Mutual Viscosity Research Articles

Nuclear Magnetic Relaxation of Nonuniform Systems

The effect of electric ions in water upon the proton magnetic relaxation is discussed. Formulas pertaining to solutions of paramagnetic and nonmagnetic ions are derived. The viscosity factor occurring in the theory for uniform systems has to be replaced by an average of inverse local viscosities weighted by the dimensions of the moving particles or by individual diffusion constants. The concept of mutual viscosity—describing the interaction between two unlike liquid layers—is helpful in correlating the numeric results. The influence of temperature and concentration has been studied experimentally. The behavior of trivalent ions like aluminum can be understood by assuming hydration. The effect of monovalent ions can be explained on the basis of a slightly decreased diffusion constant of the free water molecules. Treated as a two-phase system, the experimental results enable the evaluation of the average time of adsorption. For aluminum, this is one-hundredth of a second.

Mutual Viscosity and Diffusion in Liquid Mixtures

A theory of diffusion in liquid mixtures is proposed which shows that the intrinsic diffusion coefficient, DA, of the substance A in a mixture of A and B in which the mole fractions are respectively fA and fB is DA = kT/6 (fAηAσA + fBηABσAB) where ηA is the viscosity of the pure liquid A, ηAB is the mutual viscosity of the mixture, and σA and σAB are intermolecular distances. This leads to values of D, the measured diffusion coefficient, which are in good agreement with the experimental values, both in the limiting case when the concentration of one component is very low, and for 50% mixtures.

The Dielectric Relaxation of Polar Molecules in Solution

A simple theory of dielectric relaxation is proposed, based on the same model of a liquid as Andrade's theory of viscosity. It is shown that the relaxation time of a polar molecule in solution in a non-polar solvent should be related, not to the viscosity of the solvent, but to the ` mutual viscosity' of the solute and solvent. This quantity can be calculated from the variation of the viscosity of the solution with concentration, since the viscosity ?m of a mixture containing mole fractions fA and fB of the two substances A and B is shown to be ?m = fA2?A ?A/?m + fB2?B ?B/?m + 2fAfB?AB ?AB/?m where the ?'s are intermolecular distances, and ?AB, the mutual viscosity, represents the contribution to the total viscosity of collisions between a molecule of substance A and a molecule of substance B. The theory shows satisfactory agreement with experimental results both for pure liquids and for solutions.