Liquids, deformations with applied force

For certain materials the deformation resulting from an applied force can be very large this indicates the material is a liquid. In such cases, we deal with rate of deformation, or shear rate dy/dt or y. This is the velocity difference per unit thickness of the liquid, y is expressed in units of s-1. 

Rheology is concerned with the flow and/or deformation of matter under the influence of externally imposed mechanical forces. Two limiting types of behaviour arc possible. The deformation may reverse spontaneously (relax) when the external force is removed this is called elastic behaviour and is exhibited by rigid solids. The energy used in causing the deformation is stored, and then recovered when the solid relaxes. At the other extreme, matter flows and the flow ceases (but is not reversed) when the force is removed this is called viscous behaviour and is characteristic of simple liquids. The energy needed to maintain the flow is dissipated as heat. Between the two extremes arc systems whose response to an applied force depends on the lime-scale involved. Thus pitch behaves as an elastic solid if struck but flows if left for years on a slope. Similarly, a ball of Funny Putty , a form of silicone rubber, bounces when dropped on a hard surface, when the contact time is a few milliseconds, but flows if deformed slowly on a time-scale of seconds or minutes. Systems of this kind are said to be visco-elastic. The precise nature of the observable phenomena depends on the ratio of the time it takes for the system to relax to the time taken to make an observation. This ratio is called the Deborah number (De) ... 

This brings in the need to study the behavior of pol5mieric liquid in simple flows and for simple systems, with the hope that the knowledge gained can be appropriately used in a complex flow pattern. The word rheology is defined as the science of deformation and flow. Rheology involves measurements in controlled flow, mainly the viscometric flow in which the velocity gradients are nearly uniform in space. In these simple flows, there is an applied force where the velocity (or the equivalent shear rate) is measured or vice versa. 

An elastic solid responds to stress like a spring. It responds instantly by stretching in proportion to the applied stress, and recovers completely when the stress is removed. A viscous liquid, on the other hand, responds like a dashpot or shock absorber. It deforms with a velocity that is proportional to the stress and does not recover when the force is removed. A viscoelastic material combines the two behaviors and can be modeled as a spring and dashpot in series or parallel as shown in Figure 9.9. Newtonian fluids have pure... 

A liquid possesses a definite volume at a given temperature and pressure, but no definite shape it takes up the shape of the containing vessel. This process may be accomplished very rapidly, as in the case of water under normal conditions, or it may take a considerably longer time, as with thick treacle. When a liquid undergoes a continuous deformation under the action of gravity or of an externally applied force, the process is called flow. As a flow process takes time to complete, the liquid must be offering some resistance to flow, which may be called, quite generally, a liquid friction. 

Consider a liquid contained between two parallel plates, each of area A cm2 (Figure 8-4). The plates are h cm apart and a force of P dynes is applied on the upper plate. This shearing stress causes it to move with respect to the lower plate with a velocity of v cm s-1. The shearing stress x acts throughout the liquid contained between the plates and can be defined as the shearing force P divided by the area A, or PI A dynes/cm2. The deformation can be expressed as the mean rate of shear y or velocity gradient and is equal to the velocity difference divided by the distance between the plates y = v/h, expressed in units of s-1. 

The adsorption isotherms in Table 5.2 can be applied to both fluid and solid interfaces. The surface tension isotherms in Table 5.2, which relate a and Fj, are usually apphed to fluid interfaces, although they could also be used for sohd-liquid interfaces if a is identified with the Gibbs superficial tension. (The latter is defined as the force per unit length that opposes every increase of the wet area without any deformation of the sohd.)... 

Although the derivation of the continuity equation by use of a fixed control volume is perfectly satisfactory, it is less obvious how to apply Newton s laws of mechanics in this framework. The familiar use of these principles from coursework in classical mechanics is that they are applied to describe the motion of a specific body subject to various forces or torques. To apply these same laws to a fluid (i.e., a liquid or a gas), we introduce the concepts of material points and a material volume (or material control volume) that we denote as Vm(t). Now a material point is a continuum point that moves with the local continuum velocity of the fluid. A material volume Vm (t), is a macroscopic control volume whose shape at some initial instant, / = 0, is arbitrary, that contains a fixed set of material points. Because the material volume contains a fixed set of such points, it must move with the local continuum velocity of the fluid at every point. Hence, as illustrated in Fig. 2-3, it must deform and change volume in such a way that the local flux of mass through all points on its surface is identically zero for all time (though, of course, there may still be exchange of molecules due to random molecular motion). Because mass is neither created nor destroyed according to the principle of mass conservation, the total mass contained... 

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