Newtonian behavior, emulsions

The viscosity of a fluid arises from the internal friction of the fluid, and it manifests itself externally as the resistance of the fluid to flow. With respect to viscosity there are two broad classes of fluids Newtonian and non-Newtonian. Newtonian fluids have a constant viscosity regardless of strain rate. Low-molecular-weight pure liquids are examples of Newtonian fluids. Non-Newtonian fluids do not have a constant viscosity and will either thicken or thin when strain is applied. Polymers, colloidal suspensions, and emulsions are examples of non-Newtonian fluids [1]. To date, researchers have treated ionic liquids as Newtonian fluids, and no data indicating that there are non-Newtonian ionic liquids have so far been published. However, no research effort has yet been specifically directed towards investigation of potential non-Newtonian behavior in these systems. 

The typical viscous behavior for many non-Newtonian fluids (e.g., polymeric fluids, flocculated suspensions, colloids, foams, gels) is illustrated by the curves labeled structural in Figs. 3-5 and 3-6. These fluids exhibit Newtonian behavior at very low and very high shear rates, with shear thinning or pseudoplastic behavior at intermediate shear rates. In some materials this can be attributed to a reversible structure or network that forms in the rest or equilibrium state. When the material is sheared, the structure breaks down, resulting in a shear-dependent (shear thinning) behavior. Some real examples of this type of behavior are shown in Fig. 3-7. These show that structural viscosity behavior is exhibited by fluids as diverse as polymer solutions, blood, latex emulsions, and mud (sediment). Equations (i.e., models) that represent this type of behavior are described below. 

Viscosity is an important physical property of emulsions in terms of emulsion formation and stability (1, 4). Lissant (1 ) has described several stages of geometrical droplet rearrangement and viscosity changes as emulsions form. As the amount of internal phase introduced into an emulsion system increases, the more closely crowded the droplets become. This crowding of droplets reduces their motion and tendency to settle while imparting a "creamed" appearance to the system. The apparent viscosity continues to increase, and non-Newtonian behavior becomes more marked. Emulsions of high internal-phase ratio are actually in a "super-creamed" state. 

This unit describes a method for measuring the viscosity (r ) of Newtonian fluids. For a Newtonian fluid, viscosity is a constant at a given temperature and pressure, as defined in unit hi. i common liquids under ordinary circumstances behave in this way. Examples include pure fluids and solutions. Liquids which have suspended matter of sufficient size and concentration may deviate from Newtonian behavior. Examples of liquids exhibiting non-Newtonian behavior (unit hi. i) include polymer suspensions, emulsions, and fruit juices. Glass capillary viscometers are useful for the measurement of fluids, with the appropriate choice of capillary dimensions, for Newtonian fluids of viscosity up to 10 Pascals (Newtons m/sec 2) or 100 Poise (dynes cm/sec 2). Traditionally, these viscometers have been used in the oil industry. However, they have been adapted for use in the food industry and are commonly used for molecular weight prediction of food polymers in very dilute solutions (Daubert and Foegeding, 1998). There are three common types of capillary viscometers including Ubelohde, Ostwald, and Cannon-Fenske. These viscometers are often referred to as U-tube viscometers because they resemble the letter U (see Fig. HI.3.1). 

Let us first consider an inverted W/O emulsion made of 10% of 0.1 M NaCl large droplets dispersed in sorbitan monooleate (Span 80), a liquid surfactant which also acts as the dispersing continuous phase. At this low droplet volume fraction, the rheological properties of the premixed emulsion is essentially determined by the continuous medium. The rheological behavior of the oil phase can be described as follows it exhibits a Newtonian behavior with a viscosity of 1 Pa s up to 1000 s 1 and a pronounced shear thinning behavior above this threshold value. Between 1000 s 1 and 3000 s1, although the stress is approximately unchanged, the viscosity ratio is increased by a factor of 4. 

Foods can be classified in different manners, including as solids, gels, homogeneous liquids, suspensions of solids in liquids, and emulsions. Fluid foods are those that do not retain their shape but take the shape of their container. Fluid foods that contain significant amounts of dissolved high molecular weight compounds (polymers) and/or suspended solids exhibit non-Newtonian behavior. Many non-Newtonian foods also exhibit both viscous and elastic properties, that is, they exhibit viscoelastic behavior. 

Rheology. Bulk Viscosity Properties. The rheological properties of an emulsion are very important. High viscosity may be the reason that an emulsion is troublesome, a resistance to flow that must be dealt with, or a desirable property for which an emulsion is formulated. The simplest description applies to Newtonian behavior in laminar flow. The viscosity, r], is given in terms of the shear stress, t, and shear rate, 7, by ... 

Shear rate influences the viscosity of emulsions quite significantly when their behavior is non-Newtonian. As discussed earlier, in the low range, emulsions exhibit a Newtonian behavior, and consequently shear rate does... 

The non-Newtonian nature of emulsion-solids mixtures depends on the nature of the pure emulsions. Addition of solids to a highly shear-thinning emulsion also results in a shearthinning mixture. However, addition of solids to a fairly Newtonian bitumen emulsion results in a more complex mixture that can exhibit different non-Newtonian behaviors at different shear stress or shear rate. 

