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Frequency Scans
Published in Kevin P. Menard, Noah R. Menard, Dynamic Mechanical Analysis, 2020
Kevin P. Menard, Noah R. Menard
where the λ is the timescale of the material’s response, while t is the timescale of the measurement process, which for DMA is the inverse of the frequency of measurement.14 Rosen15 points out that the quick estimate of λ is the relaxation time taken from a creep-recovery experiment as described in Chapter 3, Section 3.4, where the time required for the material to recover to 1/e of the initial stress is defined as the relaxation time. Determination of an exact relaxation time for a polymer can be tricky and it is not uncommon to plot E’ versus E” in a variation of the Cole–Cole or Wicket plot to see if the polymer can really be treated as having a single relaxation time.16 This is a necessity for understanding whether a time–temperature superposition is valid or not and is discussed in Section 8.8. The tr is the polymer’s relaxation time, often taken as 1/the crossover frequency in radians/second, while td is the deformation time. The Deborah number is used in calculations to predict polymer behavior. If: De << 1, the material is viscous,De >> 1, the material is elastic, andDe ≅ 1, the material will act viscoelastically.
Properties of Engineering Materials and Surfaces
Published in Q. Jane Wang, Dong Zhu, Interfacial Mechanics, 2019
where U is the average velocity of the two surfaces, a the half-width or radius of Hertzian contact zone and G∞ the elastic shear modulus of lubricant. The Deborah number can be recognized as the ratio of the relaxation time for a fluid (η/G) to the time of passage of the fluid through the contact zone (2a/U). For Deborah numbers much smaller than 1.0, the lubricant behaves as a viscous fluid, while for Deborah numbers much larger than 1.0, the elastic behavior becomes dominant. When modeling friction (or sometimes called traction) under typical high pressure–high shear rate EHL conditions both viscous and elastic behaviors need to be considered, and the following Maxwell model is so far commonly used:
Rheological Principles
Published in B. R. Gupta, Rheology Applied in Polymer Processing, 2023
As the name implies these fluids posses both purely elastic and purely viscous characteristics i.e. they store a part of the deformational energy and dissipate the remaining as heat due to viscous drag. Both these behaviours influence the polymer processing. Slow process takes long time to complete and the molecules get sufficient time to uncoil, disentangle, orient and relax as the viscous nature dominates. Whereas when the process is faster the time available for the molecules to respond is much less and the elastic response dominates. In case of flow process for example if the flow is slow then if the time scale for the flow is much less than the relaxation time of the material then the elastic effect are prevalent. Whereas on the other hand if the relaxation time is larger than the time scale, and the system is relaxed completely then the viscous effects are pronounced. The ratio of time scale of flow to the relaxation time is defined as the Deborah number. It is often used to characterize the fluidity of the materials under specific flow condition. It is based on the thinking that given enough time even the solids can flow. Reiner[3b] defined a dimensionless number namely Deborah number as a ratio of some characteristic time of the material, X, to the time scale of deformation, Xs of the material and is written as De= λc/λs. The characteristic time, λc, is the time needed for the material to acquire 63.2% i.e. [1 — (1/e)] of its ultimate retarded elastic response to a step change If De> 1 the elastic effects prevail and if De< 0.5 then the viscous effects dominate.
Numerical analysis of entropy generation in the stagnation point flow of Oldroyd-B nanofluid
Published in Waves in Random and Complex Media, 2022
Shahzad Munir, Asma Maqsood, Umer Farooq, Muzamil Hussain, Muhammad Israr Siddiqui, Taseer Muhammad
Figure 2(a) portrays the impact of dimensionless Deborah number on fluid motion . It is noted that the velocity field raises as increases. It is expected that for lower values of , the viscous force of fluid is greater than elastic forces. For higher values of dimensionless Deborah number, the fluid behaves like an elastically rigid substance. Deborah number is inversely proportional to Deborah number . Figure 2(b) indicates that the enhancement of dimensionless Deborah number related to retardation time the motion of fluid decelerates. Figure 2(c) demonstrates the impact of M on . It is noted that the motion of Oldroyd-B nanofluid increases significantly with magnetic parameter.
