Liquids macroscopic/microscopic length scales

An important common feature of macroion solutions is that they are characterized by at least two distinct length scales determined by the size of macroions (an order up to lOnm in the case of ionic micellar solutions) and size of the species of primary solvent (water molecules and salt ions, i.e. few Angstroms). Considering practical colloidal macro-dispersions, like foams, gels, emulsions, etc., usually we are dealing with as many as four distinct length scales molecular scale (up to lnm) that characterizes the species of the primary solvent (water or simple electrolytes) submicroscopic or nano scale (up to lOOnm) that characterizes nanoparticles or surfactant aggregates called micelles microscopic or mesoscopic scale (up to lOO m) that encompasses liquid droplets or bubbles in emulsion and foam systems as well as other colloidal suspensions, and macroscopic scale (the walls of container etc). 

Figure 6.1 Illustration of microscopic and macroscopic length scales in gases, liquids, and solids.

Since both b and d are measurable on the molecular scale, this expression does not differ in a macroscopically thick layer from the standard lubrication mobility given by Eq. (47), and the correction becomes significant only in theimmediate vicinity of the contact line. The three microscopic scales d, 6, and A are about of the same order of magnitude. The natural choice for d is the nominal molecular diameter, identified with the cut-off distance in the van der Waals theory. The standard value is about 0.2nm. The slip length is likely to be of the same order of magnitude. The approximate relation between viscosity / and self-diffusivity D,n in a liquid yields DniV lO T/37rd. The surface diffusivity should be somewhat lower than the diffusivity in the bulk liquid, and with D/Dm 0.1 we have 6 d. 

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