Emulsion Quality. The quality of an emulsion is defined as the volume fraction (or percent) of the dispersed phase in the emulsion. The quality of emulsions strongly affects their rheology. Several studies have been reported for the relationship of isothermal shear stress to shear rate for emulsions of different qualities. OAV emulsions having qualities less than 0.5 (or 50%) exhibit Newtonian behavior, and those having higher qualities exhibit non-Newtonian behavior (9, 16, 25),... 

Figure 5. Cartesian plot of Newtonian and non-Newtonian behavior of flow of OfW macroemulsions through porous media, (t is emulsion quality.) (Reproduced with permission from reference 25. Copyright 1979 Society of Petroleum...

Figure 9 from Uzoigwe and Marsden (26) shows a plot of apparent viscosity versus emulsion quality. This graph shows that apparent viscosities increase sharply with quality particularly at low shear rates. It also shows the Newtonian behavior at low qualities and non-Newtonian behavior at high qualities. 

When using stable, dilute Newtonian emulsions through porous media, the flowing permeability, fcf, must be used in Darcy s law to describe its behavior instead of the initial or conventional permeability. When plugging due to the flow of Newtonian macroemulsions occurs, only the permeability of the porous medium should be adjusted. Emulsion rheology with respect to Newtonian and non-Newtonian behavior will be reviewed under the section Mathematical Models of Emulsion Flow in Porous Media . 

As discussed earlier, the rheology of emulsions depends on a number of factors, primary among which is the quality. Emulsions with qualities of less than 50% (oil) are considered Newtonian, whereas those having higher qualities exhibit non-Newtonian behavior. 

Emulsion Pipeline Operations. Prediction of pipeline pressure gradients is required for operation of any pipeline system. Pressure gradients for a transport emulsion flowing in commercial-size pipelines may be estimated via standard techniques because chemically stabilized emulsions exhibit rheological behavior that is nearly Newtonian. The emulsion viscosity must be known to implement these methods. The best way to determine emulsion viscosity for an application is to prepare an emulsion batch conforming to planned specifications and directly measure the pipe viscosity in a pipe loop of at least 1-in. inside diameter. Care must be taken to use the same brine composition, surfactant concentration, droplet size distribution, brine-crude-oil ratio, and temperature as are expected in the field application. In practice, a pilot-plant run may not be feasible, or there may be some disparity between pipe-loop test conditions and anticipated commercial pipeline conditions. In these cases, adjustments may be applied to the best available viscosity data using adjustment factors described later to compensate for disparities in operating parameters between the measurement conditions and the pipeline conditions. 

Most common fluids of simple structure are Newtonian (i.e., water, air, glycerine, oils, etc.). However, fluids with complex structures (i.e., high polymer melts or solutions, suspensions, emulsions, foams, etc.) are generally non-Newtonian. Examples of non-Newtonian behavior include mud, paint, ink, mayonnaise, shaving cream, polymer melts and solutions, toothpaste, etc. Many two-phase systems (e.g., suspensions, emulsions, foams, etc.) are purely viscous fluids and do not exhibit significant elastic or memory properties. However, many high polymer fluids (e.g., melts and solutions) are viscoelastic and exhibit both elastic (memory) as well as nonlinear viscous (flow) properties. A classification of material behavior is summarized in Table 5.1 (in which the subscripts have been omitted for simplicity). Only purely viscous Newtonian and non-Newtonian fluids are considered here. The properties and flow behavior of viscoelastic fluids are the subject of numerous books and papers (e.g., Darby, 1976 Bird et al., 1987). 

Industrial emulsions are usually prepared as concentrated systems, containing ( ) < 0.94. Owing to interface interactions and deformabil-ity of droplets, these systems behave rather like elastic, soft solids without any sign of Newtonian behavior. Between the highly concentrated and dilute regions, there is a wide zone of structural change reflected in a spectrum of non-Newtonian behavior. 

Experimental data Experimentally, there are three concentration regions of emulsion flow (i) dilute for (() < 0.3, characterized by nearly Newtonian behavior semi-concentrated at 0.3 < (() < with mainly pseudoplastic character and concentrated at ( ) < (()< 1.0, showing solid-like properties with modulus and yield. 

Emulsion viscosity is set to be proportional to its external phase viscosity, and this assumption is obviously correct at low internal phase content, say up to 20-30% and often at higher content as long as Newtonian behavior is exhibited. The second most important factor related to emulsion viscosity is the internal phase content, i.e., the volumetric proportion of the drops. As increasing numbers of drops crowd the emulsion external phase, the interdrop interactions produce increased friction that results in esca-... 

Bimodal emulsions are special type of highly polydispersed emulsions whose viscosity is much lower than expected from their internal phase content. In Fig. 6 a bimodal emulsion prepared with a 70% oil content (line with white circle data points labeled 70% BM) exhibits Newtonian behavior (n = 1) and a much lower viseosity than its monomodal counterpart, a feature that will be used in a later discussion. 

Liu et al. [88] have used Pickering emulsion polymerization to synthesize silica nanoparticle-armored PANI nanoparticles (PANI SiO ) (see Figure 14.11). The obtained core-shell PANIigSiO nanoparticles are polydisperse with an average diameter of near 200 nm. Shear viscosity and flow curves of this novel particle-based ER fluid exhibit Newtonian behavior in the absence of electric field, while these show substantial enhancement as a function of electric filed strength in the presence of external electric field, indicating more obvious ER effect. 

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