Hydrodynamic methods overview

In this chapter, we describe some of the more widely used and successful kinetic techniques involving controlled hydrodynamics. We briefly discuss the nature of mass transport associated with each method, and assess the attributes and drawbacks. While the application of hydrodynamic methods to liquid liquid interfaces has largely involved the study of spontaneous processes, several of these methods can be used to investigate electrochemical processes at polarized ITIES we consider these applications when appropriate. We aim to provide an historical overview of the field, but since some of the older techniques have been reviewed extensively [2,3,13], we emphasize the most recent developments and applications. 

In this section the theory behind Brownian dynamics simulation methods that are used to study diffusion-controlled biochemical processes is presented. In the first subsection two Brownian dynamics algorithms are described. The second subsection gives an overview of the theory for computing encounter rates. A discussion of electrostatics is in the third subsection followed by subsection four on hydrodynamic forces. The fifth subsection discusses the inclusion of flexibility into Brownian dynamics simulations. 

In this article we will focus on systems which comprise particles, with or without internal degrees of freedom, suspended in a simple fluid. We will first outline the necessary ingredients for a theoretical description of the dynamics, and in particular explain the concept of hydrodynamic interactions (HI). Starting from this background, we will provide a brief overview of the various simulation approaches that have been developed to treat such systems. All of these methods are based upon a description of the solute in terms of particles, while the solvent is taken into account by a simple (but sufficient) model, making use of the fact that it can be described as a Newtonian fluid. Such methods are often referred to as mesoscopic. We will then describe and derive in some detail the algorithms that have been developed by us to couple a particulate system to a LB fluid. The usefulness of these methods will then be demonstrated by applications to colloidal dispersions and polymer solutions. Some of the material presented here is a summary of previously published work. 

It is the purpose of this small series of volumes in Advances in Polymer Sciences to provide an overview of the latest developments in the field. For this, internationally renowned experts review recent work in the general area of soft matter simulations. The third volume contains three contributions. The first two chapters review several coarse-grained methods to include the effects of hydrodynamics in mesoscopic particle simulations that use an implicit solvent, whereas the last chapter deals with advanced sampling methods to study rare events. 

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