Fluids dilatant

Numerous examples of polymer flow models based on generalized Newtonian behaviour are found in non-Newtonian fluid mechanics literature. Using experimental evidence the time-independent generalized Newtonian fluids are divided into three groups. These are Bingham plastics, pseudoplastic fluids and dilatant fluids. 

Dilatant fluids (also known as shear thickening fluids) show an increase in viscosity with an increase in shear rate. Such an increase in viscosity may, or may not, be accompanied by a measurable change in the volume of the fluid (Metzener and Whitlock, 1958). Power law-type rheologicaJ equations with n > 1 are usually used to model this type of fluids. 

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

The pressure drop accompanying pipe flow of such fluids can be described in terms of a generalized Reynolds number, which for pseudoplastic or dilatant fluids takes the form ... 

Power consumption for impellers in pseudoplastic, Bingham plastic, and dilatant nonnewtonian fluids may be calculated by using the correlating lines of Fig. 18-17 if viscosity is obtained from viscosity-shear rate cuiwes as described here. For a pseudoplastic fluid, viscosity decreases as shear rate increases. A Bingham plastic is similar to a pseudoplastic fluid but requires that a minimum shear stress be exceeded for any flow to occur. For a dilatant fluid, viscosity increases as shear rate increases. 

Figure 8.5. Apparent viscosity-shear rate curves for dilatant fluid, a Newtonian fluid and pseudoplastic fluid which have the same apparent viscosity at zero shear rate...

As can be seen from this expression, there is no radial migration for Newtonian fluid (n = 1) for pseudoplastic fluid (n < 1), the migration occurs from the tube centre for dilatant fluid (n > 1), the migration is directed towards the tube centre. 

Dilatant Basically a material with the ability to increase the volume when its shape is changed. A rheological flow characteristic evidenced by an increase in viscosity with increasing rate of shear. The dilatant fluid, or inverted pseudoplastic, is one whose apparent viscosity increases simultaneously with increasing rate of shear for example, the act of stirring creates instantly an increase in resistance to stirring. 

Data for power consumption of Bingham plastic fluids have been reported and correlated by Nagata el alm) and of dilatant fluids by N.AGATA el ul.(2 ) and METZNER et al.i2V). Edwards et ai. M ) have dealt with the mixing of time-dependent thixotropic materials. 

Tripathi A, RP Chhabra. Drag on spheroidal particles in dilatant fluids. AIChE J 41 728, 1995. 

Dilanacin, molecular formula and structure, 5 98t Dilantin, folic acid and, 25 803 Dilatancy, 21 717 Dilatant flow, 7 280t 8 728 Dilatant fluids, 11 768, 769 Dilatometers, vitreous silica in, 22 441 Dilatometric techniques, 13 436... 

Dilatant Fluids. Dilatant fluids display a rheological behavior opposite to that of pseudoplastics (Figs. 2 and 3) in that the apparent... 

It is true, therefore, for Newtonian, Bingham-plastic, pseudoplastic and dilatant fluids. The same relationship can possibly be extended to thixotropic and rheopectic fluids by evaluating the shear stress at the wall over a differential length of tube, i.e., by replacing D P/4L with DdP/idL. This term will vary with distance along the pipe, however, and as no evident means of developing this relationship has been... 

Since the relationship between 8V/D and DAP/4L is independent of pipe diameter, the same is true of Eqs. (17) to (19) inclusive. They are applicable to all four types of common flow behavior, i.e., to pseudoplastic, Newtonian, Bingham-plastic, and dilatant fluids. 

The opposite conclusion would presumably apply to dilatant fluids and for these the pressure drop in a rough pipe may perhaps exceed that for a Newtonian fluid. A similar situation might also arise for Bingham-plastic and pseudoplastic materials which exhibit elastic recovery to a high degree. 

Fluids that show viscosity variations with shear rates are called non-Newtonian fluids. Depending on how the shear stress varies with the shear rate, they are categorized into pseudoplastic, dilatant, and Bingham plastic fluids (Figure 2.2). The viscosity of pseudoplastic fluids decreases with increasing shear rate, whereas dilatant fluids show an increase in viscosity with shear rate. Bingham plastic fluids do not flow until a threshold stress called the yield stress is applied, after which the shear stress increases linearly with the shear rate. In general, the shear stress r can be represented by Equation 2.6 ... 

The values of the consistency index K and the flow behavior index n of a dilatant fluid are 0.415 and 1.23, respectively. Estimate the value of the apparent viscosity of this fluid at a shear rate of 60 s T... 

Fig. 2.6 Schematic representation of pseudoplastic (a) or dilatant fluid (b) behavior of a against change in the strain (d/dt). (From ref. [7])...

In the case of fluids without yield stress, viscous and viscoelastic fluids can be distinguished. The properties of viscoelastic fluids lie between those of elastic solids and those of Newtonian fluids. There are some viscous fluids whose viscosity does not change in relation to the stress (Newtonian fluids) and some whose shear viscosity T] depends on the shear rate y (non-Newtonian fluids). If the viscosity increases when a deformation is imposed, we define the material as a shear-thickening (dilatant) fluid. If viscosity decreases, we define it as a shear-thinning fluid. 

Both polymeric and some biological reactors often contain non-Newtonian liquids in which viscosity is a function of shear rate. Basically, three types of non-Newtonian liquids are encountered power-law fluids, which consist of pseudoplastic and dilatant fluids viscoplastic (Bingham plastic) fluids and viscoelastic fluids with time-dependent viscosity. Viscoelastic fluids are encountered in bread dough and fluids containing long-chain polymers such as polyamide and polyacrylonitrite that exhibit coelastic flow behavior. These... 

The stress for pseudo-plastic and dilatent fluids is not a linear function of shear rate. For non-Newtonian fluids, the relation between t and A is not a simple proportionality because the viscosity is a function of A. For a Bingham plastic fluid, the following relationship holds ... 

Dilatant Fluids. Dilatant fluids or shear-thickening fluids are less commonly encountered than pseudoplastic (shear-thinning) fluids. Rheological dilatancy refers to an increase in the apparent viscosity with increasing shear rate (3). In many cases, viscometric data for a shear-thickening fluid can be fit by using the power law model with n > 1. Examples of fluids that are shear-thickening are concentrated solids suspensions. 

Fluids with a Yield Stress. Both pseudoplastic and dilatant fluids are characterized by the fact that no finite shear stress is required to make the fluids flow. A fluid with a yield stress is characterized by the property that a finite shear stress, To, is required to make the fluid flow. A fluid obeying... 

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