On spectral relaxation approach for Soret and Dufour effects on Sutterby fluid past a stretching sheet
Published in International Journal of Ambient Energy, 2022
G. B. Chandra Mouli, Kotha Gangadhar, B. Hema Sundar Raju
Figure 2 depicts that velocity distribution increases as power law index parameter m increases and therefore velocity distribution is more for dilatant fluids than that of Newtonian and pseudoplastic fluids. Figure 3 illustrates that in the case of pseudoplastic fluids, higher Reynolds number leads to decrease in viscous force and hence fluid flow decelerates. But for dilatant fluids, velocity profiles increase as Reynolds number increases. Deborah number De measures the fluidity characteristics of a fluid under the particular flow conditions. Figure 4 interprets that for shear thinning fluids, the fluid velocity decreases as Deborah number De increases whereas for shear thickening fluids, the velocity profiles raise for enhanced values of De. Figure 5 exhibits that temperature reduces gradually for shear thinning, Newtonian and shear thickening fluids. Higher Reynolds numbers Re and Deborah numbers De result in lesser boundary layer thickness for m < 0, as shown in Figures 6 and 7. Deborah number is defined as the ratio of the time it takes for a material to adjust to applied stresses or deformation. Temperature profiles decrease for increasing De and Re in the case of m > 0. For dilatant fluids, the rise in De and Re values leads to the increase in elastic and viscous forces, respectively, as a result enhances viscous boundary layer and reduces thermal boundary layer. Figure 8 reveals that fluid temperature raises as Dufour number Df rises. Enhancement in Prandtl number Pr reduces temperature and increases thermal boundary layer thickness, as displayed in Figure 9.
Hydromagnetic slip flow and heat transfer treatment of Maxwell fluid with hybrid nanostructure: low Prandtl numbers
Published in International Journal of Ambient Energy, 2023
Najrin Sultana, Sachin Shaw, Manoj K. Nayak, Sabyasachi Mondal
By introducing the magnetic field in the system, an additional resistance force acts in the system which known as the Lorentz force. In the presence of Lorentz force, the resistance for the system, mainly close to the surface of the rotational disc boosts up which restricted the velocity of the fluid. Due to this additional force, we have observed a reduction in the radial velocity away from the surface of the rotating disk (see Figure 2). An opposite phenomenon was observed close to the sure and it may due to the rotational motion (directly involve with radial velocity) of the disk. To follow the nature of the Lorentz force, a reduction took place for the axial velocity and tangential velocity of the fluid and further it leads to a reduction in the momentum boundary layer thickness, with increase in the values of the magnetic parameter (see Figures 5 and 8, respectively). Deborah number is denoted as a rheological characteristic of the fluidity of the materials. It is related with the viscoelastic nature of the fluid which helps the material to adjust to the applied stresses or deformation. With an increase in the Deborah number, the elastic nature of the fluid (here we have considered Maxwell fluid) increases which boosts up the axial velocity and tangential velocity (see Figures 6 and 9). It leads to an increase in the axial and tangential momentum boundary layer thickness. However, for the radial velocity , elastic nature acts in a reversed way with rotation of the disk and an opposite phenomenon observed (see Figure 3). The present problem deals with a slip condition at the surface which allows a minimum velocity at the surface of the disk. The increase in the slip parameter gives an additional velocity of the fluid at the surface which further boosts up the velocity at the surface as well as gives a width momentum boundary layer thickness. This phenomenon observed for both the axial velocity and tangential velocity (see Figures 7 and 10). For the same reason, an increment was observed in the radial momentum boundary layer thickness with an increase in slip parameter (see Figure 4).