Onset of Thermal Instabilities in the Plane Poiseuille Flow of Weakly Elastic Fluids: Viscous Dissipation Effects

The onset of thermal instabilities in the plane Poiseuille flow of weakly elastic fluids is examined through a linear stability analysis by taking into account the effects of viscous dissipation. The destabilizing thermal gradients may come from the different temperatures imposed on the external boundaries and/or from the volumetric heating induced by viscous dissipation. The rheological properties of the viscoelastic fluid are modeled using the Oldroyd-B constitutive equation. As in the Newtonian fluid case, the most unstable structures are found to be stationary longitudinal rolls (modes with axes aligned along the streamwise direction). For such structures, it is shown that the viscoelastic contribution to viscous dissipation may be reduced to one unique parameter: γ=λ1(1−Γ), where λ1 and Γ represent the relaxation time and the viscosity ratio of the viscoelastic fluid, respectively. It is found that the influence of the elasticity parameter γ on the linear stability characteristics is non-monotonic. The fluid elasticity stabilizes (destabilizes) the basic Poiseuille flow if γ<γ* (γ>γ*) where γ* is a particular value of γ that we have determined. It is also shown that when the temperature gradient imposed on the external boundaries is zero, the critical Reynolds number for the onset of such viscous dissipation/viscoelastic-induced instability may be well below the one needed to trigger the pure hydrodynamic instability in weakly elastic solutions.

Modal Analysis of Breakup Mechanisms for a Liquid Jet in Crossflow

Liquid fuel jet in Crossflow (LJIC) is a vital atomization technique significant to the aviation industry. The hydrodynamic instability mechanisms that drive a primary breakup of a transverse jet are investigated using modal and traveling wavelength analysis. This study highlights the primary breakup mechanisms for aviation fuel Jet-A, utilizing a method that could be applied to any liquid fuel. Mathematical decomposition techniques known as POD (Proper Orthogonal Decomposition) and Robust MrDMD (Multi-Resolution Dynamic Mode Decomposition) are used together to identify dominant instability flow dynamics associated with the primary breakup mechanism. Implementation of the Robust MrDMD method deconstructs the nonlinear dynamical systems into multiresolution time-scaled components to capture the intermittent coherent structures. The Robust MrDMD, in conjunction with the POD method, is applied to data points taken across the entire spray breakup regimes: enhanced capillary breakup, bag breakup, multimode breakup, and shear breakup. The dominant frequencies of breakup mechanisms are extracted and identified. These coherent structures are classified with an associated time scale and Strouhal number. Three primary breakup mechanisms, namely ligament shedding, bag breakup, and shear breakup, were identified and associated with the four breakup regimes outlined above. Further investigation portrays these breakup mechanisms to occur in conjunction with each other in each breakup regime, excluding the low Weber number Enhanced Capillary Breakup regime. Spectral analysis of the Robust MrDMD modes' entire temporal window reveals that while multiple breakup mechanisms are convolved, there is a dominant breakup route for each breakup regime. An associated particular traveling wavelength analysis further investigates each breakup mechanism. Lastly, this study explores the effects of an increased momentum flux ratio on each breakup mechanism associated with a breakup regime.

Bio-convective viscoelastic Casson nanofluid flow over a stretching sheet in the presence of induced magnetic field with Cattaneo–Christov double diffusion

Bio-convection is an important phenomenon which is described by hydrodynamic instability and pattern in suspension of biased swimming microorganisms. This hydrodynamics instability arises due to the coupling force between the motion of the micoorganisms and fluid flow. It becomes more significant when nanoparticles are immersed in the base fluid with non-Newtonian rheology. This study presents the bio-convection for a viscoelastic Casson nanofluid flow over a stretching sheet. The Cattaneo–Christov double diffusion, induced magnetic field, thermal radiation, heat generation, viscous dissipation and chemical reaction are taken into account. The boundary condition is enriched with the suction / injection and melting phenomena at the surface. Highly coupled nonlinear governing equations are simplified into a system of coupled ordinary differential equation by using proper similarity transformation. The spectral quasi-linearization method (SQLM) is used to solve the transformed governing equations numerically. Good agreement is observed with the numerical data investigated in the previous outstanding works. It is observed that the density of the motile microorganisms depends on Peclet number and bio-convective Lewis number. Bio-convection Rayleigh number increases the possibility of bio-convection in the system which results in the enhancement of temperature. It is also examined that temperature and concentration profiles increase with the Eckert number and thermophoresis parameter.

