Mesoscale

Figure C2.3.5. Mesoscale stmctures deriving from surfactants nominally exhibiting shapes corresponding to various packing parameter ranges.

The fonnation of surface aggregates of surfactants and adsorbed micelles is a challenging area of experimental research. A relatively recent summary has been edited by Shanna [51]. The details of how surfactants pack when aggregated on surfaces, with respect to the atomic level and with respect to mesoscale stmcture (geometry, shape etc.), are less well understood than for micelles free in solution. Various models have been considered for surface surfactant aggregates, but most of these models have been adopted without finn experimental support. 

Mesoscale simulations model a material as a collection of units, called beads. Each bead might represent a substructure, molecule, monomer, micelle, micro-crystalline domain, solid particle, or an arbitrary region of a fluid. Multiple beads might be connected, typically by a harmonic potential, in order to model a polymer. A simulation is then conducted in which there is an interaction potential between beads and sometimes dynamical equations of motion. This is very hard to do with extremely large molecular dynamics calculations because they would have to be very accurate to correctly reflect the small free energy differences between microstates. There are algorithms for determining an appropriate bead size from molecular dynamics and Monte Carlo simulations. 

Many of the mesoscale techniques have grown out of the polymer SCF mean field computation of microphase diagrams. Mesoscale calculations are able to predict microscopic features such as the formation of capsules, rods, droplets, mazes, cells, coils, shells, rod clusters, and droplet clusters. With enough work, an entire phase diagram can be mapped out. In order to predict these features, the simulation must incorporate shape, dynamics, shear, and interactions between beads. 

The conceptual forerunner to mesoscale dynamics is Brownian dynamics. Brownian simulations used equations of motion modified by a random force... 

Dissipative particle dynamics (DPD) is a technique for simulating the motion of mesoscale beads. The technique is superficially similar to a Brownian dynamics simulation in that it incorporates equations of motion, a dissipative (random) force, and a viscous drag between moving beads. However, the simulation uses a modified velocity Verlet algorithm to ensure that total momentum and force symmetries are conserved. This results in a simulation that obeys the Navier-Stokes equations and can thus predict flow. In order to set up these equations, there must be parameters to describe the interaction between beads, dissipative force, and drag. 

Because mesoscale methods are so new, it is very important to validate the results as much as possible. One of the best forms of validation is to compare the computational results to experimental results. Often, experimental results are not available for the system of interest, so an initial validation calculation is done for a similar system for which experimental results are available. Results may also be compared to any other applicable theoretical results. The researcher can verify that a sulficiently long simulation was run by seeing that the same end results are obtained after starting from several different initial configurations. 

Of all the topics discussed in this text, mesoscale simulations are probably at the most infantile stage of development. The idea of the mesoscale calculations is very attractive and physically reasonable. However, it is not as simple as one might expect. The choice of bead sizes and parameters is crucial to obtaining physically relevant results. More complex bead shapes are expected to be incorporated in future versions of these techniques. When using one simulation technique to derive parameters for another simulation, very small errors in a low-level calculation could result in large errors in the final stages. 

The current generation of mesoscale calculations has proven useful for pre-... 

In principle, mesoscale methods can provide a means for connecting one type of simulation to another. For example, a molecular simulation can be used to describe a lipid. One can then derive the parameters for a lipid-lipid potential. These parameters can then be used in a simulation that combines lipids to form a membrane, which, in turn, can be used to compute parameters describing a membrane as a flexible sheet. Such parameters could be used for a simulation with many cells in order to obtain parameters that describe an organ, which could be used for a whole-body biological simulation. Each step, in theory, could be modeled in a different way using parameters derived not from experiment but from a more low-level form of simulation. This situation has not yet been realized, but it is representative of one trend in computational technique development. 

The applicability of mesoscale techniques to systems difficult to describe in any other manner makes it likely that these simulations will continue to be used. At the present time, there is very little performance data available for these simulations. Researchers are advised to carefully consider the fundamental assumptions of these techniques and validate the results as much as possible. 

Polymers are difficult to model due to the large size of microcrystalline domains and the difficulties of simulating nonequilibrium systems. One approach to handling such systems is the use of mesoscale techniques as described in Chapter 35. This has been a successful approach to predicting the formation and structure of microscopic crystalline and amorphous regions. 

Commercially produced elastic materials have a number of additives. Fillers, such as carbon black, increase tensile strength and elasticity by forming weak cross links between chains. This also makes a material stilfer and increases toughness. Plasticizers may be added to soften the material. Determining the effect of additives is generally done experimentally, although mesoscale methods have the potential to simulate this. 

DPD (dissipative particle dynamics) a mesoscale algorithm DREIDING a molecular mechanics force field... 

R. A. P Ake, Mesoscale Meteorological Modeling AcAeimc Press, Orlando, Pla., 1984. 

Much of what we currently understand about the micromechanics of shock-induced plastic flow comes from macroscale measurement of wave profiles (sometimes) combined with pre- and post-shock microscopic investigation. This combination obviously results in nonuniqueness of interpretation. By this we mean that more than one micromechanical model can be consistent with all observations. In spite of these shortcomings, wave profile measurements can tell us much about the underlying micromechanics, and we describe here the relationship between the mesoscale and macroscale. 

Wallace [15], [16] gives details on effects of nonlinear material behavior and compression-induced anisotropy in initially isotropic materials for weak shocks, and Johnson et ai. [17] give results for infinitesimal compression of initially anisotropic single crystals, but the forms of the equations are the same as for (7.10)-(7.11). From these results it is easy to see where the micromechanical effects of rate-dependent plastic flow are included in the analysis the micromechanics (through the mesoscale variables and n) is contained in the term y, as given by (7.1). 

The evolution of T, is just an exercise in mesoscale thermodynamics [13]. These expressions, in combination with (7.54), incorporate concepts of heterogeneous deformation into a eonsistent mierostruetural model. Aspects of local material response under extremely rapid heating and cooling rates are still open to question. An important contribution to the micromechanical basis for heterogeneous deformation would certainly be to establish appropriate laws of flow-stress evolution due to rapid thermal cycling that would provide a physical basis for (7.54). 

Underlying all continuum and mesoscale descriptions of shock-wave compression of solids is the microscale. Physical processes on the microscale control observed dynamic material behavior in subtle ways sometimes in ways that do not fit nicely with simple preconceived macroscale ideas. The repeated cycle of experiment and theory slowly reveals the micromechanical nature of the shock-compression process. 

Generalized Mesoscale Windflow Patterns Associated with Different Combinations of Wind Direction and Ridgeline Orientation... 

Killus, J. P., Meyer, J. P., Durran, D. R., Anderson, G. E., Jerskey, T. N., and Whitten, G. Z., "Continued Research in Mesoscale Air Pollution Simulation Modeling," Vol. V, "Refinements in Numerical Analysis, Transport, Chemistry, and Pollutant Removal," Report No. ES77-142. Systems Applications, Inc., San Rafael, CA, 1977. 

Chaudhari AM, Woudenberg TM, Albin M, Goodson KE (1998) Transient liquid crystal thermometry of microfabricated PCR vessel arrays. J Microelectromech Sys 7 345-355 Cheng P, Wu WY (2006) Mesoscale and microscale phase heat transfer. In Greene G, Cho Y, Hartnett J, Bar-Cohen A (eds) Advances in heat transfer, vol 39. Elsevier, Amsterdam Choi SB, Barron RF, Warrington RQ (1991) Fluid flow and heat transfer in micro- tubes. ASME DSC 40 89-93... 

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