Liquid flow and intermolecular forces

When a Newtonian liquid flows with a mean velocity less than the critical velocity it does so in layers, without mixing on the macroscopic scale. The viscosity of the liquid arises from the forces needed to maintain the relative motion of adjacent liquid layers. 

The temperature-dependence of the viscosity of simple liquids can be discussed using the cell model as follows. Consider the cell of molecules shown in Fig. 6.2(a), where U is the average height of the potential barrier a molecule must surmount to escape from the cell. The molecule at A tries to climb over this barrier times per second, where Vq is its vibration frequency. The probabihty that the molecule at A acquires sufficient energy, as a result of a thermal fluctuation, to climb over the potential barrier is proportional to the Boltzmann factor exp (—where k is the Boltzmann constant and T is the thermodynamic temperature. Therefore, the number of successful attempts per second to surmount the potential hill, known as the jump frequency i, is  

When a shear stress is applied, the effect is to tilt the potential energy curve, as shown in Fig. 6.2(b), but for moderate shear stresses the tilt is quite small and the jump frequency is only slightly changed, though the spatial distribution of successful jumps is now biassed in the direction of the shear stress. Since the liquid viscosity will vary inversely as the jump frequency, it will show a temperature dependence of the form  

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