NON-NEWTONIAN FLUIDS

PRESENTED TO: PROF.DR.H.M. ANWAR ASGAR

PRESENTED BY: SALMAN HAROON (MSC-13-S-07) MUHAMMAD NOMAN ARIF (MSC-13-S-09) SANAULLAH KHAN (MSC-13-S-32)

Newtonian Fluids Those fluids which follow Newton law of viscositywhen shear stress is plotted against shear rate at a given temperature, the plot shows a straight line with a constant slope that is independent of shear rate. Fluid such as water, air, ethanol, and benzene are NewtonianNon-Newtonian fluids Any fluids that do not obey the Newtonian relationship between shear stress and shear rate are non-Newtonian. Aqueous solutions of high molecular weight polymers or polymer melts, and suspensions of fine particles are usually non-Newtonian.

Non-Newtonian Fluids

blood toothpaste ketchup

grease cake batter polymer melt

Models of Non-Newtonian Fluids

The expressions shown here are used to characterize the non-Newtonian behavior of fluids under equilibrium, steady shear flow conditions. models those having a direct and significant implication for suspensions, gels and pastes have been included here. grease

wet sand corn flour

Non-Newtonian Fluids

molten metal whipped

cream

paint

Power-law Model

One of the most widely used forms of the general non-Newtonian constitutive relation is a power-law model, which can be described as

where Tau is shear stress, gama is shear rate, m and n are power-law model constants. The constant, m , is a measure of the consistency of the fluid: the higher the m is, the more viscous the fluid is. n is a measure of the degree of non-Newtonian behavior: the greater the departure from the unity, the more pronounced the non-Newtonian properties of the fluid are.One of the obvious disadvantages of the power-law model is that it fails to describe the viscosity of many non-Newtonian fluids in very low and very high shear rate regions.

Cross Model

As discussed in the previous section, the power law model does not have the capability of handling Newtonian regions of shear-thinning fluids at very low and high shear rates. In order to overcome this drawback of the power-law model, Cross (1965) proposed a model that can be described as

In above equation η0 and η ∞ are the viscosities at very low

and high shear rates, respectively m and n are the model constants. At an intermediate shear rate, the Cross

model behaves like a power-law model. However, unlike the power-law model, the Cross model produces Newtonian viscosities (η0 and η∞ ) at both very low and high shear rates.

TYPES OF FLUIDS1) Newtonian Fluids2) Non-Newtonian FluidsNewtonian Fluids:Those fluids which follow newton law of viscosity.when shear stress is plotted against shear rate at a given temperature, the plot shows a straight line with a constant slope that is independent of shear rate. Fluid such as water, air, ethanol, and benzene are Newtonian.Non-Newtonian fluidsAny fluids that do not obey the Newtonian relationship between shear stress and shear rate are non-Newtonian. Aqueous solutions of high molecular weight polymers or polymer melts, and suspensions of fine particles are usually non-Newtonian.

Models of Non-Newtonian Fluids The expressions shown here are used to

characterize the non-Newtonian behavior of fluids under equilibrium, steady shear flow conditions. models those having a direct and significant implication for suspensions, gels and pastes have been included here.

Power-law Model

One of the most widely used forms of the general non-Newtonian constitutive relation is a power-law model, which can be described as

where m and n are power-law model constants. The constant, m , is a measure of the consistency of the fluid: the higher the m is, the more viscous the fluid is. n is a measure of the degree of non-Newtonian behavior: the greater the departure from the unity, the more pronounced the non-Newtonian properties of the fluid are.One of the obvious disadvantages of the power-law model is that it fails to describe the viscosity of many non-Newtonian fluids in very low and very high shear rate regions.

Cross Model

As discussed in the previous section, the power law model does not have the capability of handling Newtonian regions of shear-thinning fluids at very low and high shear rates. In order to overcome this drawback of the power-law model, Cross (1965) proposed a model that can be described as

In above equation η0 and η ∞ are the viscosities at very low

and high shear rates, respectively m and n are the model constants. At an intermediate shear rate, the Cross

model behaves like a power-law model. However, unlike the power-law model, the Cross model produces Newtonian viscosities (η0 and η∞ ) at both very low and high shear rates.

Bingham Plastic Model Many types of food stuffs exhibit a yield

stress and are said to show a plastic or viscoplastic behavior

One of the simplest viscoplastic models is the Bingham plastic model

Expression of Bingham Plastic Model

Taken from Schlumburger Oilfields

Examples of Bingham Plastic Fluids

Tooth Paste Handling of Slurries Mud flow in drilling

Bingham Plastic Fluid Example

A Bingham plastic flows in a pipe and it is observed that the central plug is 30mm diameter when the pressure drop is 100 Pa/m.Calculate the yield shear stress.Given that at a larger radius the rate of shear strain is 20 s-1 and the consistency coefficient is 0.6 Pa.s. Calculate the shear stress.

The pressure difference p acting on the cross-sectional area must produce sufficient force to overcome the shear stress ᴛ acting on the surface area of the cylindrical slug. For the slug to move, the shear stess must be atleast equal to the yield value ᴛy.Balancing the forces gives

Bingham Plastic Fluid Example

Bingham Plastic Fluid Example

Why does Bingham Plastic Model not able to handle Shear-thinning characteristics of Non-

Newtonian Fluids?

The Bingham plastic model can describe the viscosity

characteristics of a fluid with yield stress whose viscosity is

independent of shear rate

Casson Model

This model was originally introduced by Casson (1959)for the prediction of the flow behavior of pigment-oil suspensions

The Casson model is based on a structure model of the interactive behavior of solid and liquid phases of a two-phase suspension

The model describes the flow of viscoplastic fluids

where k is a Casson model constant

The Casson model shows both yield stress and shear-thinning non-Newtonian viscosity

Casson model can be described mathematically as:

Casson Model Fluids

Jelly Tomato sauce Honey Molten milk

chocolate

GelLotion

HERSCHEL-BULKLEY MODEL

The Herschel-Bulkley model extends the simple power-law model to include a yield stress as follows

Like the Casson model, it shows both yield stress and shear-thinning non-Newtonian viscosity, and is used to describe the rheological behavior of food products and biological liquids [Ferguson and Kemblowski, 1991; Holdsworth, 1993]. In addition, the Herschel-Bulkley model also gives better fit for many biological fluids and food products than both power-law and Bingham plastic models.

Powell-Eyring Model

Derived from the theory of rate processes, this relation is relevant primarily to molecular fluids, but can be used in some cases to describe the viscous behavior of polymer solutions and viscoelastic suspensions over a wide range of shear rates. Here, is the infinite shear viscosity 0 is the zero shear viscosity and the fitting parameter represents a characteristic time of the measured system. If 0 and are not known independently from experiment, these quantities may be treated as additional adjustable parameters.

Importance of Non-Newtonian Fluid In Process industries we deal different types of non-

newtonian fluids so their properties helpful in processes as

• Liquids and semisolids are usually pumped during processing, so in case of fluids if we now properties of non-newtonian fluids we avoid problems like caviation,bubbles etc.

• If we know properties of different non-newtonain fluid then we better tackle different non-nowtonian fluids like Food suc as butter, cheese, jam, ketchup, mayonnaise, soup, taffy, and yogurt Natural substances such as magma, lava, gums, and synovial fluid Slurries such as cement slurry and paper pulp, emulsions such as mayonnaise, and some kinds of dispersions.

• Viscosity plays a huge part in pump and conveyance system design.

• Viscosity may be dependent on moisture content, concentration, composition and prior treatments.