Transpoort phenomena notes

1. Transport Phenomena

2. VELOCITY GRADIENT AND RATE OF
SHEAR

3. SHEAR STRESS

4. NEWTON’S LAW OF
VISCOSITY
 Newton’s law of viscosity states that;
“Shear stress is directly proportional to the
shear rate.”
 Viscosity “µ” is a constant of proportionality.
 Fluids following this simple linearity are called
Newtonian Fluids.

5. MOMENTUM FLUX
 The units of momentum flux are the same as the
units for shear stress.
 Momentum flux normal to the direction of flow of
the fluid is proportional to the velocity gradient,
with the viscosity as the proportionality factor.

6. TYPES OF FLUIDS
Newtonian Fluids
Non-Newtonian Fluids
 Bingham Plastics
 Pseudo-Plastics
 Dilatants
 Thixotropic liquids
 Rheopectic Substances

7. TYPES OF FLUIDS (contd….)

8. Newtonian Fluids
 Follows the Newton’s law of viscosity.
 At a given temperature the viscosity of a
Newtonian fluid remains constant.

9. Non-Newtonian Fluids
 A non-Newtonian fluid is a fluid whose flow
properties differ in any way from those of
Newtonian fluids.
 EXAMPLES:
 ketchup
 custard
 toothpaste
 starch suspensions
 paint
 blood
 shampoo

10. Non-Newtonian Fluids (contd..)
 Bingham Plastics
 Pseudo-Plastics
 Dilatants
 Thixotropic liquids
 Rheopectic Substances
Time independent
flow
Time dependent
flow

11. RHEOLOGY
 Rheology is the study of the flow of materials that
behave in an interesting or unusual manner.
 Oil and water flow in familiar, normal ways,
whereas mayonnaise, peanut butter, chocolate
flow in complex and unusual ways.
 In rheology, we study the flows of unusual
materials.
 The relationships between the shear stress and
shear rate in a real fluid are part of the science

12. RHEOLOGY (contd…)
 Rheology is the study of the flow of matter,
primarily in the liquid state, but also as 'soft solids'
or solids under conditions in which they respond
with plastic flow rather than deforming elastically
in response to an applied force.
 It applies to substances which have a complex
molecular structure, such as muds, sludges,
suspensions, polymers and other glass formers
(e.g. silicates), as well as many foods and
additives, bodily fluids (e.g. blood) and other
biological materials.

13. BINGHAM PLASTIC
 A Bingham plastic is a viscoplastic material that
behaves as a rigid body at low stresses but flows
as a viscous fluid at high stress.
 EXAMPLES:
 Sewage Sludge
 Tooth paste
 Mayonnaise
 clay suspensions

14. PSEUDO-PLASTICS
 Pseudoplastic fluids have a lower apparent
viscosity at higher shear rates, and are usually
solutions of large, polymeric molecules in a
solvent with smaller molecules.
 EXAMPLES:
 Paint
 Ketchup/Tomato sauce
 Shear rate thinning fluids.

15. DILATANTS
 A dilatant is a Non-Newtonian fluid for which as
the shear rate is increased, the viscosity of the
fluid also increases.
 EXAMPLES:
 Cornflour and Water mixture
 Printing inks
 Clay slurries
 Shear rate thickening fluids

16. Time Dependent Flow
 The viscosity of some Non-Newtonian liquids
is dependent upon time as well as shear rate.
 Thixotropic liquids
 Rheopectic Substances

17. THIXOTROPIC LIQUIDS
 A liquid whose viscosity decreases with time at a
given shear rate is called a thixotropic liquid.
 Thixotropic liquids break down under continued shear
and on mixing give lower shear stress for a given
shear rate; that is, their apparent viscosity decreases
with time.
 EXAMPLES:
 asphalts
 glues
 molasses
 paint
 soap
 starch
 grease

18. RHEOPECTIC SUBSTANCES
 Liquids whose viscosity increases with time are
called rheopectic liquids
 Rheopectic substances behave in the reverse
manner, and the shear stress increases with time,
as does the apparent viscosity.
 EXAMPLES:
 Gypsum pastes
 Printers inks
 Lubricants

19. Rheological Characteristics of
Fluids

20.  Bingham Plastics:
 Over some range of shear rates, dilatant and
pseudoplastic fluids often follow a Power Law,
also called the Ostwald-de Waele equation;
 K’ = flow consistency index
 n’ = flow behavior index
 Dilatant and pseudoplastic fluids are known as
Power-law fluids.
n’ = 1 (Newtonian
Fluids)
n’ < 1 (Pseudoplastics)
n’ >1 (Dilatant fluids)

22. REYNOLDS NUMBER FOR
NEWTONIAN FLUIDS
 In a pipe, when
NRe < 2100 (Laminar Flow)
2100 < NRe < 4000 (Transition Flow)
NRe > 4000 (Turbulent Flow)

23.  For Power Law Fluids;
 Critical Reynolds number at which transition to
turbulent flow begins;