Plastic fluid

Non-Newtonian fluids include those for which a finite stress 1,. is reqjiired before continuous deformation occurs these are c ailed yield-stress materials. The Bingbam plastic fluid is the simplest yield-stress material its rheogram has a constant slope [L, called the infinite shear viscosity. 

Various types of fluids, known as plastic fluids, may be encountered, which do not start to flow until a certain minimum shear stress is reached. The relationship between shear stress and the rate of shear strain may or may not take a linear form. 

For Newtonian fluids the dynamic viscosity is constant (Equation 2-57), for power-law fluids the dynamic viscosity varies with shear rate (Equation 2-58), and for Bingham plastic fluids flow occurs only after some minimum shear stress, called the yield stress, is imposed (Equation 2-59). 

Figure 4-185. Shear stress-shear rate diagram, (a) Newtonian fluid, (b) Bingham plastic fluid, (c) Power iaw fiuid. (d) Herschei-Buckiey fiuid.

Drilling and Well Completions Bingham plastic fluid dv... 

For a Bingham plastic fluid flow in a circular pipe and annular space, the effective viscosities are given as [61]. 

Figure 3.32. (a) Shear stress distribution in pipe (b) Velocity profile for Bingham plastic fluid in pipe... 

As in the case of Newtonian fluids, one of the most important practical problems involving non-Newtonian fluids is the calculation of the pressure drop for flow in pipelines. The flow is much more likely to be streamline, or laminar, because non-Newtonian fluids usually have very much higher apparent viscosities than most simple Newtonian fluids. Furthermore, the difference in behaviour is much greater for laminar flow where viscosity plays such an important role than for turbulent flow. Attention will initially be focused on laminar-flow, with particular reference to the flow of power-law and Bingham-plastic fluids. 

For the flow of a Bingham-plastic fluid, the cross-section may be considered in two parts, as shown in Figure 3.32 ... 

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. 

Bhi KNER. J. L. and Smith, J. M- Trans. Inst. Chem. Eng. 44 (1966) T224. Anchor-agitated systems Power input with Newtonian and pseudo-plastic fluids. 

Plastic fluids are Newtonian or pseudoplastic liquids that exhibit a yield value (Fig. 3a and b, curves C). At rest they behave like a solid due to their interparticle association. The external force has to overcome these attractive forces between the particles and disrupt the structure. Beyond this point, the material changes its behavior from that of a solid to that of a liquid. The viscosity can then either be a constant (ideal Bingham liquid) or a function of the shear rate. In the latter case, the viscosity can initially decrease and then become a constant (real Bingham liquid) or continuously decrease, as in the case of a pseudoplastic liquid (Casson liquid). Plastic flow is often observed in flocculated suspensions. 

Starting with the equations for r = fn(j>) that define the power law and Bingham plastic fluids, derive the equations for the viscosity functions for these models as a function of shear stress, i.e., rj = fn(r). 

Newtonian fluids can be correlated by this method that is, the same correlation applies to both Newtonian and non-Newtonian fluids when the Newtonian Reynolds number is replaced by either Eq. (7-40) for the power law fluid model or Eq. (7-41) for the Bingham plastic fluid model. As a first approximation, therefore, we may assume that the same result would apply to friction loss in valves and fittings as described by the 2-K or 3-K models [Eq. 7-38)]. 

Grenville, R. K., Blending of viscous and pseudo-plastic fluids , Ph.D. Thesis, Cranfield Institute of Technology, Cranfield (UK) (1992). 

For non-Newtonian liquids and suspensions, an apparent viscosity is determined using correlations which include power input and the Reynolds number. Scale-up comparisons based on heat generation data only were determined by comparison of results from RC1 experiments and from a 675-liter reactor [208]. In the experiments, a Bingham plastic fluid was used to determine the film heat transfer coefficient. This presents a worst case because of the low thermal conductivity of the Bingham plastic. Calculated inside film heat transfer coefficients determined in the RC1 tests were about 60% lower than the values determined in the pilot plant reactor, even though substantial effort was made to obtain both geometric and kinematic similarity in the pilot reactor. 

The sensitivity of expls is a characteristic of great importance and can be correlated with the rate of deton. Perfect crysts and other nearly perfect elastic materials are the most sensitive, while liquids or colloids (plastic, fluid or hard) resist initiation and also have tendency to damp out-the wave of deton. The sensitivities of endothermic and exothermic compds are different and this causes them... 

Bingham Plastic or Plastic Fluids. As shown in Fig. 2, this is the simplest of all non-Newtonian fluids in the sense that the relationship between shear stress and shear rate differs from that of a Newtonian fluid only by the fact that the linear relationship does not pass through the origin. Thus a finite shearing stress r is necessary to initiate move-... 

Equation (11) states that the conventional Fanning friction factor, which may be used through Eq. (10) to calculate pipe-line pressure drops, is a unique function of two dimensionless groups for Bingham-plastic fluids. Newtonian fluids represent that special case for which r , and hence the second dimensionless group, is equal to zero. 

Weltmann (W4) presented this relationship on a friction factor-Reynolds number diagram similar to Fig. 4 for Bingham-plastic fluids. Excellent agreement between predicted and measured results was found by Salt for two carboxymethylcellulose solutions Weltmann shows no data to support her somewhat more useful rearrangement but cites three literature references for this purpose. Review of these shows that none dealt explicitly with this method of approach, as claimed. 

Pigford (P5) has stated that the heat transfer coefficients of Bingham-plastic fluids in laminar flow will be greater than those of Newtonian fluids by a factor of approximately 1 + ( ). Furthermore, the heat... 

NBt Reynolds number, dimensionless, taken as DVp/n and DVp/t) for Newtonian and Bingham-plastic fluids respectively. The generalized Reynolds number Dn V2 n p/y is applicable to all except thixotropic and rheo-pectic fluids... 

Shear stress (F/A), lb.p/sq. ft. t refers to the shear stress at the wall of a round pipe (DAP/ 4L) and r< to the shear stress at the wall of a viscometer bob Yield value or yield stress of a Bingham-plastic fluid, lb.F/sq. ft. Indicator of an unspecified functional relationship... 

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 ... 

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