Fluid Geodynamics of Deeply Buried Zones of Oil and Gas Accumulation in Sedimentary Basins

—We substantiate certain ideas concerning the key role of fluid-geodynamic processes in the evolvement of hydrocarbon accumulations at great depths, in the Earth’s crust. The presented geodynamic model of oil and gas accumulation is based on updated ideas of the structure of the Earth’s tectosphere, which includes plate, preplate, and folded complexes, and the model makes clearer the spatial scale of the organic matter transformation into hydrocarbons of the oil series. In the bottom layers of the Earth’s crust, we predict the existence of a special stagnation type of water-drive systems with the following distinguishing features: (a) different scales of manifestation, from local to regional; (b) a limited nature of processes of water exchange with the external environment; (c) absence of persistent drainage horizons (beds and interbeds); (d) alignment of hydrodynamic potentials in terms of depths and laterals; and (e) increasing importance of lithohydrochemical and organic-chemistry factors in the development of the void space of the fluid host medium. In their inner space, systems with difficult water exchange can exercise control over the evolvement and preservation of autoclave hydrocarbon systems for a long time, the key feature of the autoclave systems being spatial coincidence (localization) of the processes of oil and gas generation and accumulation. We assume that, in the settings of all-round compression, hydrodynamic instability, and no drainage, occurrence of productive zones is controlled by foci of low pore (reservoir) pressures rather than by local hypsometric highs. We present results of prediction of the development of water-drive stagnation systems occurring in the subsalt deposits of the Caspian depression within the unpenetrated areas of the subsalt profile. For the sedimentary cover at large (and ultralarge) depths, a prediction of reservoir pressures was made, which can be regarded as a necessary component in any prediction of oil and gas potential, since it makes it possible to contour some new (previously unknown) industrially significant zones of hydrocarbon accumulation.

Crystallization of Bosonic Quantum Hall States

The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids, to atoms in optical lattices and twisted bilayer graphene. Crystalline phases often compete with correlated quantum liquids, and transitions between them occur when the energy cost of forming a density wave approaches zero. A prime example occurs for electrons in high magnetic fields, where the instability of quantum Hall liquids towards a Wigner crystal is heralded by a roton-like softening of density modulations at the magnetic length. Remarkably, interacting bosons in a gauge field are also expected to form analogous liquid and crystalline states. However, combining interactions with strong synthetic magnetic fields has been a challenge for experiments on bosonic quantum gases. Here, we study the purely interaction-driven dynamics of a Landau gauge Bose-Einstein condensate in and near the lowest Landau level. We observe a spontaneous crystallization driven by condensation of magneto-rotons, excitations visible as density modulations at the magnetic length. Increasing the cloud density smoothly connects this behaviour to a quantum version of the Kelvin-Helmholtz hydrodynamic instability, driven by the sheared internal flow profile of the rapidly rotating condensate. At long times the condensate self-organizes into a persistent array of droplets, separated by vortex streets, which are stabilized by a balance of interactions and effective magnetic forces.

Localized Breakup Instabilities for a Liquid Jet in Crossflow

Liquid fuel jet in Crossflow (LJIC) is significant to the aviation industry since it is a vital technique for atomization. The hydrodynamic instability mechanisms that drive a transverse jet’s primary breakup were investigated using modal and traveling wavelength analysis. This study highlights the primary breakup mechanisms for aviation fuel Jet-A. However, the techniques discussed are applicable to any liquid. Mathematical decomposition techniques are known as POD (Proper Orthogonal Decomposition), and MrDMD (Multi-Resolution Dynamic Mode Decomposition) are used together to identify dominant instability flow dynamics associated with the primary breakup mechanism. Implementation of the MrDMD method deconstructs the nonlinear dynamical systems into multiresolution time-scaled components that capture the intermittent coherent structures. The MrDMD, in conjunction with the POD method, is applied to data points taken across the entire spray breakup regimes, which are: enhanced capillary breakup, bag breakup, multimode breakup, and shear breakup. The dominant frequencies of both breakup regimes are extracted and identified. These coherent structures are classified with an associated time scale and Strouhal number. Characterization of the traveling column and surface wavelengths are conducted and associated with a known instability model. It is found that the Plateau-Rayleigh instability model predicts columns wavelengths similar to wavelengths found in dominant modes associated with a capillary breakup. Rayleigh Taylor’s instability model matches well with bag and multimode breakup. Small scale surface wavelengths associated with a shear breakup are correlated to a modified Rayleigh Taylor instability model founded by Wang et al. [1]. Furthermore, an atomization model that predicts the Sauter Mean Diameter associated with the dominant small-scale surface traveling wavelengths is established.