Neutral Polymers Hydrodynamic Interaction

We can analyze this force in more detail. To begin with, remember the simple case of a shear flow created if two parallel plates are moved against each other with constant velocity v. Here, a linear velocity profile evolves, like that included in Fig. 8.16. The power that has to be supplied is given by 

Vs denotes the viscosity of the fluid, Lz is the thickness of the liquid layer, and the product LxLy gives the area of the plates. The expression on the right-hand side states that the power dissipated per unit volume is proportional to Vs and to the square of the velocity gradient. Here, the result was obtained for the particular case of a constant velocity gradient. Theories for the general 

The flow field v r) produced by the particle if it is dragged with a constant velocity u through the liquid can generally be described as 

Here we introduced another tensor, of third rank, with components hijk- The formulated dependence is of the linear type, therefore, holds for Newtonian liquids. All low molar mass liquids behave in Newtonian manner, at least for ordinary velocities. If Eq. (8.138) is inserted into Eq. (8.135), followed by an integration over the whole flow field, the dissipated power is obtained 

we introduced yet another tensor, with components (3ki It is specific for the particle and depends on its size and shape. 

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In order to resolve these challenges, it is essential to account for chain connectivity, hydrodynamic interactions, electrostatic interactions, and distribution of counterions and their dynamics. It is possible to identify three distinct scenarios (a) polyelectrolyte solutions with high concentrations of added salt, (b) dilute polyelectrolyte solutions without added salt, and (c) polyelectrolyte solutions above overlap concentration and without added salt. If the salt concentration is high and if there is no macrophase separation, the polyelectrolyte solution behaves as a solution of neutral polymers in a good solvent, due to the screening of electrostatic interaction. Therefore for scenario... 

In this work, we address to the first point our objectives were to explore the modifications of the electrical double layer and hydrodynamic properties of a jS ferric hydrous oxide colloid in aqueous media, interacting with non-hydrolyz polyac lamide, a neutral polymer. The j8 ferric hydrous oxide particles are ellipsoidal shaped particles and the electrical double layer features can be determined through the electrical polarizability of the ellipse. Electro-optical determinations were complemented by measuring the electrophoretic mobility at various polymer coverage. 

Interfacial Tension. Another property of the polymer is the ability to bind up water. Depending on the nature of the polymer, charged or neutral, the hydrodynamic volume or the electrical double layer will be affected by both salinity and temperature. Usually it will decrease as salinity and temperature increase. Kalpakci et al. [J3] suggested that a dissociative surfactant-polymer interaction would have synergistic effects... 

First, the fundamental forces between neutral colloidal spheres are the same as the fundamental forces between neutral polymers. Polymers and colloids are equally subject to excluded-volume forces, hydrodynamic forces, van der Waals interactions, and to the random thermal forces that drive Browiuan motion. 

What physical forces affect colloid dynamics Three forces acting on neutral colloids are readily identified, namely random thermal forces, hydrodynamic interactions, and direct interactions. The random thermal forces are created by fluctuations in the surrounding medium they cause polymers and colloids to perform Brownian motion. As shown by fluctuation-dissipation theorems, the random forces on different colloid particles are not independent they have cross-correlations. The cross-correlations are described by the hydrodynamic interaction tensors, which determine how the Brownian displacements of nearby colloidal particles are correlated. The hydrodynamic drag experienced by a moving particle, as modified by hydrodynamic interactions with other nearby particles, is also described by a hydrodynamic interaction tensor. 

Fourth, I consider solutions of hard-sphere colloids. Neutral polymers and neutral colloids interact through precisely the same forces. They have hydrodynamic interactions, and they cannot interpenetrate. They differ only in their geometry. As will be seen, Iheir dynamic behaviors are also quite similar, speaking to the possible significance of topological interactions in polymer dynamics. 

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