Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.

The non-linear field theories of mechanics

Slip occurs in the flow of two-phase systems because of the displacement of the disperse phase away from solid boundaries. This arises from steric, hydrodynamic, viscoelastic and chemical forces and constraints acting on the disperse phase immediately adjacent to the walls. The enrichment of the boundary near the wall with the continuous (and usually low-viscosity) phase means that any flow of the fluid over the boundary is easier because of the lubrication effect. Because this effect is usually confined to a very narrow layer — with typical thickness of 0.1–10 μm—it so resembles the slip of solids over surfaces that it has historically been given the same terminology. The restoring force for all the forces that cause an increase in concentration is usually osmotic, and this will always limit the effective slip. In dilute systems, concentration gradients can be present over relatively large distances out from walls, giving what might be interpreted on an overall basis as a thick solvent-only layer. However, as the concentration of the system increases, the layer gets thinner and thinner because it is more difficult to create with the large reverse osmotic force present. However, the enormous increase in the bulk viscosity with increase in concentration means that although thinner, the layer becomes, paradoxically, even more important. Slip manifests itself in such a way that viscosity measured in different size geometries gives different answers if calculated the normal way — in particular the apparent viscosity decreases with decrease in geometry size (e.g. tube radius). Also, in single flow curves unexpected lower Newtonian plateaus are sometimes seen, with an apparent yield stress at even lower stresses. Sudden breaks in the flow curve can also be seen. Large particles as the disperse phase (remember flocs are large particles), with a large dependence of viscosity on the concentration of the dispersed phase are the circumstances which can give slip, especially if coupled with smooth walls and small flow dimensions. The effect is usually greatest at low speeds/flow rates. When the viscometer walls and particles carry like electrostatic charges and the continuous phase is electrically conducted, slip can be assumed. In many cases we need to characterise the slip effects seen in viscometers because they will also be seen in flow in smooth pipes and condults in manufacturing plants. This is usually done by relating the wall shear stress to a slip velocity using a power-law relationship. When the bulk flow has also been characterized, the flow in real situations can be calculated. To characterise slip, it is necessary to change the size of the geometry, and the results extrapolated to very large size to extract unambigouos bulk-flow and slip data respectively. A number of mathematical manipulations are necessary to retrieve these data. We can make attempts to eliminate slip by altering the physical or chemical character of the walls. This is usually done physically by roughening or profiling, but in the extreme, a vane can be used. This latter geometry has the advantage of being easy to make and clean. In either case—by extrapolation or elimination—we end up with the bulk flow properties. This is important in situations where we are trying to understand the microstructure/flow interactions.

A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscometers: its cause, character, and cure

Determination of the density and the viscosities of biodiesel–diesel fuel blends

Simple ionic liquids have long been held to be designer solvents, based upon the ability to independently vary their cations and anions. The formation of mixtures of ionic liquids increases this synthetic flexibility. We review the available literature of these ionic liquid mixtures to identify how their properties change and the possibility for their application.

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Mixtures of ionic liquids.

Basic properties of palm oil biodiesel–diesel blends

ARRHENIUS1 proposed the following expression for the viscosity of a solution : where ηs is the viscosity of the solution ; N1 and η1 are the mole fraction and the viscosity of component 1 ; N2 and η2 the mole fraction and the viscosity of component 2. However, both positive and negative deviations from this equation are found to occur. From a comparison of vapour pressures and viscosities of solutions, we deduced that in many cases the following equation yields closer agreement with experimental results : where d is a characteristic constant of the system. The accompanying graph shows curves calculated according to equations 1 and 2 (with d = -0·0224) for the system trans-decalin—cis-decalin. The points on the graph represent the experimental results of Bird and Daly2.

Mixture Law for Viscosity

UNDER the above heading, we presented a note in Nature1 in which we directed attention to certain peculiar phenomena observed with concentrated solutions of rubber or of aluminium soaps in hydrocarbons and gave an explanation. These phenomena concerned secondary flows, high inlet losses for flow in pipes, existence of retardation layers with flow in small-diameter pipes and an increase in the surface energies of these systems when they are strained. It was noticed that the free energy of these systems increased on straining. Due to absence of experimental data, this increase in free energy was ascribed to a decrease in entropy, in analogy with the kinetic theory of rubber elasticity.

Rheological Properties of High-Viscosity Solutions of Long Molecules

ICE, paper and regenerated cellulose, Nylon (unstretched and lightly stretched), and to a certain extent natural cellulose, lignin and wool are typical examples of hydrogen-bond dominated solids (whose mechanical properties are mostly controlled by the density and characteristics of the hydrogen bond). Previously1 I have shown that for these materials, Young's modulus E is related to N, the effective number of H bonds per cm3 responding to unidirectional stress, by E = kN1/3. For cellulosics k is ∼ 8 × 102 when E is in Pa. Two major rheological characteristics of hydrogen-bond dominated solids are their ready softening by water and their relaxation of stress with time under constant strain. Thus, EW/E0, the ratio of the modulus at w g H2O/g solid to the modulus at w= 0, drops to very small values for paper at saturation. Similarly, Et/E0, the modulus at time t to E at t = 0 in a stress relaxation experiment, drops to small ratios at high values of t. I postulate that both types of loss in E arise from reductions in N, through H-bond dissociation. I find this dissociation can be in one of three modes: I, II and III.

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Three modes of dissociation of H bonds in hydrogen-bond dominated solids

THE viscosity of a liquid can usually be represented by η = A.eEvisc./RT, where η is the viscosity; A is a constant; Evisc is the energy of viscosity; R is the gas constant; T is the absolute temperature. In connexion with other work, it was deduced that the energy of viscosity should equal the work of cohesion for unassociated and non-metallic liquids. The work of cohesion has been defined by Harkins1 as the energy required to form a surface in a liquid and is equal to twice the surface energy. Now if both the energy of viscosity and the work of cohesion are expressed as calories per mole, they are nearly equal for unassociated liquids.

Energy of Viscosity as a Measure of the Cohesion of Liquids

As a result of a detailed consideration of the mechanism of viscosity of liquids, Fig. 1 was obtained. It is a graph of the logarithm of viscosity of the n-paraffin hydrocarbons from n-butane to n-octa-decane (represented by the figures opposite the respective points), against the function TB/T, or the absolute boiling temperature/absolute temperature of measurement.

Alfred H. Nissan

Papers

Mixture Law for Viscosity

Rheological Properties of High-Viscosity Solutions of Long Molecules

Three modes of dissociation of H bonds in hydrogen-bond dominated solids

Energy of Viscosity as a Measure of the Cohesion of Liquids

Viscosity of Liquids