Normal Stresses of sheared Suspensions in crystalline States

This presentation extends a geometric analysis on viscosity of solutions in crystalline states to their respective 2^nd normal stress . This extension establishes a key relationship between the structured-suspension viscosity and its normal stress components .  For a non-colloidal mixture, it is shown that the 2^nd normal stress  equals the average-shear stress on the solid particles plus a constant dependent on the solutions’ crystalline state. The analysis deduces that  the second normal stress is negative always when the system possesses ordered states.  Experimental and numerical data on  for non-colloidal equal-size spherical suspensions reveal three distinct particle concentration spectra each characterized by the effective crystalline state of the particles in the mixture.   A comparison of this analysis and experimental data on  suggests a crystalline transition from simple cubic to face-centered cubic states when the particle volume fraction exceeds 45%, in agreement with light scattering observations and viscosity data.