scholarly journals A review of the second normal-stress difference; its importance in various flows, measurement techniques, results for various complex fluids and theoretical predictions

2021 ◽  
Vol 292 ◽  
pp. 104522
Author(s):  
O. Maklad ◽  
R.J. Poole
Keyword(s):  
Normal Stress ◽  
Complex Fluids ◽  
Measurement Techniques ◽  
Normal Stress Difference ◽  
Stress Difference ◽  
Second Normal Stress Difference ◽  
Theoretical Predictions

Suspensions in a tilted trough: second normal stress difference

2011 ◽  
Vol 686 ◽  
pp. 26-39 ◽  
Author(s):  
Étienne Couturier ◽  
François Boyer ◽  
Olivier Pouliquen ◽  
Élisabeth Guazzelli
Keyword(s):  
Shear Stress ◽  
Normal Stress ◽  
Volume Fraction ◽  
Behavioural Change ◽  
Normal Stress Difference ◽  
Stress Difference ◽  
Rigid Spheres ◽  
First Normal Stress Difference ◽  
Second Normal Stress Difference ◽  
Neutrally Buoyant

AbstractWe measure the second normal-stress difference in suspensions of non-Brownian neutrally buoyant rigid spheres dispersed in a Newtonian fluid. We use a method inspired by Wineman & Pipkin (Acta Mechanica, vol. 2, 1966, pp. 104–115) and Tanner (Trans. Soc. Rheol., vol. 14, 1970, pp. 483–507), which relies on the examination of the shape of the suspension free surface in a tilted trough flow. The second normal-stress difference is found to be negative and linear in shear stress. The ratio of the second normal-stress difference to shear stress increases with increasing volume fraction. A clear behavioural change exhibiting a strong (approximately linear) growth in the magnitude of this ratio with volume fraction is seen above a volume fraction of 0.22. By comparing our results with previous data obtained for the same batch of spheres by Boyer, Pouliquen & Guazzeli (J. Fluid Mech., 2011, doi:10.1017/jfm.2011.272), the ratio of the first normal-stress difference to the shear stress is estimated and its magnitude is found to be very small.

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