Detailed graph of Shear Stress vs Shear Rate

1. Thixotropic – (Printer’s Ink)
Velocity Gradient (Deformation Rate)
Velocity
Gradient
(Deformation
Rate)
Rheopectic
Bingham/Ideal Plastic –
(Toothpaste, Drilling Mud)
Elastic
Solid
𝜏 = 𝜇
𝑑𝑢
𝑑𝑦
+ 𝐵
Ideal Fluid (𝒖 = 0 or 𝝉 = 0)
𝒅𝒖
𝒅𝒚
𝝉(𝒌𝑵/𝒎𝟐)
Newtonian – (Water, Air, Gasoline)
Yield
Stress (𝝉𝟎)
Dilatant – (Solution with suspended sand, Starch)
Shear Thickening
Pseudo Plastic – (Blood, Paint, Paper Pulp)
Shear Thinning
𝜏 = 𝜇
𝑑𝑢
𝑑𝑦
Newtonian Fluid : –
Non-Newtonian Fluid : –
𝜏 = 𝜇𝑎𝑝𝑝
𝑑𝑢
𝑑𝑦
+ 𝐵
𝜇𝑎𝑝𝑝 = 𝜇
𝑑𝑢
𝑑𝑦
−
,
1) n = 1, B = 𝝉𝟎 Bingham Plastic Fluid
2) n > 1, B = 0 Dilatant Fluid
3) n < 1, B = 0 Pseudoplastic Fluid
1) 𝛕 ↑ → 𝛍𝐚𝐩𝐩 ↑ → Rheopectic Fluid
2) 𝛕 ↑ → 𝛍𝐚𝐩𝐩 ↑ → Thixotropic Fluid
𝛍𝐚𝐩𝐩
𝐭