Viscosity
Pure liquids

In contrast with gases, there is no simple yet accurate picture for the molecular origins of viscosity in liquids.

At the simplest level of description, the relative motion of adjacent layers in a liquid is opposed primarily by attractive molecular forcesacting across the layer boundary. In this picture, one (correctly) expects viscosity to decrease with increasing temperature. This is becauseincreasing temperature increases the random thermal motion of the molecules, which makes it easier for them to overcome their attractive interactions.

Building on this visualization, a simple theory can be constructed in analogy with the discrete structure of a solid: groups of molecules in a liquid are visualized as forming "cages" which surround and enclose single molecules. These cages can be occupied or unoccupied, andstronger molecular attraction corresponds to stronger cages.Due to random thermal motion, a molecule "hops" between cages at a rate which varies inversely with the strength of molecular attractions. In equilibrium these "hops" are not biased in any direction.On the other hand, in order for two adjacent layers to move relative to each other, the "hops" must be biased in the directionof the relative motion. The force required to sustain this directed motion can be estimated for a given shear rate, leading to

where N A {\displaystyle N_{\text{A}}} is the Avogadro constant, h {\displaystyle h} is the Planck constant, V {\displaystyle V} is the volume of a mole of liquid, and T b {\displaystyle T_{\text{b}}} is the normal boiling point. This result has the same form as the well-known empirical relation

where A {\displaystyle A} and B {\displaystyle B} are constants fit from data. On the other hand, several authors express caution with respect to this model.Errors as large as 30% can be encountered using equation (1), compared with fitting equation (2) to experimental data. More fundamentally, the physical assumptions underlying equation (1) have been criticized. It has also been argued that the exponential dependence in equation (1) does not necessarily describe experimental observations more accurately than simpler, non-exponential expressions.

In light of these shortcomings, the development of a less ad hoc model is a matter of practical interest. Foregoing simplicity in favor of precision, it is possible to write rigorous expressions for viscosity starting from the fundamental equations of motion for molecules. A classic example of this approach is Irving–Kirkwood theory. On the other hand, such expressions are given as averages over multiparticle correlation functions and are therefore difficult to apply in practice.

In general, empirically derived expressions (based on existing viscosity measurements) appear to be the only consistently reliable means of calculating viscosity in liquids.

Local atomic structure changes observed in undercooled liquids on cooling below the equilibrium melting temperature either in terms of radial distribution function g (r) or structure factor S (Q) are found to be directly responsible for the liquid fragility: deviation of the temperature dependence of viscosity of the undercooled liquid from the Arrhenius equation (2) through modification of the activation energy for viscous flow. At the same time equilibrium liquids follow the Arrhenius equation.
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