217 research outputs found
A new approach to the deformation fields method for solving complex flows using integral constitutive equations
No full textIn this paper, we present a newapproach to the deformation fields method that has recently been introduced to solveintegral type models in complex flows (E.A.J.F. Peters, M.A. Hulsen, B.H.A.A. van den Brule, J. Non-NewtonianFluid Mechanics 89 (2000) 209 -228). The new approach is based on a change of the reference time of the fields froman absolute time to a time relative to the current time. This basically removes most, if not all, stability and accuracyproblems that exist in the original method compared to using differential models. Also the new implementation ismuch more flexible with respect to the time integral discretisation, opening the way to adaptive refinement. The newimplementation has been tested for two problems: the standard 2:1 benchmark of a the flow around a sphere usin! ga UCM model and the flow around a sphere in a different geometry using a PSM model
Simulating fluctuating mesoscopic dynamics using three dimensional Voronoi cells
No full textMaterials such as micro-phase separated liquids, colloidal suspensions and polymeric materials have structure on a mesoscopic length scale. The relevant length scales are well beyond the microscopic level. Therefore the materials are, locally, well characterized by a thermodynamic state and by the macroscopic transport properties such as the viscosity. Thermal fluctuations are, however, still of significant importance for the dynamics of the structure of such a liquid. The presented method describes blobs of material by dividing space in discrete volumes by means of a three-dimensional Voronoi tessellation. Each discrete volume obeys local thermal equilibrium. Because the volume of a Voronoi cell is well defined it is easy to impose a local equation of state. The time evolution of the volumes obeys conservation of energy and momentum, and is thermodynamically consistent. Furthermore thermal fluctuating and dissipative forces are imposed that obey fluctuation-dissipation. This technique has significant benefits compared to other mesoscopic techniques such as DPD. In these other techniques fluctuations obey fluctuation-dissipation relations, but coarse-grained degrees of freedom are not modeled by means of a local entropy (or free energy). Another drawback of DPD is that transport coefficients such as the viscosity are not primary input variables but have to be determined by means of a "numerical experiment". A major advantage of the new method is that locally the equation of state of a cell can be imposed. Therefore any kind of matter can be modeled. Also complicated systems such as liquid-vapor mixture fall into the range of possibilities. Transport coefficients such as viscosity can be given any value. The dynamics obeys 'fluctuating hydrodynamics'. Fluxes based on chemical potential differences can be introduced such that mixtures can be studied. In the case of demixing initially diffuse boundaries that are a few cells in width will evolve. When the width becomes much smaller than the cell size sharp interfaces are formed. These interfaces are naturally localized at the boundaries between cells. In this case the boundaries between different species can be assigned thermodynamic properties such as an interfacial energy. In this talk I will discuss some numerical details that make the three dimensional simulation of by means of Voronoi cells possible. Next, I will discuss a few modeling issues and will finish with the presentation of interesting results of three dimensional simulations
Efficient Brownian dynamics simulation of particles near walls. II. Sticky walls
Get PDFIn this paper we treat a boundary condition, the sticky boundary, which appears to be quite useful in mesoscopic models. The sticky boundary is modeled as an infinitely deep, infinitely narrow, potential well adjacent to a reflecting boundary. The free energy corresponding to this boundary is finite. The boundary condition, which can be viewed as an intermediate between the absorbing and reflecting boundary condition, may have many applications, e.g., for the simulation of the partial adsorption of polymer molecules to walls and for the modeling of solvent quality. We will derive an efficient Brownian dynamics algorithm, capable of handling interactions of a diffusing particle with a sticky wall. Our approach avoids the large discretization errors that occur in the simulation of boundary interactions within the standard Brownian dynamics approach. The essence of our method was presented before [E. Peters and T. Barenbrug, Phys. Rev. E (to be published)]. The treatment of the wall as proposed here is quite general, and therefore not limited to the use within Brownian dynamics. In other simulation techniques which aim at treating the dynamics of mesoscopic particles near walls, we expect it to be of use as well
Modeling and optimization of simulated moving bed reactor (SMBR) for isomerization of glucose to fructose and its separation
No full textDetailed fluctuation theorem for mesoscopic modeling
Get PDF\u3cp\u3eThe detailed fluctuation theorem is derived. The basic assumptions are phase space incompressibility (Liouville’s theorem) and time reversibility on the microscopic level. The theorem relates the conditional probability to end up in a mesoscopic state [Formula presented] at time [Formula presented], starting from [Formula presented] at time [Formula presented], to the time-reversed process. The ratio of these two probability densities is related to the entropy difference of the two mesoscopic states. The fluctuation theorem remains valid even far from equilibrium as long as the local equilibrium condition is obeyed. It is shown that the theorem imposes constraints on the form mesoscopic equations can take. For stochastic differential equations a generalized kinetic form is derived. The fluctuation theorem can be used to derive thermodynamically consistent simulation techniques. At the end of this paper the relation with the GENERIC formalism is discussed.\u3c/p\u3
Projection operator formalism and entropy
No full textThe entropy definition is deduced by means of (re)deriving the generalized non-linear Langevin equation using Zwanzig projector operator formalism. It is shown to be necessarily related to an invariant measure which, in classical mechanics, can always be taken to be the Liouville measure. It is not true that one is free to choose a \ relevant\ probability d. independently as is done in other flavors of projection operator formalism. This observation induces an entropy expression which is valid also outside the thermodn. limit and in far from equil. situations. The Zwanzig projection operator formalism therefore gives a deductive derivation of non-equil., and equil., thermodn. The entropy definition found is closely related to the (generalized) microcanonical Boltzmann-Planck definition but with some subtle differences. No \ shell thickness\ arguments are needed, nor desirable, for a rigorous definition. The entropy expression depends on the choice of macroscopic variables and does not exactly transform as a scalar quantity. The relation with expressions used in the GENERIC formalism are discussed
Technoeconomic analysis of sustainable routes for conversion of bio-based feedstock to valuable products with integrated pre-combustion Carbon Dioxide Capture
No full text- …
