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Introduction to the Continuum Fluid
Published in Tasos C. Papanastasiou, Georgios C. Georgiou, Andreas N. Alexandrou, ViscousFluid Flow, 2021
Tasos C. Papanastasiou, Georgios C. Georgiou, Andreas N. Alexandrou
Generalized Newtonian fluids are viscous inelastic fluids that still follow Eq. (2.12), but the viscosity itself is a function of the rate of strain tensor D; more precisely, the viscosity is a function of the second invariant of D, η=η(IID). A fluid is said to be shear thinning if its viscosity is a decreasing function of IID; when the opposite is true, the fluid is said to be shear thickening. Bingham-plastic fluids are generalized Newtonian fluids that exhibit yield stress. The material flows only when the applied shear stress exceeds the finite yield stress. A Herschel-Bulkley fluid is a generalization of the Bingham fluid where, upon deformation, the viscosity is either shear thinning or shear thickening. The dependence of the shear stress on IID is illustrated in Fig. 2.1, for various non-Newtonian fluids.
Fundamental Concepts
Published in William S. Janna, Introduction to Fluid Mechanics, Sixth Edition, 2020
Chocolate mixtures, drilling muds, greases, paint, paper pulp, soap, toothpaste, and sewage sludge are examples of Bingham plastic fluids (see Figure 1.5). These fluids behave as solids until an initial yield stress τ0 is exceeded. Beyond τ0, Bingham plastics behave like Newtonian fluids. The descriptive equation is τ=τ0+μ0dVdy
Flows, Gradients, and Transport Properties
Published in Joel L. Plawsky, Transport Phenomena Fundamentals, 2020
A Bingham plastic is a Newtonian fluid that has a yield stress. Below the yield stress level, the fluid will not flow yet above it, it flows with constant viscosity. τ=−μoγ˙±τoBingham
Performance of environmentally friendly silica nanoparticles-enhanced drilling mud from sugarcane bagasse
Published in Particulate Science and Technology, 2021
DF is a non-Newtonian fluid that show nonlinear shear thinning behavior with a yield stress. The rheological study of DFs was conducted at different concentrations (0.5, 0.7 and 1.0 wt. %) of SBSN at different temperatures 80 °C, 100 °C and 120 °C. The results obtained were fitted with Bingham–Plastic and Herschel–Bulkley models to predict the rheological behavior of SBSN-drilling mud. The Bingham–Plastic model includes both yield stress and a limiting viscosity at finite shear rate (Bingham 1916) where is the shear stress, is the yield point or yield stress, is the plastic viscosity, and is the shear rate. This model was found to be inadequate because shear stress/shear rate is no longer linear and it overestimates the fluid yield stress (yield point).
Performance prediction of a centrifugal pump delivering non-Newtonian slurry
Published in Particulate Science and Technology, 2018
K. R. Mrinal, Md. Hamid Siddique, Abdus Samad
The Bingham plastic model is the simplest rheological model, but accuracy is lesser as compared with the power law and Herschel–Bulkely model. In the Bingham plastic model, a minimum shear stress (yield stress) is required to overcome the yield point so that the fluid starts flowing. Once the yield point has exceeded, the shear stress is directly proportional to shear rate with a slope called plastic viscosity. The plastic viscosity and yield stress increase with increase in the solid concentration. Increase in solid concentration causes increase in the particle–particle contact which results in increase in plastics viscosity. The plastics viscosity for 3% and 5% bentonite slurry are 0.0075 and 0.013 Pa.sec, respectively. Slurry B is more viscous than slurry A.
Salt contamination and temperature impacts on the rheological and electrical resistivity behaviors of water based drilling mud
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2020
Aram M. Raheem, Cumaraswamy Vipulanandan
At the start, the Bingham plastic model was used and this model involves a yield stress (τo) with a constraining viscosity (μp) at a determinate shear strain rate. However, the drilling mud exhibits a nonlinear flow function for both shear thickening and shear thinning relationships where a concept of constant plastic viscosity is not preserved. The Herschel-Bulkley (H-B) model expresses a fluid with three factors as follows (Tang and Kalyon 2004):