Search results for "Boltzmann equation"
showing 10 items of 49 documents
Distribution potential in electrified microemulsions with potential determining salts
2018
Abstract The electrical polarization of lamellar and water-in-oil microemulsions composed of the aqueous solution of a potential determining salt (PDS), an organic solvent and a nonionic surfactant has been studied. The distribution of the PDS ions across the interface between two immiscible electrolyte solutions (ITIES) generates an electrical potential difference which can be used to control charge transfer processes. In macroscopic ITIES, this distribution potential is independent of the PDS concentration and can be determined from the electroneutrality condition far from the interface. In microemulsions, on the contrary, the distribution potential is smaller in magnitude and depends on …
Enhanced ion transfer rate due to the presence of zwitterionic phospholipid monolayers at the ITIES
2000
Abstract The transfer of cations across phospholipid monolayers at ITIES is studied both experimentally and theoretically. Further evidence of the enhanced rate for cation transfer due to the presence of the monolayer is presented, and a theoretical model that can explain these observations is worked out. The system considered experimentally is Li + ion transfer across a hemispherical water ∣ 1,2-dichloroethane interface covered by distearoyl phosphatidylcholine. The theoretical description is based on the electrical double layer correction to the Butler–Volmer equation, coupled with a solution of the Poisson–Boltzmann equation across the interfacial region. The phospholipid monolayer is mo…
A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures
2016
In this short paper, we formally derive the thin spray equation for a steady Stokes gas, i.e. the equation consists in a coupling between a kinetic (Vlasov type) equation for the dispersed phase and a (steady) Stokes equation for the gas. Our starting point is a system of Boltzmann equations for a binary gas mixture. The derivation follows the procedure already outlined in [Bernard-Desvillettes-Golse-Ricci, arXiv:1608.00422 [math.AP]] where the evolution of the gas is governed by the Navier-Stokes equation.
Charged particles at fluid interfaces as a probe into structural details of a double layer
2011
Electrostatic interactions between charged, distant colloids in a bulk electrolyte solution do not depend on the inherent structure of ions and a solvent forming a double layer. For charged colloids trapped at an interface between an electrolyte and air this no longer holds; as the electrostatic interactions are mediated via air and the field lines determining the interactions originate at the charged surface, these details come into prominence. Using the Langevin-Poisson-Boltzmann equation we investigate how steric effects and the polarization saturation of a solvent effect the contact potential at the colloid surface and, in consequence, the long range interactions between colloids trappe…
Force probe simulations using a hybrid scheme with virtual sites.
2017
Hybrid simulations, in which a part of the system is treated with atomistic resolution and the remainder is represented on a coarse-grained level, allow for fast sampling while using the accuracy of atomistic force fields. We apply a hybrid scheme to study the mechanical unfolding and refolding of a molecular complex using force probe molecular dynamics (FPMD) simulations. The degrees of freedom of the solvent molecules are treated in a coarse-grained manner while atomistic resolution is retained for the solute. The coupling between the solvent and the solute is provided using virtual sites. We test two different common coarse-graining procedures, the iterative Boltzmann inversion method an…
Coherent quasiparticle approximation (cQPA) and nonlocal coherence
2010
We show that the dynamical Wigner functions for noninteracting fermions and bosons can have complex singularity structures with a number of new solutions accompanying the usual mass-shell dispersion relations. These new shell solutions are shown to encode the information of the quantum coherence between particles and antiparticles, left and right moving chiral states and/or between different flavour states. Analogously to the usual derivation of the Boltzmann equation, we impose this extended phase space structure on the full interacting theory. This extension of the quasiparticle approximation gives rise to a self-consistent equation of motion for a density matrix that combines the quantum…
Pore entrance effects on the electrical potential distribution in charged porous membranes and ion channels
2007
Abstract Models for the electrical potential distribution in the interfacial region between a fixed charge membrane and an electrolyte solution have traditionally employed the Donnan equilibrium formalism that assumes discontinuous changes in concentrations and electric potential. In the case of the charged capillary membrane model, we propose to check rigorously the validity of this approach by solving the linearized Poisson–Boltzmann equation for the diffuse electrical double layer at the membrane|solution interface. The comparison of the resulting axial distribution for the electric potential with the Donnan potential drop shows that the discontinuous approach is only valid for membrane …
Derivation of Models for Thin Sprays from a Multiphase Boltzmann Model
2017
We shall review the validation of a class of models for thin sprays where a Vlasov type equation is coupled to an hydrodynamic equation of Navier–Stokes or Stokes type. We present a formal derivation of these models from a multiphase Boltzmann system for a binary mixture: under suitable assumptions on the collision kernels and in appropriate asymptotics (resp. for the two different limit models), we prove the convergence of solutions to the multiphase Boltzmann model to distributional solutions to the Vlasov–Navier–Stokes or Vlasov–Stokes system. The proofs are based on the procedure followed in Bardos et al. (J Stat Phys 63:323–344 (1991), [2]) and explicit evaluations of the coupling term…
Non-Local Scattering Kernel and the Hydrodynamic Limit
2007
In this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory. We consider the possibility that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall. This results in a scattering kernel which is a non-local generalization of the classical Maxwell scattering kernel. The proposed scattering kernel satisfies a global mass conservation law and a generalized reciprocity relation. We study the hydrodynamic limit performing a Knudsen layer analysis, and derive a new class of (weakly) nonlocal boundary conditions to be imposed to the Navier-Stokes equations.
On the generalization of the Boltzmann equation
1974
Starting from the Liouville equation and making use of projection operator techniques we obtain a compact equation for the rate of change of then-particle momentum distribution function to any order in the density. This equation is exact in the thermodynamic limit. The terms up to second order in the density are studied and expressions are given for the errors committed when one makes the usual hypothesis to derive generalized Boltzmann equations. Finally the Choh-Uhlenbeck operator is obtained under additional assumptions.