VISCOUS DRAG COMPONENT

If the relative velocity is sufficiently low, the fluid streamlines can follow the contour of the body almost completely all the way around (this is called creeping flow). For this case, the microscopic momentum balance equations in spherical coordinates for the two-dimensional flow [vr(r, 0), v0(r, 0)] of a Newtonian fluid were solved by Stokes for the distribution of pressure and the local stress components. These equations can then be integrated over the surface of the sphere to determine the total drag acting on the sphere, two-thirds of which results from viscous drag and one-third from the non-uniform pressure distribution (refered to as form drag). The result can be expressed in dimensionless form as a theoretical expression for the drag coefficient ... 

When a low frequency AC electric field is imposed, the particle oscillates around its mean position and platy particles may become optimally aligned with the field. At high frequencies, neither particle shift nor alignment takes place. However, translational movement of dispersed particles can be attained in an asymmetric AC field (without a DC component). The observed drift is attributed to the velocity-dependent viscous drag force in relation to double layer polarization as sketched in Figure 2 for reference, bacteria swim at 0.02-1 mm/s. For more details see Palomino [2], The field frequency co must be low enough such that ionic concentrations and hydrodynamic fields may adjust to... 

We can attempt to analyze, from the molecular viewpoint, the way in which viscous drag arises. If a surface is set in motion in a gas, the molecules striking the surface will, if the surface is rough," rebound with a larger component of momentum in the direction of the motion. These molecules will in turn collide with other molecules and through a chain process transfer the added momentum received from the moving surface... 

Stress required to break the aggregate network. Pa Static yield stress. Pa Tangential components of stress. Pa Stress dissipated due to viscous drag. Pa Stress tensor... 

These are older techniques and are no longer much used. A solute alters the viscosity of the solvent. The ion and its solvent molecules exert a viscous drag on the rest of the solvent and the change in viscosity can be used to calculate a total hydration number which is then split up into its individual components. However, viscosity measurements are normally used as an aid to developing a structural interpretation of solvation (see Section 13.8), and to give correction factors in conductance equations (see Section 12.10). 

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