Memory, fluids with

Thermotropic chiral LCs whose pitch vary strongly with temperature can be used as crude thermometers since the color of the material will change as the pitch is changed. LC color transitions are used on many aquarium and pool thermometers. Other LC materials change color when stretched or stressed. Thus, LC sheets are often used in industry to look for hot spots, map heat flow, measure stress distribution patterns, etc. The LC in fluid form is used to detect electrically generated hot spots for failure analysis in the semiconductor industry. LC memory units with extensive capacity were used in Space Shuttle navigation equipment. 

Extracellular antigens are detected by APCs, such as lymphocytes, macrophages, and dendritic cells in interstitial fluid and blood. These detect the hapten and engulf the whole antigenic complex. Then, when inside the APC, the complex is partly dismantled and peptides attached to proteins similar to immunoglobulins, known as MHC II. The modified peptide-hapten complex is moved to the surface of the APC and presented as a complex with MHC to T-helper cells (CD4+), which activates and instructs the APC to make antibodies to the hapten and also B cells (memory cells with "memory" of the hapten) to proliferate. These events lead to types I to III responses. 

Coleman,B D., Noll,W. Simple fluids with fading memory, pp. 530-552. In Proc. of the International Symposium on Second-Order Effects in Elasticity, Plasticity, and Fluid Dynamics, Haifa. New York Pergamon Press 1962. 

J.U. Kim, Global smooth solutions for the equations of motion of a nonlinear fluid with fading memory,, rch. Rat. Mech. Anal., 79 (1982) 97-130. 

The time-dependent growth of Nx after start-up of steady shearing for a polyethylene melt is shown in Fig. 1-10. Note that at steady state the first normal stress difference is larger than the shear stress at this particular shear rate. The normal stress differences usually are more shear-rate-dependent than the shear stress. In fact, if the isotropic liquid belongs to a fairly general class known as viscoelastic simple fluids with fading memory (Coleman and Noll 1961), then at low shear rates the normal stress differences depend quadratically... 

Many constitutive equations have been proposed in addition to those indicated above, which are special cases of fluids with memory. Most of these expressions arise from the generalization of linear viscoelasticity equations to nonlinear processes whenever they obey the material indifference principle. However, these generalizations are not unique, because there are many equations that reduce to the same linear equation. It should be noted that a determined choice among the possible generalizations may be suitable for certain types of fluids or special kinds of deformations. In any case, the use of relatively simple expressions is justified by the fact that they can predict, at least qualitatively, the behavior of complex fluids. 

Visco-elastic or memory fluids Fluids with elastic properties that allow them to spring back after the release of a shear force. Examples include egg-white and rubber cement. 

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). 

C. Fluid with a higher order memory in volume... 

B. Fluid with memory in volume has constitutive equations (2.7) and therefore by (2.12) we have... 

Summing the results for model B— fluid with memory to volume—we can see that thermodynamic responses U, S, F depend only on T, V and free energy F is a potential for entropy S but only for equilibrium pressure P°. Gibbs equations are... 

As a model, we use the uniform fluid with volume memory B (2.7) from Sects. 2.1,... 

In the last two centuries, a lot of attempts and discussion have been made on the elucidation and development of the various constitutive models of liquids. Some of the theoretical models that can be mentioned here are Boltzmann, Maxwell (UCM, LCM, COM, 1PM), Voight or Kelvin, Jeffrey, Reiner-Rivelin, Newton, Oldroyd, Giesekus, graded fluids, composite fluids, retarded fluids with a strong backbone and fading memory, and so on. Further and deeper knowledge related to the physical and mathematical consequences of the structural models of liquids and of the elasticity of liquids can be found in Ref. [6]. 

We now show that the elaborate formalism we have developed is a convenient starting point for approximations. The type of approximations one makes depends, of course, on the nature of the problem. In our case, which is a classical fluid with short-range forces, we want to rewrite G as a sum of pieces, one of which leads to the Boltzmann-Enskog memory function. We can do this by applying the identity... 

It is our purpose here to explain how the notions of Ericksen can be carried over to a viscoelastic model, namely the BKZ memory fluid, as was done by Bernstein and Zapas [2]. In fact, with a proper formulation of the principles involved, the analysis of Ericksen carries over in large part up to the onset of... 

Between the extremes of viscous fluids and elastic solids are materials that seem to exhibit both traits. These are called viscoelastic materials or memory fluids, and their dual nature becomes most evident when we subject them to time-dependent (unsteady) tests. The three major types of unsteady tests are the so-called relaxation, creep and dynamic tests. In the previous sections, we gave definitions and descriptions for stress, strain and deformation rates. These quantities are now used in defining the various unsteady tests. Thus, in a relaxation test the sample is subjected to a sudden, constant, strain. The stress shoots up in response and then gradually decays ( relaxes ). In the creep test, a sudden stress is applied and held constant. Now the strain picks up quickly and then, while continuing to increase, slows down on its rate of increase. We say the material creeps under the constant stress. In dynamic tests, one confining wall is made to move periodically with respect to another. One monitors both the strain and the stress as a function of time. 

Papaiiastasiou, T. C., Scriven, L. E. and Macoski, C. W., 1987. A finite element method for liquid with memory. J. Non-Newtonian Fluid Mech 22, 271-288. 

Actually, some fluids and solids have both elastic (solid) properties and viscous (fluid) properties. These are said to be viscoelastic and are most notably materials composed of high polymers. The complete description of the rheological properties of these materials may involve a function relating the stress and strain as well as derivatives or integrals of these with respect to time. Because the elastic properties of these materials (both fluids and solids) impart memory to the material (as described previously), which results in a tendency to recover to a preferred state upon the removal of the force (stress), they are often termed memory materials and exhibit time-dependent properties. 

The function iKt-t ) may be interpreted as a memory function having a form as shown in Figure 3.14. For an elastic solid, iff has the value unity at all times, while for a purely viscous liquid iff has the value unity at thfe current time but zero at all other times. Thus, a solid behaves as if it remembers the whole of its deformation history, while a purely viscous liquid responds only to its instantaneous deformation rate and is uninfluenced by its history. The viscoelastic fluid is intermediate, behaving as if it had a memory that fades exponentially with time. The purely elastic solid and the purely viscous fluid are just extreme cases of viscoelastic behaviour. 

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