Elements of Polymer Science
E. Desmond Goddard, James V. Gruber in Principles of Polymer Science and Technology in Cosmetics and Personal Care, 1999
Therefore, a liquid is said to exhibit Newtonian flow, if η is independent of Substances that show deviations from this flow pattern are termed non-Newtonian. There are two broad classes of non-Newtonian fluids: Fluids with shear stresses that at any point depend on the shear rates only, and are independent of time. These include Bingham plastics, or materials that require a minimum amount of stress (yield stress) before deformation, pseudo-plastics or shear-thinning fluids, which exhibit a decrease of shear stress with shear rate, and dilatants, or shear-thickening fluids, for which the stress increases with the shear rate.Fluids in which the ratio of shear stress to shear rate depends on time. They fall into two categories: thixotropic fluids, in which the microstructure of the fluid progressively breaks down and the viscosity decreases, and rheopectic fluids, where the applied shear promotes gradual formation of structure, and the viscosity increases with shear.
Rheological Aspects of Capsule Shell Excipients and the Manufacture of Encapsulated Formulations
Larry L. Augsburger, Stephen W. Hoag in Pharmaceutical Dosage Forms, 2017
where η is the Newtonian viscosity (mPa·s), σ is the shear stress (Pa), and is the rate of shear (s−1). Newtonian fluids obey Equation 14.1; that is, there is a direct, time-independent, constant proportionality between σ and , so that η is the same irrespective of σ or . Macromolecular solutions, however, seldom exhibit true Newtonian behavior unless solution concentrations are very low. While non-Newtonian fluid rheology encompasses shear-thinning, shear-thickening, or plastic behavior, sometimes accompanied by time dependency (i.e., thixotropy or rheopexy) [5], most polymeric or macromolecular solutions exhibit shear-thinning behavior when sheared.
Friction, Lubrication, Wear and Corrosion
Manoj Ramachandran, Tom Nunn in Basic Orthopaedic Sciences, 2018
where shear stress is the force per unit area required to produce shearing action (measured in dynes/cm2), shear rate is a measure of the change in speed at which the intermediate layers of fluid move with respect to each other (measured in reciprocal seconds – s−1) and viscosity is measured in poise, such that a material requiring a shear stress of 1 dyne/cm2 to produce a shear rate of s−1 has a viscosity of 1 poise. Newton’s law of viscosity states that this ratio is a constant and so fluids that adhere to this law are called Newtonian. Non-Newtonian fluids do not follow this law, and therefore their viscosity is not constant and changes as the shear rate changes.
Compressive stress relaxation behavior of articular cartilage and its effects on fluid pressure and solid displacement due to non-Newtonian flow
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2021
Different models are used to explain non-Newtonian fluids: Viscoelastic fluid, Herschel-Bulkley, Ellis fluid, power-law, Bingham fluid, etc (Bird et al. 1960; Pascal 1984; Mazumdar 1992; Sochi 2009). Darcy’s law needs to be modified for these non-Newtonian models. For example, the relation between pressure gradient and velocity is no longer linear for power-law fluid. A modified Darcy’s law has been developed for power-law fluid flow through packed porous media by Christopher and Middleman (Christopher and Middleman 1965). They used experiments to test their mathematical model when the diluted polymer solution flows through the packed tube. Experimental results are then compared with a similar study with an Ellis fluid model by Sadowski (Sadowski 1965). A theoretical model was presented by Hayes et al. (1996) to examine the pressure drop and velocity for the flow of power-law fluid through a porous bed packed with spherical particles. They reviewed the work of different authors (Christopher and Middleman 1965; Sadowski 1965) on development and modification of intrinsic permeability and Darcy’s law for non-Newtonian fluids.
Fabrication and analysis of chitosan oligosaccharide based mucoadhesive patch for oromucosal drug delivery
Published in Drug Development and Industrial Pharmacy, 2022
Ashwini Kumar, Ram Kumar Sahu, Shibu Chameettachal, Falguni Pati, Awanish Kumar
Human saliva is a non-Newtonian fluid i.e. its viscosity changes with a change in shear stress. Non-Newtonian fluids are further classified as dilatant and pseudoplastic. Dilatant fluids show an increase in viscosity with an increase in stress while the relation between the viscosity and shear stress is inversely proportional in the case of pseudoplastic fluid. Therefore, human saliva is non-Newtonian pseudoplastic in nature [36]. The viscosity study of our in-house formulated artificial saliva (ASC and ASX with 0.1% CMC and XG respectively) revealed that ASC is showing dilatant behavior while ASX shows pseudoplastic behavior (Figure 3(a and b)). At this stage, we discontinued the ASC solution while we proceeded with ASX. Further, we analyzed the viscosity for ASX with 0.5% w/v XG and ASX with 0.075% w/v XG (Figure 3(c and d)). ASX with 0.075% XG revealed a viscosity pattern like that of human saliva as reported in other publications [37,38]. With the final simulated salivary formulation, the viscosity was measured to be around 4.3 mPa.s at a shear rate of 20/second while it was approximately 2.5 mPa.s at a shear rate of 40/second. At a shear rate of 100/second, the viscosity is recorded to be approximately 2 mPa.s.
Hemodynamic study in 3D printed stenotic coronary artery models: experimental validation and transient simulation
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2021
Violeta Carvalho, Nelson Rodrigues, Ricardo Ribeiro, Pedro F. Costa, José C. F. Teixeira, Rui A. Lima, Senhorinha F. C. F. Teixeira
Due to its impact on society, this disease has been extensively studied and several investigations can be found in the literature (Carvalho, Maia, et al. 2020). In recent years, most of the hemodynamic studies have used computational fluid dynamics (CFD) techniques to better understand atherosclerosis by considering blood as a single-phase Newtonian (J. Wu et al. 2015; Doutel et al. 2018; Kelidis and Konstantinidis 2018; Biglarian et al. 2020; Nagargoje and Gupta 2020) and non-Newtonian fluid (Liu et al. 2015; Mulani and Jagad 2015; Pinto and Campos 2016; Kamangar et al. 2017; Kabir et al. 2018). In fact, in large blood vessels, blood behaves as a homogeneous Newtonian fluid, due to the high shear rates, however, in the presence of lower shear rates, it behaves as a non-Newtonian fluid. These non-Newtonian properties of blood are mainly attributed to the behavior of red blood cells (RBCs), which at very low shear rates, tend to form aggregates and the apparent blood viscosity increases. In addition, cell orientation, deformation, and relative positioning of RBCs are also relevant factors to blood’s shear-thinning behavior (Formaggia et al. 2009; Rubenstein et al. 2015; Pinho et al. 2017). Indeed, when steady-state simulations are considered, the Newtonian assumption is a good approximation. However, the blood flow presents a pulsatile nature and there are periods of both low and high shear rates, thus the consideration of non-Newtonian models is important.
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