Tangential Stress Components Research Articles

A second-order theory for shear deformation of drops

A liquid drop is supposed suspended in an immiscible liquid of equal density that undergoes slow steady shear flow. From a solution of Stokes' creeping motion equations in which the tangential component of normal stress is assumed continuous across the drop surface, the equation giving the drop shape is found approximately, cubes and higher powers of the deformation parameter D I being neglected compared to unity. D I is proportional to the product of the velocity gradient, the drop radius, the suspending liquid's viscosity, and the reciprocal of the interfacial tension. To second order in D I the drop is not ellipsoidal and in Couette flow its angle of maximum extension, measured from the direction of the velocity gradient, exceeds 1 4 π , approaching 1 2 π for viscous drops at larger D I. The results agree qualitatively with previous experimental descriptions of the deformation phenomenon, but quantitative agreement between calculated angles of maximum extension and previously reported measurements is not found. The disagreement may be due to different interpretations of the angle of maximum extension or more probably to impeded transmission of tangential stress at the interface.

Wind-generated waves in thin liquid films

In the presence of an air stream, a uniform liquid film on a horizontal flat plate may be unstable to small disturbances, and waves may arise. In this paper the hydrodynamic stability of thin liquid films is examined both experimentally and theoretically.The experiments concern water films thinner than those which have been examined in the past. It is found that, when the film thickness is sufficiently small, a previously unknown type of instability occurs. The theoretical analysis explains this surprising phenomenon.Due to interaction of the mean airflow and small disturbances of the liquid-air interface, normal and tangential stress perturbations are produced at the liquid surface. It is shown that small wave-like disturbances become unstable when the joint influence of the component of normal stress in phase with the wave elevation and the component of tangential stress in phase with the wave slope is sufficient to overcome the ‘stiffness’ of the liquid surface due to gravity and surface tension. It is found that the destabilizing role of the tangential stress component is dominant for very thin films, and that instability may occur whatever the velocity of the air stream, provided the film is made sufficiently thin.

送気式井筒の沈下時における井筒内の応力変化について

In order to contribute to the rational design of a shaft well which is sunk by air blow and also to the safe sinking operation, the authors have measured the stress in the well of the Shaft 1 of the Ariake coal mine.It has been found that the stress variation occurring during subsidence depended upon the nature of ground at and the depth of the bottom of the well and could be classified into three types. For each type, the variations in the tangential and axial stress components as well as their causes have been cleared out. The greatest stress variation was the decrease in the compresseive tangential stress during subsidence. It amounted to 9 kg/cm2 on the average, 35 kg/cm2 on the maximum when the well was sunk to a greater depth. It has been concluded that the major cause of this stress decrease is the outside deflection of the cutting shoe.

Rheological behaviour of continuously sheared polythene

A commercial grade of polythene has been tested between its melting point and 190° C at constant shear rates from 0.1 to 9.8 s-1. A disk-and-cone rheometer was used, and an improved technique introduced to provide a complete picture of the pressure distribution in the flowing melt by measuring each normal and tangential stress component individually. Changes of great complexity occurred with increasing shear, and varied with temperature and rate of shear, but simple relations could be established between the stress components and the measured strain recovery. These relations were not much affected by the imposed conditions and were in reasonable agreement with Weissenberg's theory when account was taken of an appropriate correction to his calculated recoverable strain. Moreover, the normal stress component in the axial direction was shown to be equal to that in the radial direction, in quantitative agreement with Weissenberg's theory. Changes occurred in the material during shearing, and increased with the applied shear and with the stress, but were reversible and vanished on resting. The observed behaviour is attributed to successive structural changes in the polymer, and an attempt is made to define equivalent structural states produced at different rates of shear.