![]() ![]() If the two cylinders rotate in opposite sense then spiral vortex flow arises. Subsequently, upon increasing the angular speed of the cylinder the system undergoes a progression of instabilities which lead to states with greater spatio-temporal complexity, with the next state being called wavy vortex flow. Taylor showed that when the angular velocity of the inner cylinder is increased above a certain threshold, Couette flow becomes unstable and a secondary steady state characterized by axisymmetric toroidal vortices, known as Taylor vortex flow, emerges. Taylor's paper became a cornerstone in the development of hydrodynamic stability theory and demonstrated that the no-slip condition, which was in dispute by the scientific community at the time, was the correct boundary condition for viscous flows at a solid boundary. Sir Geoffrey Ingram Taylor investigated the stability of Couette flow in a ground-breaking paper. This basic state is known as circular Couette flow, after Maurice Marie Alfred Couette, who used this experimental device as a means to measure viscosity. For low angular velocities, measured by the Reynolds number Re, the flow is steady and purely azimuthal. The chains tend to align with the applied stress.Īt high temperatures there is viscous flow.In fluid dynamics, the Taylor–Couette flow consists of a viscous fluid confined in the gap between two rotating cylinders. There is an elastic region ending in brittle fracture.Īt normal temperatures polymers have a non-linear elastic region with a smaller modulus (slope) and a yield point followed by limited plasticity before fracture.Īt warm temperatures the modulus decreases further and there is a larger easy glide region due to secondary bonds breaking and reforming. Temperature has a stronger effect on the secondary bonds than the primary bonds.Īt low temperatures, polymers like most materials, are brittle. Polymers are long chains of atoms joined together with primary bondsīut cross linked between chains with secondary bonds. In the above graph) and the material is then said to be a solid. The change to a glass is smooth with a gradual increase in viscosity.Īt some point there will be a large increase in viscosity and this is called the glass transition temperature (T g The change to a crystal is abrupt with a sudden increase in the viscosity coefficient. Link with long range order to form a crystal. If liquid SiO 2 cools slowly then the tetrahedrons can jostle past each other into their lowest energy configurations and The tetrahedrons are linked in random orientations by secondary bonds, thus forming a glass. If liquid SiO 2 cools quickly then the tetrahedral units do not have time to move to their lowest energy configuration and Viscous drag acts not only between the fluid and the upper plate but also between adjacent laminas of fluid.Ībove 1600° SiO 2 is a liquid with its tetrahedral base units in random motion. The thin layers (or laminas) are held back by viscous drag between the surfaces of the layers.įor example, if two flat solid plates are separated by a viscous fluid,Īn external force is needed to slide the top plate at constant speed over the fixed lower plate. Laminar flow occurs when a fluid can be pictured as split into thin layers which slide smoothly over each other. ![]() The easiest case to consider is laminar flow. In fluid flow, viscosity is the force that opposes motion in and of a fluid. With solids, friction is the force that opposes motion between two surfaces pressed together. Poiseuille's Law and Laminar flow in a tube ![]() ![]() In this lecture the following are introduced: This is an introduction to Electricity, Strength of Materials and Waves. Peter's Index Physics Home Lecture 6 Course Index Lecture 8 ![]()
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