Bingham liquids

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. 

Figure 6.5. Friction factors in laminar and turbulent flows of power-law and Bingham liquids, (a) For pseudoplastic liquids represented by tw = K [WID) , with K and n constant or dependent on r l/V/ = [4.0/(n )0 75] log10[Re /( "2)] — 0.40/(k )1 2j, [Dodge and Metzner, AIChE J. 5, 159 (7959)]. (b) For Bingham plastics, ReB = DVp/pB, He = 10D2plp% [Hanks and Dadia, AIChE J. 17, 554 (J971)].

Binders for agglomeration, 354,355 Bingham liquids, 104, 105, 107-109,711 Biochemical glossary, 657 Blasius equation, faction factor, 69 Blenders, in fine, 300-302 sketches, 302 power, 300... 

Figure 6.5. Friction factors in laminar and turbulent flows of power-law and Bingham liquids, (a) For pseudoplastic liquids represented by = K (WID f, with K and n constant or dependent on 1/Vf= -0.40/(n ) [Dodge and Metzner,...

Needless to say, the Bingham liquid is also non-Newtonian. This may be shown by calcvilating the "apparent viscosity" n, defined as the ratio between shear stress and rate of shear. 

Liquids which display plastic flow are called Bingham liquids. Patton TC (1964) Paint flow and pigment dispersion. Interscience Pubhshers Inc., New York. 

Bingham Liquid n Liquid exhibiting plastic flow. See Plastic Flow. 

Adsorption on Kaolinite. For kaolinite, the polymer adsorption density is strongly dependent on the solid/liquid ratio, S/L, of the clay suspension. As S/L increases, adsorption decreases. This S/L dependence cannot be due totally to autocoagulation of the clay particles since this dependence is observed even in the absence of Ca2+ at pH 7 and at low ionic strength where auto-coagulation as measured by the Bingham yield stress is relatively weak (21). Furthermore, complete dispersion of the particles in solvent by ultra-sonication before addition of... 

A vertical belt is moving upward continuously through a liquid bath, at a velocity V. A film of the liquid adheres to the belt, which tends to drain downward due to gravity. The equilibrium thickness of the film is determined by the steady-state condition at which the downward drainage velocity of the surface of the film is exactly equal to the upward velocity of the belt. Derive an equation for the film thickness if the fluid is (a) Newtonian (b) a Bingham plastic. 

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. 

So far we have restricted our discussion to Newtonian liquids, but the analysis will change somewhat if the systems are non-Newtonian. A useful illustration of the problems that arise is the case of a Bingham plastic. This gives us a linear response, as does a Newtonian liquid, but in this case there is an intercept or yield stress. The constitutive equation for a Bingham plastic is... 

The branch of science related to the study of deformation and flow of materials was given the name rheology by Bingham, whom some call the father of modern rheology. The prefix rheo is derived from the Greek rheos, meaning current of flow. The study of rheology includes two vastly different branches of mechanics—fluid and solid. The polymer scientist is usually concerned with viscoelastic materials that act as both solids and liquids. 

Transitional Flow. Reynolds numbers and friction factors at which the flow changes from laminar to turbulent are indicated by the breaks in the plots of Figures 6.4(a) and (b). For Bingham models, data are shown directly on Figure 6.6. For power-law liquids an equation for the critical Reynolds number is due to Mishra and Triparthi [Trans. IChE 51, T141 (1973)],... 

Feed rheology (liquid) Newtonjan/pseudoplastic/dilatant/Bingham plastic/thixotropic/rheopectic/viscoelastic... 

One simple rheological model that is often used to describe the behavior of foams is thai of a Bingham plastic. This applies for hows over length scales sufficient ly large that the foam can be reasonably considered as a continuous medium. The Bingham plastic model combines the properties of a yield stress like that of a solid with the viscous flow of a liquid. 

The melt flow under isothermal conditions, when it is described by the rheological equation for the Newtonian or power law liquid, has been studied in detail63 66). The flow of the non-Newtonian liquid in the channels of non-round cross section for the liquid obeying the Sutterby equation have also been studied 67). In particular, the flow in the channels of rectangular and trigonal cross section was studied. In the analysis of the non-isothermal flow, attention should be paid to the analysis 68) of pseudo-plastic Bingham media. 

The Bingham Fluid. The Bingham fluid is an empirical model that represents the rheological behavior of materials that exhibit a no flow region below certain yield stresses, tv, such as polymer emulsions and slurries. Since the material flows like a Newtonian liquid above the yield stress, the Bingham model can be represented by... 

Non-Newtonian Flow For isothermal laminar flow of time-independent non-Newtonian liquids, integration of the Cauchy momentum equations yields the fully developed velocity profile and flow rate-pressure drop relations. For the Bingham plastic fluid described by Eq. (6-3), in a pipe of diameter D and a pressure drop per unit length AP/L, the flow rate is given by... 

If a sample shows elastic, solid-like deformation below a certain shear stress ay and starts flowing above this value, ay is called a yield stress value. This phenomenon can occur even in solutions with quite low viscosity. A practical indication for the existence of a yield stress value is the trapping of bubbles in the liquid Small air bubbles that are shaken into the sample do not rise for a long time whereas they climb up to the surface sooner or later in a liquid without yield stress even if their viscosity is much higher. A simple model for the description of a liquid with a yield stress is called Bingham s solid ... 

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... 

Toothpaste is a material that has to be solid at rest and liquid when sheared. We will assume that it behaves as a Bingham fluid, and is described by two parameters ... 

In concentrated suspensions, the particles touch each other. If there is also an attraction between the particles, the suspension may not flow when the shear stress is small it is a solid (Figure C4-14). The stress at which the liquid starts moving is known as the yield stress. Once the liquid yields, it often behaves like a Newtonian liquid with a constant differential viscosity. The behaviour of such Bingham fluids is similar to that of shear thinning fluids ... 

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