Ignacio Zúñiga

Boundary conditions in dissipative particle dynamics

We study a continuum model for simulating solid boundaries of a DPD fluid. A layer of frozen DPD particles is placed on the wall boundary and a continuum limit is taken. This produces effective dissipative and random forces. In addition, a reflection at the wall must be specified in order to confine the fluid. Three different wall reflection laws are studied and their effectiveness in producing stick boundary conditions and correct temperature distributions is assessed by simulation of a planar Couette flow.

Boundary Models in DPD

We present a model for treating solid boundaries of a DPD fluid. The basic idea is to model the stick boundary conditions by assuming that a layer of DPD particles is stuck on the boundary. By taking a continuum limit of this layer effective dissipative and stochastic forces on the fluid DPD particles are obtained. The boundary model is tested by a simulation of planar Couette flow which allows the performance of vicosimetric measurements. We analyze the conditions that ensure a proper stick boundary condition for an impenetrable wall, comparing with previous methods used.

Force autocorrelation function in Brownian motion theory

The force autocorrelation function of an infinitely massive Brownian particle is studied with a molecular dynamics simulation. The plateau time problem, the calculation of the friction coefficient, and the relationship between the stochastic and real force are discussed.

Shear-flow instabilities in non-flow-aligning nematic liquid crystals

Abstract This paper investigates theoretically the stability of non-flow-aligning nematics in simple shear flow by analyzing the relevant continuum equations. With the aid of numerical techniques, it proves possible to predict thresholds for instability to perturbations both within and out of the shear plane, based on the full equations without approximations. The results obtained are consistent with corresponding experimental studies.

Microscopic derivation of discrete hydrodynamics

By using the standard theory of coarse graining based on Zwanzigs projection operator, we derive the dynamic equations for discrete hydrodynamic variables. These hydrodynamic variables are defined in terms of the Delaunay triangulation. The resulting microscopically derived equations can be understood, a posteriori, as a discretization on an arbitrary irregular grid of the Navier-Stokes equations. The microscopic derivation provides a set of discrete equations that exactly conserves mass, momentum, and energy and the dissipative part of the dynamics produces strict entropy increase. In addition, the microscopic derivation provides a practical implementation of thermal fluctuations in a way that the fluctuation-dissipation theorem is satisfied exactly. This paper points toward a close connection between coarse-graining procedures from microscopic dynamics and discretization schemes for partial differential equations.

Molecular dynamics analysis of transitions between rotational isomers in polymethylene

Molecular dynamics trajectories have been computed and analyzed for linear chains, with sizes ranging from C10H22 to C100H202, and for cyclic C100H200. All hydrogen atoms are included discretely. All bond lengths, bond angles, and torsion angles are variable. Hazard plots show a tendency, at very short times, for correlations between rotational isomeric transitions at bond i and i±2, in much the same manner as in the Brownian dynamics simulations reported by Helfand and co‐workers. This correlation of next nearest neighbor bonds in isolated polyethylene chains is much weaker than the correlation found for next nearest neighbor CH–CH2 bonds in poly(1,4‐trans‐butadiene) confined to the channel formed by crystalline perhydrotriphenylene [Dodge and Mattice, Macromolecules 24, 2709 (1991)]. Less than half of the rotational isomeric transitions observed in the entire trajectory for C50H102 can be described as strongly coupled next nearest neighbor transitions. If correlated motions are identified with successiv...

On the definition of discrete hydrodynamic variables

The Green-Kubo formula for discrete hydrodynamic variables involves information about not only the fluid transport coefficients but also about discrete versions of the differential operators that govern the evolution of the discrete variables. This gives an intimate connection between discretization procedures in fluid dynamics and coarse-graining procedures used to obtain hydrodynamic behavior of molecular fluids. We observed that a natural definition of discrete hydrodynamic variables in terms of Voronoi cells leads to a Green-Kubo formula which is divergent, rendering the full coarse-graining strategy useless. In order to understand this subtle issue, in the present paper we consider the coarse graining of noninteracting Brownian particles. The discrete hydrodynamic variable for this problem is the number of particles within Voronoi cells. Thanks to the simplicity of the model we spot the origin of the singular behavior of the correlation functions. We offer an alternative definition, based on the concept of a Delaunay cell that behaves properly, suggesting the use of the Delaunay construction for the coarse graining of molecular fluids at the discrete hydrodynamic level.

Orientational instabilities in plane poiseuille flow of certain nematic liquid crystals

Abstract This paper obtains numerical solutions of the continuum equations for nematic liquid crystals for flow in a channel under a pressure gradient, and examines their stability with respect to certain disturbances. The analysis includes both planar and homeotropic initial alignments, and also cases in which the viscous coefficient α3 is positive as well as negative. Our main objective is the calculation of instability thresholds for particular perturbations both in and out of the shear plane, and our predictions are compared with relevant experimental observations.

A theoretical investigation of Benard-Couette instabilities in nematic liquid crystals

Employing continuum theory, this paper investigates the onset of homogeneous and roll instabilities in Couette flow of a nematic liquid crystal when a radial temperature gradient is present. The arrangement considered is that in which the anisotropic axis of the liquid crystal is initially aligned parallel to the axis of the circular cylinders. Using an orthonormalisation method, the authors present accurate numerical results for the shear rate thresholds as a function of the applied thermal gradient. It is shown that a positive thermal gradient reduces the roll threshold but that a thermal gradient of either sign has no effect on the homogeneous threshold. They therefore predict a value phi T for the radial temperature gradient at which there is a transition from a homogeneous to a roll-type instability. In addition they demonstrate the important effect rotation has through the centrifugal force.

Intramolecular excimer formation in model compounds for polyesters. Diesters from 2-naphthol and aliphatic dicarboxylic acids

Abstract The propensity for the formation of bends in the flexible spacer in polyesters containing naphthyl units has been examined by the study of the fluorescence of a series of diesters. Steady state fluorescence spectra have been measured for the diesters NaphOOC(CH2)mCOONaph, m = 2–6, ‘ Naph ’ = 2- naphthyl , in dilute solution in solvents of differing viscosity, η. The dependence of the degree of intramolecular excimer formation on m, under circumstances where the dynamics of rotational isomerism in the flexible spacer is suppressed, is evaluated by extrapolation of the measurements to infinite η. The extrapolated results exhibit an odd-even effect, with the more intense excimer emission being observed when m is odd. The odd-even effect is rationalized by a rotational isomeric state analysis of the diesters.