Herschel–Bulkley fluid

About: Herschel–Bulkley fluid is a research topic. Over the lifetime, 1946 publications have been published within this topic receiving 49318 citations.

Stability of rheometric viscoelastic fluid flow with respect to shear perturbations

Abstract: Flow between two plates is considered for a fluid obeying the DeWitt rheological equation of state with the Jaumann derivative. It is found analytically that the steady-state Couette flow is stable or unstable with respect to plane shear perturbations when the Weissenberg numbers are less or greater than unity, respectively. The flow acceleration stage is studied analytically and numerically, a comparison with the case of an Oldroyd fluid is carried out, and the neutral stability curves are constructed. The fundamental role of perturbations of the type considered among the set of instability types which can act on the fluid in such a flow is noted.

On an evolutionary nonlinear fluid model in the limiting case

Abstract: We consider the two-dimesional spatially periodic problem for an evolutionary system describing unsteady motions of the fluid with shear-dependent viscosity under general assumptions on the form of nonlinear stress tensors that includes those with pstructure. The global-in-time existence of a weak solution is established. Some models where the nonlinear operator corresponds to the case p = 1 are covered by this analysis.

Resonator Based Superposition Rheometry

Abstract: This thesis presents a measurement device consisting of a rotational rheometer in combination with a mechanical resonator. The superposition of conventional shear rate and a very small oscillatory shear offers the possibility to investigate the material behavior of non-Newtonian fluids. The structure of a complex fluid is changed by shearing. An equilibrium state depending on the disruption by shearing and the internal reforming evolves. This structure can be described by a complex viscosity consisting of viscosity and elasticity. The resonator operated by a phase locked loop measures the complex viscosity. The first part of the work describes the operation principle of the resonator. The determination of the mechanical behaviour of the resonator in air and in contact with the fluid permits the calculation of the complex viscosity. The resonator is driven electromagnetically and the phase between the excitation force and the resulting oscillating velocity is controlled by a feed back loop. Two phases and their corresponding frequencies are used in order to deduce the resonant frequency and quality factor of the operating mode. A single degree of freedom (SDOF) oscillation equation describes the resonator’s behaviour and permits the calculation of the complex viscosity by solving an implicit equation. The superposition of the constant and oscillatory shear flow is possible either in a parallel or orthogonal way. Both variants have been realised. The second part describes the design of two resonators: the plate on rod resonator (POR ) used for the parallel and the orthogonal resonator (OR ) for the orthogonal superposition. Their main requirement was a low resonant frequency. The change of structure of a complex fluid is better observable the lower the frequency is. For the constant shear rate a UDS 200 from Anton Paar was used. The third part derives the equation for the coupling of the fluid motion to the resonator characteristics. The POR is used as a replacement of the bottom plate of a conventional rotational rheometer. Hence plate-plate and cone-plate geometries can be used. The OR involves a Couette geometry. The different fluid resonator interaction models are derived and their applicability is discussed. A further consideration is the investigation of the assumption that the top plate or top cone is at rest. Finally the measurement error is deduced. It is used for the calculation of the complex viscosity. The measurement precision and accuracy is analysed in the fourth part. The

Magnetohydrodynamic flow of a non-Newtonian fluid past a porous plate

Abstract: This article studies the laminar flow of an electrically conducting non-Newtonian fluid (Rivlin-Encksen type) past an infinite porous flat plate to a step function change in suction velocity in the presence of a transverse magnetic field. The Laplace transform technique has been employed to solve the basic differential equations. The solutions of the velocity profile and skin-friction are obtained and the effects of the visco-elastic parameter, the magnetic field and the time parameter on the fluid flow have been studied in several tables.

Some Exact Solutions of Second Grade Fluid over the Plane moving with Constant Acceleration

Abstract: Many materials such as clay coatings, drilling muds,suspensions, certain oils and greases, polymer melts,elastomers and many emulsions have been treated as non– Newtonian fluids. It is difficult to suggest a singlemodel which exhibits all properties of non–Newtonianfluids as in caseof the Newtonian fluids. They cannotbe described in a simple model as for the Newtonian fluids and there has been much confusion overthe classification of non–Newtonian fluids. However,non–Newtonian fluids may be classified as: (i) fluidsfor which the shear stress depends on the shear rate; (ii) fluids for which the relation between the shearstress and shear rate depends on time; (iii) fluidswhich possess both elastic and viscous properties called visco elastic fluids or elastico–viscous fluids.Because of great diversity in the physical structure of non–Newtonian fluids, it does not seem possible to recommend a single constitutive equation for usein the cases described in (i) , (ii) and (iii) . Therefore,many constitutive equations for non–Newtonian fluids have been proposed. Most of them are empirical orsemi–empirical. For more general threedimensionalrepresentations the method of continuum mechanics is needed. Although many constitutive equationshave been suggested, many questions are still unsolved.Some of the continuum models do not givesatisfactory results in accordance with the availableexperimental data. Therefore, in many practical applications, empirical or semi–empirical equations havebeen used. A constitutive equation is a relation between stressand the local properties of the fluid. For a fluid at restthe stress is determined wholly by the static pressure.Although in the case of a fluid in relative motion therelation between stress and the local properties of thefluid is more complicated, some modifications maybe made such as the stress being dependent only onthe instantaneous distribution of fluid velocity in theneighborhood of the element. This distribution maybe expressed only in terms of the velocity gradientcomponents such as for a Newtonian fluid. However,non-Newtonian fluids cannot be described as simple as Newtonian fluids. One of the most popular modelsfor non-Newtonian fluids is the model that is called the second–order fluid or second grade fluid [6]