Non-newtonian Fluids

Non-Newtonian FluidsTypes 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 fluids.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.

2 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.Models of Non-Newtonian Fluids

Grease ,ketchup,whippe cream,blood,paint, andnail polishwet sand corn flourNon-Newtonian Fluidsbloodtoothpasteketchup

greasecake batterpolymer meltNature of Non-Newtonian fluids: slurries, significantly viscous fluids, highly concentrated solutions, polymer melts4Non-Newtonian Fluidsmolten metalwhipped creampaint

More examples of non-Newtonian fluids.5Power-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 equation0 and are the viscosities at very low and high shear rates, respectivelym 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 (0 and ) 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, and it can be expressed as follows

In above equation y is a constant that is interpreted as yield stressm B is a model constant that is interpreted as plastic viscosity.Basically, the Bingham plastic model can describe the viscosity characteristics of a fluid with yield stress whose viscosity is independent of shear rate. Therefore, the Bingham plastic model does not have the ability to handle the shear-thinning characteristics of non-Newtonian fluids.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 that can be mathematically described as follows

where k is a Casson model constant. The Casson model shows both yield stress and shear-thinning non-Newtonian viscosity. For materials such as blood and food products, it provides better fit than the Bingham plastic modelHerschel-Bulkley ModelThe 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 asbutter, cheese,jam,ketchup,mayonnaise,soup,taffy, andyogurt Natural substances such asmagma,lava,gums, andsynovial fluid Slurriessuch as cement slurry and paper pulp,emulsionssuch as mayonnaise, and some kinds ofdispersions.

Viscosity plays a huge part in pump and conveyance system design.Viscosity may be dependent on moisture content, concentration, composition and prior treatments.