A review on rising bubble dynamics in viscosity-stratified fluids

Systems with a bubble rising in a fluid, which has a variation of viscosity in space and time can be found in various natural phenomena and industrial applications, including food processing, oil extraction, waste processing and biochemical reactors, to name a few. A review of the aspects studied in the literature on this phenomenon, the gaps that exist and the direction for further numerical and experimental studies to address these gaps is presented

Double-diffusive instability in core-annular pipe flow

The instability in a pressure-driven core-annular flow of two miscible fluids having the same densities, but different viscosities, in the presence of two scalars diffusing at different rates (double-diffusive effect) is investigated via linear stability analysis and axisymmetric direct numerical simulation. It is found that the double-diffusive flow in a cylindrical pipe exhibits strikingly different stability characteristics compared to the double-diffusive flow in a planar channel and the equivalent single-component flow (wherein viscosity stratification is achieved due to the variation of one scalar) in a cylindrical pipe. The flow which is stable in the context of single-component systems now becomes unstable in the presence of two scalars diffusing at different rates. It is shown that increasing the diffusivity ratio enhances the instability. In contrast to the single fluid flow through a pipe (the Hagen-Poiseuille flow), the faster growing axisymmetric eigenmode is found to be more unstable than the corresponding corkscrew mode for the parameter values considered, for which the equivalent single-component flow is stable to both the axisymmetric and corkscrew modes. Unlike single-component flows of two miscible fluids in a cylindrical pipe, it is shown that the diffusivity and the radial location of the mixed layer have non-monotonic influences on the instability characteristics. An attempt is made to understand the underlying mechanism of this instability by conducting the energy budget and inviscid stability analyses. The investigation of linear instability due to the double-diffusive phenomenon is extended to the nonlinear regime via axisymmetric direct numerical simulations. It is found that in the nonlinear regime the flow becomes unstable in the presence of double-diffusive effect, which is consistent with the predictions of linear stability theory. A new type of instability pattern of an elliptical shape is observed in the nonlinear simulations in the presence of double-diffusive effect

Two-layer channel flow involving a fluid with time-dependent viscosity

A pressure-driven two-layer channel flow of a Newtonian fluid with constant viscosity (top layer) and a fluid with a time-dependent viscosity (bottom layer) is numerically investigated. The bottom layer goes through an aging process in which its viscosity increases due to the formation of internal structure, which is represented by a Coussot-type relationship. The resultant flow dynamics is the consequence of the competition between structuration and destructuration, as characterized by the dimensionless timescale for structuration (tau) and the dimensionless material property (beta) of the bottom fluid. The development of Kelvin-Helmholtz type instabilities (roll-up structures) observed in the Newtonian constant viscosity case was found to be suppressed as the viscosity of the bottom layer increased over time. It is found that, for the set of parameters considered in the present study, the bottom layer almost behaves like a Newtonian fluid with constant viscosity for tau greater than 10 and beta greater than 1. It is also shown that decreasing the value of the Froude number stabilizes the interfacial instabilities. The wavelength of the interfacial wave increases as the capillary number increases.Comment: 10 pages, 9 figures, Environmental Fluid Mechanic

Spatio-temporal linear stability of double-diffusive two-fluid channel flow

Absolute instabilities in shear flows can cause a catastrophic breakdown into a new unsteady state, or even into turbulence. We demonstrate that in a double-diffusive channel flow with a viscosity stratification across the channel, rapidly growing absolute instability may be obtained at Reynolds numbers of a few hundreds. The instability is much weaker in an equivalent single solute fluid with the same viscosity contrast, or even in one which is made up only of the more dangerous of the two diffusing species. This is a novel characteristic of double-diffusive systems driven by viscosity, rather than density variations. Convective instabilities too are stronger in the double-diffusive case

