Mesoscopic flows

The off-grid particle methods, such as DPD and FPM, can capture easily mesoscopic scales of hundreds of micrometers employing up to 10 fluid particles currently, i.e., the scales in which temperature fluctuations and depletion forces interact with mesoscopic flows. Therefore, gridless particle methods can mimic the complex dynamics of fluid particles in the mesoscale more realistically than LEG. The FPMs also save computational time taken by molecular dynamics for calculating thermal noise. Instead, in DPD and FPM, we introduce the random Brownian force. 

Liquids are able to flow. Complicated stream patterns arise, dependent on geometric shape of the surrounding of the liquid and of the initial conditions. Physicists tend to simplify things by considering well-defined situations. What could be the simplest configurations where flow occurs Suppose we had two parallel plates and a liquid drop squeezed in between. Let us keep the lower plate at rest and move the upper plate at constant velocity in a parallel direction, so that the plate separation distance keeps constant. Near each of the plates, the velocities of the liquid and the plate are equal due to the friction between plate and liquid. Hence a velocity field that describes the stream builds up, (Fig. 15). In the simplest case the velocity is linear in the spatial coordinate perpendicular to the plates. It is a shear flow, as different planes of liquid slide over each other. This is true for a simple as well as for a complex fluid. But what will happen to the mesoscopic structure of a complex fluid How is it affected Is it destroyed or can it even be built up For a review of theories and experiments, see Ref. 122. Let us look into some recent works. 

Since MPC dynamics yields the hydrodynamic equations on long distance and time scales, it provides a mesoscopic simulation algorithm for investigation of fluid flow that complements other mesoscopic methods. Since it is a particle-based scheme it incorporates fluctuations, which are essential in many applications. For macroscopic fluid flow averaging is required to obtain the deterministic flow fields. In spite of the additional averaging that is required the method has the advantage that it is numerically stable, does not suffer from lattice artifacts in the structure of the Navier-Stokes equations, and boundary conditions are easily implemented. 

Hybrid MPC-MD schemes are an appropriate way to describe bead-spring polymer motions in solution because they combine a mesoscopic treatment of the polymer chain with a mesoscopic treatment of the solvent in a way that accounts for all hydrodynamic effects. These methods also allow one to treat polymer dynamics in fluid flows. 

A. Malevanets and R. Kapral, Mesoscopic multi-particle collision model for fluid flow and molecular dynamics, in Novel Methods in Soft Matter Simulations, M. Karttunen, I. Vattulainen, and A. Lukkarinen (eds.), Springer-Verlag, Berlin, 2003, p. 113. 

T. Ihle and D. M. Kroll, Stochastic rotation dynamics a Galilean-invariant mesoscopic model for fluid flow, Phys. Rev. E 63, 020201(R) (2001). 

E. Allahyarov and G. Gompper, Mesoscopic solvent simulations multiparticle-collision dynamics of three-dimensional flows, Phys. Rev. E 66, 036702 (2002). 

The plastic deformation patterns can be revealed by etch-pit and/or X-ray scattering studies of indentations in crystals. These show that the deformation around indentations (in crystals) consists of heterogeneous rosettes which are qualitatively different from the homogeneous deformation fields expected from the deformation of a continuum (Chaudhri, 2004). This is, of course, because plastic deformation itself is (a) an atomically heterogeneous process mediated by the motion of dislocations and (b) mesoscopically heterogeneous because dislocation motion occurs in bands of plastic shear (Figure 2.2). In other words, plastic deformation is discontinuous at not one, but two, levels of the states of aggregation in solids. It is by no means continuous. And, it is by no means time independent it is a flow process. 

The occurrence of kinetic instabilities as well as oscillatory and even chaotic temporal behavior of a catalytic reaction under steady-state flow conditions can be traced back to the nonlinear character of the differential equations describing the kinetics coupled to transport processes (diffusion and heat conductance). Studies with single crystal surfaces revealed the formation of a large wealth of concentration patterns of the adsorbates on mesoscopic (say pm) length scales which can be studied experimentally by suitable tools and theoretically within the framework of nonlinear dynamics. [31]... 

To say nothing about the different equivalent forms of the theory of the Brownian motion that has been discussed by many authors (Chandrasekhar 1943 Gardiner 1983), there exist different approaches (Rouse 1953 Zimm 1956 Cerf 1958 Peterlin 1967) to the dynamics of a bead-spring chain in the flow of viscous liquid.1 In this chapter, we shall try to formulate the theory in a unified way, embracing all the above-mentioned approaches simultaneously. Some parameters are used to characterise the motion of the particles and interaction inside the coil. This phenomenological (or, better to say, mesoscopic) approach permits the formulation of overall results regardless to the extent to which the mechanism of a particular effect is understood. 

Miiller-Plathe F (2002) Coarse-graining in polymer simulation From the atomistic to the mesoscopic scale and back. J Chem Phys Phys Chem 3 754—769 Muller R, Picot C, Zang YH, Froelich D (1990) Polymer chain conformation in the melt during steady elongational flow as measured by SANS. Temporary network model. Macromolecules 23(9) 2577—2582... 

The correlation between rheology and thermodynamics is likely to prove a fruitful area for investigation in the future. Very little is as yet known about the detailed mechanisms of non-linear viscoelastic flows, such as those involved in large-amplitude oscillatory shear. Mesoscopic modelling will no doubt throw light on the role of defects in such flows. This is likely to involve both analytical models, and mesoscopic simulation techniques such as Lattice... 

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