Stirring Newtonian liquids

Consider a stirred tank vessel having a Newtonian liquid of density p and viseosity p, is agitated by an impeller of diameter D, rotating at a rotational speed N. Let the tank diameter be D, the impeller width W, and the liquid depth H. The power P required for agitation of a single-phase liquid ean be expressed as ... 

Considering a stirred vessel in which a Newtonian liquid of viscosity p, and density p is agitated by an impeller of diameter D rotating at a speed N the tank diameter is DT, and the other dimensions are as shown in Figure 7.5, then, the functional dependence of the power input to the liquid P on the independent variables (fx, p, N, D, DT, g, other geometric dimensions) may be expressed as ... 

For laminar flow of a Newtonian liquid in a stirred tank, the power Pa is given by the equation... 

The rates of heat transfer between the fermentation broth and the heat-transfer fluid (such as steam or cooling water flowing through the external jacket or the coil) can be estimated from the data provided in Chapter 5. For example, the film coefficient of heat transfer to or from the broth contained in a jacketed or coiled stirred-tank fermentor can be estimated using Equation 5.13. In the case of non-Newtonian liquids, the apparent viscosity, as defined by Equation 2.6, should be used. 

The effects of broth viscosity on k a in aerated stirred tanks and bubble columns is apparent from Equations 7.37 and 7.41, respectively. These equations can be applied to ordinary non-Newtonian liquids with the use of apparent viscosity as defined by Equation 2.6. Although liquid-phase diffusivity generally decreases with increasing viscosity, it should be noted that at equal temperatures, the gas diffusivities in aqueous polymer solutions are almost equal to those in water. 

Homogenization of miscible liquids, i.e. leveling out the concentration differences by stirring, is represented in Newtonian liquids by the pi-space... 

Let s designate a force such as stirring or spreading a shear force. By shearing we mean forcing the molecules to slide past each other. No matter how hard we stir a pot of water or a jar of honey at constant temperature, the viscosity remains the same because both are Newtonian liquids. But what happens when we stir some polymer solutions It depends. Not all of the examples we discuss below are true solutions. So we ll use the broader term fluid. ... 

Skelland and Kanel [513] established, that the relationship [512] given by them in Table 6.1 was also fully applicable, if a Newtonian liquid (diisobutyl ketone) was stirred into a pseudoplastic liquid (aqueous solutions of Carbopol 934, a stongly acidic acrylic acid polymer), if its apparent density, which obeys the power law of Metzner and Otto, was appropriately taken into consideration. 

In the following section the heat transfer process is considered in a homogeneous Newtonian liquid as a function of stirring conditions and is represented in the pi space Nu, Pr, Re, Vis, D/d. ... 

Henzier H.-J., Obernosterer G., Effect of Mixing Behaviour on Gas-liquid Mass Transfer in Highly Viscous, Stirred non-Newtonian Liquids, Chem. Eng. Technol. 14 (1991), p. 1-10... 

It is worth remembering that the power requirements of geometrically similar stirred tanks are proportional to N3 ds in the turbulent regime, and to N2 d3 in the laminar regime. Equal power per unit liquid volume is sometimes used as a criterion for scale-up. Details of stirrer power requirements for non-Newtonian liquids are provided in Section 12.2. 

Y.S. Fangary, M. Barigou, J.P.K. Seville,, D.J. Parker, "Ruid Trajectories in a Stirred Vessel of Non-newtonian Liquid Using Positron Emission Particle Tracking", Chem. Eng. Sci., 2000, 55, 5969-5979. 

EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER DURING STIRRING OF NON-NEWTONIAN LIQUIDS. 

EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER DURING STIRRING OF NON-NEWTONIAN LIQUIDS. //ENGLISH TRANSUTION OF ZH. PRIKLAD. KHIM. 39 /11/ 2475-83,... 

Simple liquids such as solvents have the same viscosity no matter how fast they are stirred (Barnes, 2000). These are Newtonian liquids. Polymer solutions differ from simple liquids in the way they react to stirring (Wicks et al., 2007). Polymer molecules impart a structure to the liquid. The structure is disturbed while the solution is stirred vigorously. There are a number of different behaviours on stirring. Viscosity can reduce on stirring (shear thinning) as the molecules line up in the direction of flow, so reducing the viscosity... 

Conclusions and recommendations for laminar mixing The equations presented in sections 4.2.3.1 and 4.23.2 give only a rough indication of the flow and mixing phenomena in laminar flow in stirred tanks (of Newtonian liquids). There are as yet no theories that are generally applicable to this type of mixing problems. There are several reasons for this ... 

The final main category of non-Newtonian behaviour is viscoelasticity. As the name implies, viscoelastic fluids exhibit a combination of ordinary liquid-like (viscous) and solid-like (elastic) behaviour. The most important viscoelastic fluids are molten polymers but other materials containing macromolecules or long flexible particles, such as fibre suspensions, are viscoelastic. An everyday example of purely viscous and viscoelastic behaviour can be seen with different types of soup. When a thin , watery soup is stirred in a bowl and the stirring then stopped, the soup continues to flow round the bowl and gradually comes to rest. This is an example of purely viscous behaviour. In contrast, with certain thick soups, on cessation of stirring the soup rapidly slows down and then recoils slightly. 

Values of kj a for viscoelastic liquids in aerated stirred tanks are substantially smaller than those in inelastic liquids. Moreover, less breakage of gas bubbles in the vicinity ofthe impeller occurs in viscoelastic liquids. The following dimensionless equation [8] (a modified form of Equation 7.37) can be used to correlate kj a in sparged stirred tanks for non-Newtonian (including viscoelastic) liquids ... 

Estimate the liquid-phase volumetric coefficient of oxygen transfer for a stirred-tank fermentor with a diameter of 1.8 m, containing a viscous non-Newtonian broth, with consistency index K = 0.39, flow behavior index n = 0.74,... 

When we pour a solution, or stir it or shake it, we are applying a stress to the solution and are deforming it. For a Newtonian fluid, this deformation is irreversible. If we pour some olive oil from a bottle into a frying pan, the liquid flows across the bottom of the pan, assuming a new shape. On the other hand, if we stretch a rubber band and then release it, the rubber band returns to its original shape. This deformation is completely reversible, and is called elastic. These two types of deformation, reversible (elastic) and irre- /... 

Newtonian. Viscosity is independent of shear rate. Pure liquids usually show this type of behavior. No matter how fast water is stirred, the viscosity stays the same. 

There are a number of research studies, which have dealt with heat transfer in stirred tanks with non-Newtonian fluids. These were exclusively pseudoplastic liquids, whose viscosity obeys the power law (aqueous CMC, PAA and Carbopol solutions). 

In biotechnology bubble columns equipped with stirrers are currently almost exclusively used, because classic bubble columns cannot realize the necessary mass and heat transfer due to the increasing viscosity of the fermentation medium. Stirred tanks with H/D > 3 with several stirring devices arranged above one another on the same shaft are used, in which the heat transfer proceeds in an increasingly viscous, non-Newtonian, gassed liquid. 

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