Newtonian liquids, liquid-solid hydrodynamics

The presence of a gas in the suspension results in an increase of the stirrer speed required to establish the state of complete suspension. The propeller usually requires a higher speed than the turbine. Furthermore, a critical volume gas flow exists above which drastic sedimentation of particles occurs. Hence, homogenisation of the suspension requires an increase of the rotational speed and/or a decrease of the gas flow rate. The hydrodynamics of suspensions with a solid fraction exceeding 0.25-0.3 becomes very complex because such suspensions behave like non-Newtonian liquids. This produces problems in the scale-up of operations. Hydrodynamics, gas hold-up, mass-transfer coefficients, etc. have been widely studied and many correlations can be found in literature (see e.g. Shah, 1991). 

The Newtonian viscosity of a liquid is modified, and may become non-Newtonian, if it contains colloidal particles. This results from the complex interplay of interactions including hydrodynamic interactions between the liquid and solid particles, attractive or repulsive forces between the particles, and, in concentrated systems, direct particle-particle contact. 

Miflti-phase mixtures may be transported horizontally, vertically, or at an inclination to the horizontal in pipes and, in the case of liquid-solid mixtures, in open channels. Although there is some degree of similarity between the hydrodynamic behaviour of the various types of multi-phase flows, the range of physical properties is so wide that each system must be considered separately even when the hquids are Newtonian. Liquids may have densities up to three orders of magnitude greater than gases, but they are virtually incompressible. 

Dispersion of a solid or liquid in a liquid affects the viscosity. In many cases Newtonian flow behavior is transformed into non-Newtonian flow behavior. Shear thinning results from the ability of the solid particles or liquid droplets to come together to form network structures when at rest or under low shear. With increasing shear the interlinked structure gradually breaks down, and the resistance to flow decreases. The viscosity of a dispersed system depends on hydrodynamic interactions between particles or droplets and the liquid, particle-particle interactions (bumping), and interparticle attractions that promote the formation of aggregates, floes, and networks. 

Some concerns direcfly related to atomizer operation include inadequate mixing of liquid and gas, incomplete droplet evaporation, hydrodynamic iastabiUty, formation of nonuniform sprays, uneven deposition of liquid particles on solid surfaces, and drifting of small droplets. Other possible problems include difficulty in achieving ignition, poor combustion efficiency, and incorrect rates of evaporation, chemical reaction, solidification, or deposition. Atomizers must also provide the desired spray angle and pattern, penetration, concentration, and particle size distribution. In certain appHcations, they must handle high viscosity or non-Newtonian fluids, or provide extremely fine sprays for rapid cooling. 

Obviously, at very high contact pressures, the lubricating liquid between the two surfaces rapidly increases in viscosity until it must attain the consistency of a solid or wax rather than a liquid. In such a case, it is easy to see why some lubricating oils that exhibit such thickening behavior show better performance than would be predicted for classic hydrodynamic theories. It also helps explain why other materials (e.g., sihcone oils), which have less dramatic viscosity increases with pressure, do not perform as well under extreme conditions. In the viscosity range where elastohydrodynamic lubrication occurs, fluids may begin to exhibit non-Newtonian behavior leading to a more complicated relationship in terms of lubricant effectiveness. 

Thin films of polymers are formed by dropping a small amount of a solution of a polymer onto the carrier electrode, and then spinning it at several thousands r.p.m. As in the case of A1 or A2, the redox-active compound is added to the polymer solution or diffused afterwards from a solution. During centrifugal spinning the evaporation of the solution leads to an increase of the concentration of the polymer causing an increased viscosity and the formation of a solid film. Only in the case of Newtonian fluids does the solution of the hydrodynamic equations lead asymptotically to a uniform layer thickness that is independent of the liquid profile at the start of the rotation The thickness of the films depends on the rotation speed, the evaporation rate and the initial viscosity... 

Consider a molecular liquid with Newtonian behaviour (see Chapter 4) such as water, benzene, alcohol, decane, etc. The addition of a spherical particle to the liquid will increase its viscosity due to the additional energy dissipation related to the hydrodynamic interaction between the liquid and the sphere. Further addition of spherical particles increases the viscosity of the suspension linearly. Einstein developed the relationship between the viscosity of a dilute suspension and the volume fraction of solid spherical particles as follows (Einstein, 1906) ... 

Einstein s analysis was based on the assumption that the particles are far enough apart so that they do not influence each other. Once the volume fraction of solids reaches about 10%, the average separation distance between particles is about equal to their diameter. This is when the hydrodynamic disturbance of the liquid by one sphere begins to influence other spheres. In this semi-dilute concentration regime (about 7-15 vol% solids), the hydrodynamic interactions between spheres results in positive deviation for Einstein s relationship. Batchelor (1977) extended the analysis to include higher order terms in volume fraction and found that the suspension viscosities are still Newtonian but increase with volume fraction according to ... 

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