) and (17) are the projection operators, and I is the identity matrix.…”

“…The Lagrangian description of motion employed in the DP methods assumes appropriate quantification of interaction forces, which include conservative, dissipative and random forces (and moments). One of the most advanced methods in this field is the dissipative particle dynamics (DPD) method for fluids, introduced by Hoogerbrugge and Koelman [6], further generalized theoretically, particularly by Espanol and co-authors [7][8][9][10][11][12][13][14][15][16], Flekkoy and co-authors [2,3], and in [17][18][19], and applied to various problems [20][21][22][23][24]. The DPD method will be described here in some detail and used subsequently.…”