Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Oseen

Oseen C W 1929 The theory of liquid crystals Trans. Faraday See. 29 883-99... [Pg.2569]

Since the hydrodynamic interaction decreases as the inverse distance between the beads (Eq. 27), it is expected that it should vary with the degree of polymer chain distortion. This is not considered in the Zimm model which assumes a constant hydrodynamic interaction given by the equilibrium averaging of the Oseen tensor (Eq. 34). [Pg.95]

If the Brownian particles were macroscopic in size, the solvent could be treated as a viscous continuum, and the particles would couple to the continuum solvent through appropriate boundary conditions. Then the two-particle friction may be calculated by solving the Navier-Stokes equations in the presence of the two fixed particles. The simplest approximation for hydrodynamic interactions is through the Oseen tensor [54],... [Pg.119]

We can take the Rouse term l/ ke 02rm/0m2 (ke = 3kBT//2) entropic spring constant) into consideration formally, if we define the element Tnm of the Oseen tensor as Tnm = E/ . The equation of motion (13) thus becomes... [Pg.66]

The equations of motion (75) can also be solved for polymers in good solvents. Averaging the Oseen tensor over the equilibrium segment distribution then gives = l/ n — m Y t 1 = p3v/rz and Dz kBT/r sNY are obtained for the relaxation times and the diffusion constant. The same relations as (80) and (82) follow as a function of the end-to-end distance with slightly altered numerical factors. In the same way, a solution of equations of motion (75), without any orientational averaging of the hydrodynamic field, merely leads to slightly modified numerical factors [35], In conclusion, Table 4 summarizes the essential assertions for the Zimm and Rouse model and compares them. [Pg.68]

In the case of dynamic mechanical relaxation the Zimm model leads to a specific frequency ( ) dependence of the storage [G ( )] and loss [G"(cd)] part of the intrinsic shear modulus [G ( )] [1]. The smallest relaxation rate l/xz [see Eq. (80)], which determines the position of the log G (oi) and log G"(o>) curves on the logarithmic -scale relates to 2Z(Q), if R3/xz is compared with Q(Q)/Q3. The experimental results from dilute PDMS and PS solutions under -conditions [113,114] fit perfectly to the theoretically predicted line shape of the components of the modulus. In addition l/xz is in complete agreement with the theoretical prediction based on the pre-averaged Oseen tensor. [Pg.81]

A model that can take these findings into account is based on the idea that the screening of hydrodynamic interactions is incomplete and that a residual part is still active on distances r > H(c) [40,117]. As a consequence the solvent viscosity r s in the Oseen tensor is replaced by an effective... [Pg.112]

Oseen(3) employs just the first two terms of equation 3.6 to give ... [Pg.150]

All measurements, of course, have to be made at a finite concentration. This implies that interparticle interactions cannot be fully neglected. However, in very dilute solutions we can safely assume that more than two particles have only an extremely small chance to meet [72]. Thus only the interaction between two particles has to be considered. There are two types of interaction between particles in solution. One results from thermodynamic interactions (repulsion or attraction), and the other is caused by the distortion of the laminar fiow due to the presence of the macromolecules. If the particles are isolated only the laminar flow field is perturbed, and this determines the intrinsic viscosity but when the particles come closer together the distorted flow fields start to overlap and cause a further increase of the viscosity. The latter is called the hydrodynamic interaction and was calculated by Oseen to various approximations [3,73]. Figure 7 elucidates the effect. [Pg.134]

When we use the Fourier representation of the Oseen tensor G, Ay is given by... [Pg.23]

Such a decomposition of the diffusion coefficient has previously been noted by Pattle et al.(l ) Now we must evaluate >. The time-integrated velocity correlation function Aj j is due to the hydrodynamic interaction and can be described by the Oseen tensor. The Oseen tensor is related to the velocity perturbation caused by the hydrodynamic force, F. By checking units, we see that A is the Oseen tensor times the energy term, k T, or... [Pg.51]

Note 3 The names of Oseen, Zocher, and Frank are associated with the development of the theory for the elastic behaviour of nematics and so the elastic constants may also be described as the Oseen-Zocher-Frank constants, although the term Frank constants is frequently used. [Pg.128]


See other pages where Oseen is mentioned: [Pg.2557]    [Pg.76]    [Pg.91]    [Pg.92]    [Pg.119]    [Pg.120]    [Pg.123]    [Pg.124]    [Pg.65]    [Pg.71]    [Pg.73]    [Pg.73]    [Pg.73]    [Pg.77]    [Pg.81]    [Pg.82]    [Pg.245]    [Pg.338]    [Pg.150]    [Pg.188]    [Pg.38]    [Pg.57]    [Pg.109]    [Pg.192]    [Pg.7]    [Pg.35]    [Pg.123]    [Pg.220]    [Pg.52]    [Pg.142]    [Pg.71]    [Pg.97]    [Pg.123]    [Pg.156]    [Pg.159]   
See also in sourсe #XX -- [ Pg.380 ]

See also in sourсe #XX -- [ Pg.58 , Pg.194 , Pg.343 ]

See also in sourсe #XX -- [ Pg.11 ]

See also in sourсe #XX -- [ Pg.7 ]




SEARCH



Average Oseen tensor

Basset, Boussinesq, and Oseen (BBO) Equation

Basset-Boussinesq-Oseen equation

Continuum theory Oseen-Zocher-Frank elasticity

Curvature elasticity the Oseen-Zocher-Frank equations

Equations Oseen

Frank-Oseen Theory

Frank-Oseen constants

Frank-Oseen elastic energy

Frank-Oseen energy

Frank-Oseen free energy

Generalized Ewald-Oseen Extinction Theorem

Hydrodynamic equations Oseen

Hydrodynamic interaction Oseen tensor

Hydrodynamic tensor, Oseen

Oseen approximation

Oseen chiral nematics

Oseen diffusion

Oseen drag

Oseen interaction

Oseen interaction tensor

Oseen nematics

Oseen tensor

Oseen theory

Oseen-Frank expression

Oseens and Higher Approximations as Re

Oseen’s approximation

Oseen’s equations

Oseen’s law

Screened Oseen tensor

The Basset, Boussinesq, Oseen, and Tchen equation

The Frank-Oseen Elastic Energy

The Frank-Oseen Energy

The Oseen tensor

Unscreened Oseen tensor

© 2024 chempedia.info