CP 502 Advanced Fluid Mechanics Incompressible Flow of

CP 502 Advanced Fluid Mechanics Incompressible Flow of Viscous Fluids Set 05: Basics in Non-Newtonian Fluids Prof. R. Shanthini 20 June 2019

Flow Characteristics of Non-Newtonian Fluids Prof. R. Shanthini 20 June 2019

CP 511 – Flow Characteristics of Non-Newtonian Fluids Psuedoplastic fluid (power law / shear thinning) Dilatant fluid (shear thickening) Prof. R. Shanthini 20 June 2019

Mathematical model where - shear stress, - shear rate, K and n are regarded as model factors Prof. R. Shanthini 20 June 2019

Newtonian Fluids where K > 0 and n = 1 Prof. R. Shanthini 20 June 2019

Newtonian Fluids Eg: Water Fruit juice Milk Vegetable oil Prof. R. Shanthini 20 June 2019

Psuedoplastic (or Shear Thinning) Fluids Prof. R. Shanthini 20 June 2019 The apparent viscosity decreases with increasing shear rate

Psuedoplastic (or Shear Thinning) Fluids where K > 0 and 0 < n < 1 - condensed milk - fruit pastes - vegetable soups - thawed whole egg (raw egg is Newtonian) - concentrated apple juice (single-strength apple juice is Newtonian) Prof. R. Shanthini 20 June 2019 The apparent viscosity decreases with increasing shear rate

Dilatant fluid (or Shear Thickening) Liquids Prof. R. Shanthini 20 June 2019 The apparent viscosity increases with increasing shear rate

Dilatant fluid (or Shear Thickening) Liquids where K > 0 and 1 < n < ∞ - 60% suspension of corn starch in water - Some types of honey Prof. R. Shanthini 20 June 2019 The apparent viscosity increases with increasing shear rate

Flow Characteristics of Non-Newtonian Fluids (Herschel Bulkley) Yield stress Prof. R. Shanthini 20 June 2019 Time-independent models

Bingham plastic Liquids It is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. No response prior to the application of yield stress. Beyond the application of yield stress, the response is similar to a Newtonian fluid. Prof. R. Shanthini 20 June 2019

Bingham plastic Liquids - Mathematical model where K > 0 and n = 1 where - shear stress - shear rate 0 - yield stress K - consistency coefficient n - flow behaviour index Prof. R. Shanthini 20 June 2019

Bingham plastic Liquids Mayonnaise is a Bingham plastic. The surface has ridges and peaks because Bingham plastics mimic solids under low shear stresses. Tooth paste Tomato paste Prof. R. Shanthini 20 June 2019

Herschel-Bulkley Liquids It is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. No response prior to the application of yield stress. Beyond the application of yield stress, the response is similar to a shear- thinning fluid. Prof. R. Shanthini 20 June 2019

Herschel-Bulkley Liquids - Mathematical model where K > 0 and 0 < n < ∞ Minced fish paste Raisin paste Prof. R. Shanthini 20 June 2019

Casson model for chocolate flow Consistency coefficient is Yield stress is Prof. R. Shanthini 20 June 2019

Rheological data for Swedish commercial chocolate at 40 o. C is provided. Using Casson model, determine the consistency coefficient and the yield stress. Shear rate Shear stress 0. 099 28. 6 13. 1 178. 5 0. 14 35. 7 15. 9 201. 1 0. 199 42. 8 17. 9 221. 3 0. 39 52. 4 19. 9 235. 6 0. 79 61. 9 1. 6 71. 4 2. 4 80. 9 3. 9 100 6. 4 123. 8 7. 9 133. 3 11. 5 164. 2 Prof. R. Shanthini 20 June 2019 Unit of shear rate is per s Unit of shear stress is ? ? ?

Thixotropic and Rheopectic fluids Time-dependent models Prof. R. Shanthini 20 June 2019 Time-independent models

Prof. R. Shanthini 20 June 2019