THE RELATIONSHIP BETWEEN THE LINEAR (OSCILLATORY) AND NONLINEAR (STEADY-STATE) FLOW PROPERTIES OF A SERIES OF POLYMER AND COLLOIDAL SYSTEMS

The Cox-Merz empirical relationship between the linear (oscillatory) and nonlinear (steady-state) viscosities has been shown to be valid for many polymeric systems. Here, we present an equivalent expression to relate the linear (G') and nonlinear (N1) elastic properties of viscoelastic systems. Like the (Cox-Merz relationship, it uses a combination of elastic and viscous parameters. The modified form of the storage modulus is then equivalent to the Cox-Merz complex viscosity. It can be used to correlate with (half) the normal force at numerically equal circular frequency and shear rate, respectively. This new expression and the Cox-Merz rule are tested for a range of polymeric and colloidal systems. It is found that both expressions work for the polymeric systems considered, but fail for the colloidal systems. In the latter, the steady state values of viscosity and elasticity are consistently low, and replacing them by the complex viscosity and our new elastic expression only makes matters worse. For polymer systems, we suggest this is a general but not universal observation, since we are aware of exceptions to the rule that polymeric systems obey the Cox-Merz rule for viscosity and our rule for elasticity. For colloidal systems we find that either rule is obeyed for any of our systems.