Newtonian fluids

All those Fluids are known as newtonian Fluids for which shear stress (τ) is directly proportional to rate of shear strain (dθ/dt).

τ ∝ dθ/dt

τ = μ*(dθ/dt) or τ = μ*(du/dy) ; because from derivation in ; because from derivation in Lecture - 4 we know that dθ/dt = du/dy

Above equation is also termed as newton's law of viscosity. The relation of above equation is linear, where μ represent viscosity and is constant with respect to rate of shear strain.

in the below figure graphical representation of different Newtonian fluids are shown-

In above graph oil is having maximum slope because viscosity in oil is more and air is having minimum slope because viscosity of air is less, whereas water lies between oil and air because viscosity of water is less than oil but more than air.

A straight line passing through origin having constant slope is representing Newtonian fluids. Example are water, oil, mercury, air, petrol.



Non Newtonian fluids

A non-Newtonian fluid is a fluif that d oes not follow Newton's law of viscosity , i.e. constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. For example, ketchup becomes runnier when shaken and is thus a non-Newtonian fluid. The equation for non newtonian Fluids is

τ = A*(du/dy)^n + B

Here 'A' represents flow consistency index

'n' represents flow behaviour index

'B' represents yield shear stress

If in this equation when n=1 & B=0 then it became newtonian fluid.

Let's study the different cases of non newtonian fluid

Case 1 : VARIATION OF VISCOSITY (μ) WITH RESPECT TO RATE OF SHEAR STRESS (dθ/dt)



Dilatant fluid - In dilatant fluids viscosity will increase with respect to rate of shear stress, therefore the slope of graph will be of increasing nature. Dilatant fluid are shear thickening fluid for example water and sugar solution. For these fluids value of flow behaviour Index (n) is positive and yield shear stress (B) is zero. Graph of dilatant fluid are shown in figure below Pseudo plastic fluids - In pseudo plastic fluids viscosity will decrease with respect to rate of shear stress, therefore the slope of graph will be of decreasing nature. Pseudoplastic fluid are shear thinning fluid for example paint, blood, lipstick. For these Fluids value of flow behaviour index (n) is negative and yield shear stress (B) is zero. Graph of pseudoplastic fluid is shown in figure below

Bingham fluids - in bingham fluids slope of craft will remain constant but the line of graph will not intersect the origin point. Here flow behaviour index (n) is equal to 1 and yield shear stress (B) will not be equal to zero. Examples for toothpaste and gel. Graph of bingham fluid is shown in figure below

Case 2 : VARIATION OF VISCOSITY (μ) WITH RESPECT TO TIME

Rheopectic fluids - In Rheopectic fluids viscosity will increase with respect to time. For these Fluids value of flow behaviour index (n) is positive and yield shear stress (B) is not equal to zero. Graph of rheopectic Fluids is shown in figure below

Thixotropic fluids - In thixotropic fluids viscosity will decrease with respect to time. For these fluids value of flow behaviour index (n) is negative and yield shear stress (B) is not equal to zero. Graph of thixotropic fluids is shown in figure below