Fluid Mechanics
Non-Newtonian Fluid Mechanics
Rheology
Modeling of Physical Systems
Earlier Work
Viscoplastic Squeeze Flows
The squeeze film geometry occurs for the close approach of a pair of surfaces, and conforms to the classical lubrication paradigm. The approach leads to a sharp growth in the pressure within the narrow gap (between the surfaces), this growth being proportional to the fluid viscosity. While squeeze-flow problems have been analyzed extensively for Newtonian fluids, we here consider the same for viscoplastic fluids between plate/disk surfaces. Here, the viscoplastic rheology have been modeled using the Bingham, Casson and Herschel-Bulkley constitutive equations. For such fluids, flow occurs only in the regions where the stress exceeds a certain yield threshold which is known as yield stress. A leading-order lubrication analysis predicts the existence of a central unyielded zone bracketed between near-wall regions. This leads to the well known squeeze-film paradox, since simple kinematic arguments show that there must be a finite velocity gradient even in the unyielded zone, thereby precluding the existence of such regions. This paradox may, however, be resolved within the framework of a matched asymptotic expansions approach where one postulates separate expansions within the yielded and apparently unyielded (plastic) zones. In this regard, we follow the approach suggested by Balmforth and Craster (1999) in the context of a Bingham fluid. The yielded zones conform to the lubrication paradigm with the shear stress being much greater than all other stress components. On the other hand, the shear and extensional stresses are comparable in the ‘plastic region’, with the overall stress magnitude being asymptotically close to but just above the yield threshold. Recently, Muravleva (2015, 2017) has analyzed the flow behaviour of Bingham material in both planar and axisymmetric geometries using the method of matched asymptotic expansions. Based on the above method, we circumvent the aforementioned paradox, and develop asymptotic solutions for the squeeze flow of more complicated viscoplastic models like, Casson and Herschel-Bulkley fluid models. The effect of the yield threshold on the pseudo-yield surface (that separates the sheared and plastic zones), pressure distribution and squeeze force for different values of Casson and Herschel-Bulkley material yield stresses are investigated. Further, in the case of Bingham fluid, we investigate the combined effects of the fluid inertia and yield stress on the pressure distribution and the squeeze force.
Thixotropic fluid flows in abrupt expansions
Many structured fluids (i.e., fluids with micro-structure) belong to the class of fluid called thixotropic fluids. Some examples of these types of fluids are paints, suspensions, polymers, etc. Our intention is to analyze the axisymmetric flow of thixotropic materials through abrupt expansions using finite element methods. In this part, we are investigating the effects of the thixotropic material parameters on the shape and length of the recirculation zones that occur in the corners of the abrupt expansion.
Circular hydraulic jump
We present results from experiments and a numerical study of the circular hydraulic jump. Our focus is the dependence of the jump radius on the momentum flux at the inlet. Various empirical relationships available in the literature implicitly assume the jump radius to be independent of this quantity, [Bohr et al, 1993, J. Fluid Mech.] and prescribe the jump-radius to scale only with the mass-flow rate, the kinematic viscosity and gravity. In this study, we propose that momentum flux is an additional parameter which strongly influences the jump radius and provide experimental and numerical evidence fo the same. We then rationalize our results by providing an explanation for the significant influence of the momentum flux on the jump-radius.
Rheodynamic lubrication using Viscoplastic lubricants
Lubrication of modern machines using non-Newtonian lubricants has been an emerging area of interest for researchers around the world. Moreover, lubricants of viscoplastic type are gaining importance in the recent trends in lubrication theory. Some of the important fluids which belong to this class are Bingham Plastics, Casson fluids and Herschel-Bulkley fluids. The present work is a study on these types of Viscoplastic fluids, namely, the Bingham Plastic and Herschel-Bulkley fluids in Squeeze Film Bearings. There are different constitutive equations (or models) to represent Bingham fluids like the two-constant Bingham model, the Biviscosity model and the Papanastasiou model. But the most widely used two-constant model of the Bingham fluid has been considered in the present context. Further, a generalisation of the two-constant Bingham model has been considered for Herschel-Bulkley fluids. Hence, the present study gives an overview of the squeeze film problems using Bingham and Herschel-Bulkley lubricants. The aim of the present work is to analyze the effects of fluid inertia, sinusoidal squeeze motion and curvature variation of a Squeeze Film Bearing with circular and rectangular geometries using Bingham Plastic and Herschel-Bulkley fluids as lubricants. We have investigated the effects of fluid inertia and sinusoidal squeeze motion in circular and rectangular geometries using Bingham and Herschel-Bulkley lubricants. Further, the effects of curvature variation on the bearing properties using Bingham lubricants have also been studied.