Dynamics of an air bubble rising in constant and varying viscosity media

The dynamics of a gas bubble rising in a liquid is observed in many natural phenomena, and also in industrial applications. Due to its practical relevance, this has been studied from many centuries and it continues to be a problem of great interest even today. The main objectives of the thesis are to investigate some novel problems on bubble rising in viscosity varying systems. In several situations one could observed viscosity stratified media. Two of them are considered in this work. (a) When viscosity stratification is inherently present in the surrounding medium (say, viscosity of the outer fluid is increasing linearly with height). (b) When the outer fluid is a non-Newtonian fluid, wherein the surrounding fluid viscosity varies due to the shear caused by the motion of the bubble. Three-dimensional numerical simulations and experiments are performed to study these flows. The flow dynamics is governed by mass, momentum and energy conservation equations. A volume-of-fluid (VoF) approach is used to track the interface separating the fluids. The computational and experimental approaches used in this study are discussed in Chapter 2. The validations of the present numerical solver are also performed in the same chapter. In order to compare the bubble behaviour in a medium with varying viscosity with that observed in a constant viscosity medium (standard system), the dynamics of a rising bubble in a standard air-water system is also investigated

Three-dimensional linear instability in pressure-driven two-layer channel flow of a Newtonian and a Herschel-Bulkley fluid

The three-dimensional linear stability characteristics of pressure-driven two-layer channel flow are considered, wherein a Newtonian fluid layer overlies a layer of a Herschel-Bulkley fluid. We focus on the parameter ranges for which Squire's theorem for the two-layer Newtonian problem does not exist. The modified Orr-Sommerfeld and Squire equations in each layer are derived and solved using an efficient spectral collocation method. Our results demonstrate the presence of three-dimensional instabilities for situations where the square root of the viscosity ratio is larger than the thickness ratio of the two layers; these "interfacial" mode instabilities are also present when density stratification is destabilizing. These results may be of particular interest to researchers studying the transient growth and nonlinear stability of two-fluid non-Newtonian flows. We also show that the "shear" modes, which are present at sufficiently large Reynolds numbers, are most unstable to two-dimensional disturbances

Evaporating Falling Drop

There-dimensional numerical simulations are carried out to investigate the dynamics of a drop undergoing evaporation and falling due to gravity. In order to accurately capture the interfacial phenomena dynamic adaptive grid refinement has been incorporated. The results are presented in terms of spatio-temporal evolution of the shape of the drop, along with the contours of the vapour concentration generated due to evaporation. This study has implications in natural phenomena, such as rainfall, dew formation and several industrial applications undergoing phase change. A parametric study of this phenomenon will be presented at the conference

Motion of an air bubble under the action of thermocapillary and buoyancy forces

A novel way to handle surface tension gradient driven flows is developed in the volume-of-fluid (VoF) framework. Using an open source Navier-Stokes solver, {\it Basilisk}, and the present formulation, we investigate thermocapillary migration of drops/bubbles in a surrounding medium. Several validation exercises have been performed, which demonstrate that the present solver is a robust one to investigate interfacial flows with variable surface tension. It is well known that it is a challenging task to numerically model the tangential and normal surface forces arising due to interfacial tension. We have shown that the present method does not require the artificial smearing of surface tension about the interface, and thus predicts the theoretical value of the terminal velocity of bubble/drop migrating due to an imposed temperature gradient very well. It is also demonstrated that the present solver provides accurate results for problems exhibiting the gravity and thermocapillary forces simultaneously, and useful for systems with high viscosity and density ratios.Comment: 30 pages, 16 figures, submitted to Computers and Fluid

Super-linear speed-up of a parallel multigrid Navier-Stokes solver on Flosolver

In parallel computing, scalability is an important issue and getting linear speed-ups is difficult for most codes. Super-linear speed up has been achieved on an eight-processor Flosolver system for a multigrid Navier-Stokes code. The physical problem solved, the parallelization method, the speed-ups obtained and possible explanations for this result are discussed here