Hydrodynamic preservation

These models are designed to reproduce the random movement of flexible polymer chains in a solvent or melt in a more or less realistic way. Simulational results which reproduce in simple cases the so-called Rouse [49] or Zimm [50] dynamics, depending on whether hydrodynamic interactions in the system are neglected or not, appear appropriate for studying diffusion, relaxation, and transport properties in general. In all dynamic models the monomers perform small displacements per unit time while the connectivity of the chains is preserved during the simulation. 

External numbering-up benefits from true repetition of the fluidic path, and hence preserves all the transport properties and hydrodynamics, determined in advance for a single-device operation. This is commonly believed to result in a... 

MPC dynamics is able to describe hydrodynamic interactions because it preserves the conservation laws, in particular, momentum conservation, on which these interactions rely. Thus we can test the validity of such an... 

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. 

For point particles governed by Stokes law, the Stokes number is the only criterion other than geometry that determines similitude for the shape of the particle trajectories. To ensure hydrodynamic similarity, in general, the collector Reynolds number also must be preserved, as well as the ratio I = R/a, called the interception parameter. Then, the collection efficiency of particles hitting an obstacle such as a cylinder has the form ... 

Consequently, realistic simulations were not possible until Brady and Bossis [4] developed accurate approximations for the many-body hydrodynamics. By first preserving lubrication effects in the near field through a... 

The occurrence of hydrodynamic lift forces principally leaves two options to perform the FFF experiment either the field force is increased to offset the lift forces and confine the particles close to the wall [226], or they can be adjusted to allow the particles to gain a significant elevation above the wall, where they form hyperlayers. The first mechanism preserves the steric mechanism, whereas the latter is the mechanism of lift-hyperlayer FFF (see Sect. 2.8.2). From these considerations, it becomes clear that the mechanism of steric-FFF is more complicated than the normal mode operation, necessarily requiring a calibration prior to measurement. This calibration is performed using a double logarithmic plot of the retention time tr vs. the known hydrodynamic diameter dH of a standard particle. From the slope and intercept, one can obtain the calibration constants Sd and trl by using the equation [293] ... 

The properties of a low expansion ratio foam are controlled mainly by changing the rate of the kinetic processes running in it. To decelerate the hydrodynamic processes in order to preserve its structure for a longer time (for instance, in the formation of polymer or frozen foams), the following measures can be recommended i) to use a foam generation mode that allows producing a foam of a uniform expansion ratio such are the stream type generators and some mechanical devices that mix the solutions ii) to produce a foam of maximum dispersity... 

Most of these types of equipment have at least several hundred installations. The sizing of full scale equipment still requires pilot planting of particular systems. The scaleup procedures require geometrical and hydrodynamic similarities between the pilot and full scale plants. Hydrodynamic similarity implies equalities of droplet diameters, fractional holdups, and linear superficial velocities. Also preserved are the specific radial discharge rates, defined by QIDH = (volumetric flow rate)/(vessel dia) (compartment height). 

The preservation of hydrocarbons accumulated in a trap that is no longer replenished, depends on the type of trap, the type of accumulated hydrocarbon and the subsequent geological and associated hydrodynamic evolution of the sedimentary basin (Section 5.4). 

Table 6.1 Relations between type of sedimentary basin, hydrodynamic condition, hydrocarbon migration, accumulation and preservation ...

For the mechanical behavior of two particle-fluid systems to be simitar, it is necessary to have geometric, hydrodynamic, and particle trajectory similarity. Hydrodynamic similarity is achieved by fixing the Reynolds number for the flow around the collector. By (4.26), similarity of the particle trajectories depends on the Stokes number. Trajectory similarity also requires that the particle come within one radius of the surface at the same relative location. This means that the interception parameter, R = dp/L, must also be preserved. 

For the hydrodynamic part of the problem, we preserve all the most important assumptions, equations, and boundary conditions used above in Section 5.10. 

If one is interested in properties that vary on very long distance and time scales it is possible that a drastic simplification of the molecular dynamics will still provide a faithful representation of these properties. Hydrodynamic flows are a good example. As long as the dynamics preserves the basic conservation laws of mass, momentum and energy, on sufficiently long scales the system will be described by the Navier-Stokes equations. This observation is the basis for the construction of a variety of particle-based methods for simulating hydrodynamic flows and reaction-diffusion dynamics. (There are other phase space methods that are widely used to simulate hydrodynamic flows which are not particle-based, e.g. the lattice Boltzmann method [125], which fall outside the scope of this account of MD simulation.)... 

With the introduction of heat into the bed, the original reservoir conditions are still preserved at the hydrodynamic front of displacement e.g., the oil is being driven with water at the temperature of the formation. 

---