Gap-Dependent Apparent Shear Rate

1 GAP-DEPENDENT APPARENT SHEAR RATE. Indirect evidence of slip, as well as a measurement of its magnitude, can be extracted from the flow curve (shear stress versus shear rate) measured at different rheometer gaps (Mooney 1931). If slip occurs, one expects the slip velocity V (a) to depend on the shear stress a, but not on the gap h. Thus, if a fluid is sheared in a plane Couette device with one plate moving and one stationary, and the gap h is varied with the shear stress a held fixed, there will be a velocity jump of magnitude Vs(ct) at the interfaces between the fluid and each of the two plates. There will also be a velocity gradient (a) in the bulk of the fluid thus the velocity of the moving surface will be y = 2V,(a) + y (a)/i. The apparent shear rate V/h will therefore be 

A plot of yapp against 1 / h will then be a straight line with slope 2Vs. This method has been used to measure the slip velocity for polyethylene melts in a sliding plate (plane Couette) rheometer by Hatzikiriakos and Dealy (1991). Analogous methods have been applied to shearing flows of melts in capillaries and in plate-and-plate rheometers (Mooney 1931 Henson and Mackay 1995 Wang and Drda 1996). 

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