Hydrodynamic effect

The hydrodynamic equations describe the relationships between the applied forces and the fluid velocities. As given by Leslie, in linear approximation, they are 

The viscous tensor as obtained from thermodynamic considerations and symmetry properties is defined in terms of velocity gradients and director orientations as 

In Chap. 2, Sect. 6.6 and Chap. 6, Sect. 2.3, the phenomenon of hydro-dynamic repulsion was referred to, but not discussed in any detail. While this effect is strictly a many-body effect, it can be approximated very well by a simple model. The motion of one solute, A, necessarily requires that the surrounding solvent moves aside to let the A molecule pass. The motion of the solvent near A in turn requires more distant solvent molecules to move. This action is transmitted by collision, but effectively the solute A entrains solvent molecules to move in the same direction as it is doing itself. The degree of the entrainment of solvent decreases as the 

Posch et al. [456b] found from a molecular dynamics simulation that the diffusion coefficient, D(r) increased at short distances, a result in marked contrast to Emeis and Fehder [456a]. Further work is keenly awaited. 

The exact range of hydrodynamic repulsion is uncertain. Chap. 9, Sect. 3 follows Zwanzig [444] and Deutch and Felderhof [70] and uses a distance-dependent diffusion coefficient, D r), to model the reduced rate of relative diffusion together or apart at short distances. The classical hydrodynamic result (Chap. 9, Sect. 3.3) is D r) = D 1 —Ijr) where I = 3aia2/(ai + 02) and 02 the reactant radii. Even at the encounter 

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A recent design of the maximum bubble pressure instrument for measurement of dynamic surface tension allows resolution in the millisecond time frame [119, 120]. This was accomplished by increasing the system volume relative to that of the bubble and by using electric and acoustic sensors to track the bubble formation frequency. Miller and co-workers also assessed the hydrodynamic effects arising at short bubble formation times with experiments on very viscous liquids [121]. They proposed a correction procedure to improve reliability at short times. This technique is applicable to the study of surfactant and polymer adsorption from solution [101, 120]. 

The duration of the response results primarily from the rate of elution of the sample, and not on any inherent limitation in the response time of the electrode. This is a characteristic of ion-selective electrodes, but amperometric responses depend not only on the duration of elution but also on flow rate because of the hydrodynamic effects discussed previously. 

Molecular dynamics, in contrast to MC simulations, is a typical model in which hydrodynamic effects are incorporated in the behavior of polymer solutions and may be properly accounted for. In the so-called nonequilibrium molecular dynamics method [54], Newton s equations of a (classical) many-particle problem are iteratively solved whereby quantities of both macroscopic and microscopic interest are expressed in terms of the configurational quantities such as the space coordinates or velocities of all particles. In addition, shear flow may be imposed by the homogeneous shear flow algorithm of Evans [56]. 

In [343] it was shown, with regard to the hydrodynamic effect of fillers on the viscoelastic properties of composites, that the dynamic functions must obey the following equations ... 

Some of these questions have strict and unambiguous answers, in a mathematical model, to other answers are derived from extensive empirical material. The present paper will discuss the problems formulated above, but concerning only rheological properties of filled polymer melts, leaving out the discussion of specific hydrodynamic effects occurring during their flow in channels of different geometrical form. 

The Rouse model, as given by the system of Eq, (21), describes the dynamics of a connected body displaying local interactions. In the Zimm model, on the other hand, the interactions among the segments are delocalized due to the inclusion of long range hydrodynamic effects. For this reason, the solution of the system of coupled equations and its transformation into normal mode coordinates are much more laborious than with the Rouse model. In order to uncouple the system of matrix equations, Zimm replaced S2U by its average over the equilibrium distribution function ... 

The slopes of the different curves correspond to the fuU electrohydrodynamic effect, ( ) + ( ) pj, where the first term expresses the hydrodynamic effect, and the second is the consequence of the distortion of the electrical double layer that surrounds the particles. To determine this second term and, more exactly, the primary electroviscous coefficient, pi. 

Due to the absence of a hydrodynamic effect, boundary film thickness is expected to be independent of speed of surface movement, as can be observed in the left part of the Stribeck curve. This is a significant criterion that distinguishes boundary lubrication from EHL and mixed lubrica-... 

The CMP process is regarded as a combination of chemical effect, mechanical effect, and hydrodynamic effect [110-116]. Based on contact mechanics, hydrodynamics theories and abrasive wear mechanisms, a great deal of models on material removal mechanisms in CMP have been proposed [110,111,117-121]. Although there is still a lack of a model that is able to describe the entire available CMP process, during which erosion and abrasive wear are agreed to be two basic effects. 

Hydrodynamic effects on suspended particles in an STR may be broadly categorized as time-averaged, time-dependent and collision-related. Time-averaged shear rates are most commonly considered. Maximum shear rates, and accordingly maximum stresses, are assumed to occur in the impeller region. Time-dependent effects, on the other hand, are attributable to turbulent velocity fluctuations. The relevant turbulent Reynolds stresses are frequently evaluated in terms of the characteristic size and velocity of the turbulent eddies and are generally found to predominate over viscous effects. 

Johnson et al. [186] measured diffusion of fluorescein-labeled macromolecules in agarose gels. Their data agreed well with Eq. (85), which combined the hydrodynamic effects with the steric hindrance factors. Gibbs and Johnson [131] measured diffusion of proteins and smaller molecules in polyacrylamide gels using pulsed-field gradient NMR methods and found their data to fit the stretched exponential form... 

If the preceding analysis of hydrodynamic effects of the polymer molecule is valid, K should be a constant independent both of the polymer molecular weight and of the solvent. It may, however, vary somewhat with the temperature inasmuch as the unperturbed molecular extension rl/M may change with temperature, for it will be recalled that rl is modified by hindrances to free rotation the effects of which will, in general, be temperature-dependent. Equations (26), (27), and (10) will be shown to suffice for the general treatment of intrinsic viscosities. 

Porous packed systems represent in addition to the hydrodynamic effect, the possibility for separation due to size-related exclusion of particles from the pores, essentially LEG. In this section a brief overview of some of o ir more recent results pertaining to the question of pore size distribution effects will be given, fore detailed discussions are presented elsewhere (23>2U). 

Rp will decrease however, we see the opposite effect due to the presence of the porous matrix, indicating the hydrodynamic effects exhibited within the interstitial void regions are significantly less than those within the pores. 

The methodology discussed previously can be applied to the study of colloidal suspensions where a number of different molecular forces and hydrodynamic effects come into play to determine the dynamics. As an illustration, we briefly describe one example of an MPC simulation of a colloidal suspension of claylike particles where comparisons between simulation and experiment have been made [42, 60]. Experiments were carried out on a suspension of AI2O3 particles. For this system electrostatic repulsive and van der Waals attractive forces are important, as are lubrication and contact forces. All of these forces were included in the simulations. A mapping of the MPC simulation parameters onto the space and time scales of the real system is given in Hecht et al. [42], The calculations were carried out with an imposed shear field. 

There have been other MPC dynamics studies of hydrodynamic effects on the transport properties of colloidal suspensions [61-64]. In addition, vesicles that can deform under flow have also been investigated using hybrid MPC-MD schemes [65-69]. 

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. 

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