Colloidal dynamic modeling

Multiparticle collision dynamics describes the interactions in a many-body system in terms of effective collisions that occur at discrete time intervals. Although the dynamics is a simplified representation of real dynamics, it conserves mass, momentum, and energy and preserves phase space volumes. Consequently, it retains many of the basic characteristics of classical Newtonian dynamics. The statistical mechanical basis of multiparticle collision dynamics is well established. Starting with the specification of the dynamics and the collision model, one may verify its dynamical properties, derive macroscopic laws, and, perhaps most importantly, obtain expressions for the transport coefficients. These features distinguish MPC dynamics from a number of other mesoscopic schemes. In order to describe solute motion in solution, MPC dynamics may be combined with molecular dynamics to construct hybrid schemes that can be used to explore a variety of phenomena. The fact that hydrodynamic interactions are properly accounted for in hybrid MPC-MD dynamics makes it a useful tool for the investigation of polymer and colloid dynamics. Since it is a particle-based scheme it incorporates fluctuations so that the reactive and nonreactive dynamics in small systems where such effects are important can be studied. 

Models of colloid dynamics are far ahead of the ability to test the models using in situ data. 

From Colloidal Dynamics Acustosizer, Acustosizer II, and Zeta Probe From Dispersion Technology DT models 300 and 1200 (illustrated in [306])... 

Frenklach, M. Harris, S. J. 1987 Aerosol dynamics modeling using the method of moments. Journal of Colloid and Interface Science 118, 252-261. 

Alexandridis P and Hatton T A 1995 Poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) block copolymer surfactants in aqueous solutions and at interfaces thermodynamics, structure, dynamics, modeling Colloids Surf. A 96 1-46... 

Zukoski IV, C.F. and SaviUe, D.A., The interpretation of electrokinetic measurements using a dynamic model of the Stem layer. I. The dynamic model, J. Colloid Interface Sci., 114, 32, 1986. 

FIGURE 26.2 Schematic diagram showing the apphcahihty of various kinds of numerical models to study the diverse spatial and temporal scales associated with the multitudinous phenomena spanning over multiple scales in the modehng of colloidal dynamics and flows in porous media. 

Comparison with models for colloid dynamics indicates that the drag coefficients for single-chain diffusion and for chain sedimentation are not the same at elevated matrix concentrations. Experiments testing this assertion for polymer solutions... 

Modern synthetic methods allow preparation of highly monodisperse spherical particles that at least approach closely the behavior of hard-spheres, in that interactions other than volume exclusion have only small influences on the thermodynamic properties of the system. These particles provide simple model systems for comparison with theories of colloidal dynamics. Because the hard-sphere potential energy is 0 or 00, the thermodynamic and static structural properties of a hard-sphere system are determined by the volume fraction of the spheres but are not affected by the temperature. Solutions of hard spheres are not simple hard-sphere systems. At very small separations, the molecular granularity of the solvent modifies the direct and hydrodynamic interactions between suspended particles. 

BoUntineanu D, Grest G, Lechman J, Pierce F, Plimpton S, Schunk R (2014) Particle dynamics modeling methods for colloid suspensions. Comput Part Mech pp 1-36... 

A second catch is the noise. If one observes the movements of a colloidal particle, the Brownian motion will be evident. There may be a constant drift in the dynamics, but the movement will be irregular. Likewise, if one observes a phase-separating liquid mixture on the mesoscale, the concentration levels would not be steady, but fluctuating. The thermodynamic mean-field model neglects all fluctuations, but they can be restored in the dynamical equations, similar to added noise in particle Brownian dynamics models. The result is a set of stochastic diffusion equations, with an additional random noise source tj [20]. In principle, the value and spectrum of the noise is dictated by a fluctuation dissipation theorem, but usually one simply takes a white noise source. 

Juarez-Maldonado, R., Chdvez-Rojo, M. A., Ramtrez-Gonzdlez, P. E., Yeomans-Reyna, L., and Medina-Noyola, M. 2007. Simplified self-consistent theory of colloid dynamics. Phys. Rev. E 76 062502. Sahimi, M. 1993. Flow phenomena in rocks From continuum models to fractals, percolation, cellular automata, and simulating annealing. Rev. Mod. Phys. 65 1393. 

Iadda89] Ladd, A.J.C. and D.Frenkel, Dynamics of colloidal dispersions via lattice-gas models of an incompressible fluid, pages 242-245 in [mann89]. 

Molecularly motivated empiricisms, such as the solubility parameter concept, have been valuable in dealing with mixtures of weakly interacting small molecules where surface forces are small. However, they are completely inadequate for mixtures that involve macromolecules, associating entities like surfactants, and rod-like or plate-like species that can form ordered phases. New theories and models are needed to describe and understand these systems. This is an active research area where advances could lead to better understanding of the dynamics of polymers and colloids in solution, the rheological and mechanical properties of these solutions, and, more generally, the fluid mechaiucs of non-Newtonian liquids. 

To address these challenges, chemical engineers will need state-of-the-art analytical instruments, particularly those that can provide information about microstmctures for sizes down to atomic dimensions, surface properties in the presence of bulk fluids, and dynamic processes with time constants of less than a nanosecond. It will also be essential that chemical engineers become familiar with modem theoretical concepts of surface physics and chemistry, colloid physical chemistry, and rheology, particrrlarly as it apphes to free surface flow and flow near solid bormdaries. The application of theoretical concepts to rmderstanding the factors controlling surface properties and the evaluation of complex process models will require access to supercomputers. 

This paper presents the physical mechanism and the structure of a comprehensive dynamic Emulsion Polymerization Model (EPM). EPM combines the theory of coagulative nucleation of homogeneously nucleated precursors with detailed species material and energy balances to calculate the time evolution of the concentration, size, and colloidal characteristics of latex particles, the monomer conversions, the copolymer composition, and molecular weight in an emulsion system. The capabilities of EPM are demonstrated by comparisons of its predictions with experimental data from the literature covering styrene and styrene/methyl methacrylate polymerizations. EPM can successfully simulate continuous and batch reactors over a wide range of initiator and added surfactant concentrations. 

The above model assumes that both components are dynamically symmetric, that they have same viscosities and densities, and that the deformations of the phase matrix is much slower than the internal rheological time [164], However, for a large class of systems, such as polymer solutions, colloidal suspension, and so on, these assumptions are not valid. To describe the phase separation in dynamically asymmetric mixtures, the model should treat the motion of each component separately ( two-fluid models [98]). Let Vi (r, t) and v2(r, t) be the velocities of components 1 and 2, respectively. Then, the basic equations for a viscoelastic model are [164—166]... 

It is important to propose molecular and theoretical models to describe the forces, energy, structure and dynamics of water near mineral surfaces. Our understanding of experimental results concerning hydration forces, the hydrophobic effect, swelling, reaction kinetics and adsorption mechanisms in aqueous colloidal systems is rapidly advancing as a result of recent Monte Carlo (MC) and molecular dynamics (MO) models for water properties near model surfaces. This paper reviews the basic MC and MD simulation techniques, compares and contrasts the merits and limitations of various models for water-water interactions and surface-water interactions, and proposes an interaction potential model which would be useful in simulating water near hydrophilic surfaces. In addition, results from selected MC and MD simulations of water near hydrophobic surfaces are discussed in relation to experimental results, to theories of the double layer, and to structural forces in interfacial systems. 

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