Analysis of the Sensitivity of Surface Shear Instruments

A cylindrically symmetric surface shear trough, utilizing a torsion pendulum, is widely used to probe the material properties of surface films. A systematic analysis of the sensitivity of such an instrument is presented. The performance is shown to be governed by four dimensionless factors: two geometric parameters involving the trough (the ratio of the wall to the rotor radius and the ratio of the fluid depth to the rotor radius) and two physical parameters (involving the bulk and surface viscosities and the Reynolds number of the substrate flow). To examine the effects of each of these four factors, a theoretical analysis is made of the effects of the depth and radius of the trough on both continuous and oscillatory rotor rotations. In each case the exact solution of the ñuid flow problem is developed, from which the torque exerted on the rotor by the surface film and the surface velocity distribution are obtained. The effects of each of the four dimensionless factors on the performance of the surface shear trough are presented graphically. The sensitivity of the shear trough to the material properties of the surface film and to the driving frequency is discussed. Some ways to improve the design of surface shear trough instruments are suggested.