Capacitance matrix technique for avoiding spurious eigenmodes in the solution of hydrodynamic stability problems by Chebyshev collocation method

We present a simple technique for avoiding physically spurious eigenmodes that often occur in the solution of hydrodynamic stability problems by the Chebyshev collocation method. The method is demonstrated on the solution of the Orr-Sommerfeld equation for plane Poiseuille flow. Following the standard approach, the original fourth order differential equation is factorised into two second-order equations using a vorticity-type auxiliary variable with unknown boundary values which are then eliminated by a capacitance matrix approach. However the elimination is constrained by the conservation of the structure of matrix eigenvalue problem, it can be done in two basically different ways. A straightforward application of the method results in a couple of physically spurious eigenvalues which are either huge or close to zero depending on the way the vorticity boundary conditions are eliminated. The zero eigenvalues can be shifted to any prescribed value and thus removed by a slight modification of the second approach.Comment: 10 pages, 1 figure, minor revision, to appear in J. Comp. Phy

Autocatalytic plume pinch-off

A localized source of buoyancy flux in a non-reactive fluid medium creates a plume. The flux can be provided by either heat, a compositional difference between the fluid comprising the plume and its surroundings, or a combination of both. For autocatalytic plumes produced by the iodate-arsenous acid reaction, however, buoyancy is produced along the entire reacting interface between the plume and its surroundings. Buoyancy production at the moving interface drives fluid motion, which in turn generates flow that advects the reaction front. As a consequence of this interplay between fluid flow and chemical reaction, autocatalytic plumes exhibit a rich dynamics during their ascent through the reactant medium. One of the more interesting dynamical features is the production of an accelerating vortical plume head that in certain cases pinches-off and detaches from the upwelling conduit. After pinch-off, a new plume head forms in the conduit below, and this can lead to multiple generations of plume heads for a single plume initiation. We investigated the pinch-off process using both experimentation and simulation. Experiments were performed using various concentrations of glycerol, in which it was found that repeated pinch-off occurs exclusively in a specific concentration range. Autocatalytic plume simulations revealed that pinch-off is triggered by the appearance of accelerating flow in the plume conduit.Comment: 10 figures. Accepted for publication in Phys Rev E. See also http://www.physics.utoronto.ca/nonlinear/papers_chemwave.htm

Thermomagnetic convection of magnetic fluids in a cylindrical geometry

The thermomagnetic convection of magnetic fluids in a cylindrical geometry subjected to a homogeneous magnetic field is studied. The study is motivated by a novel thermal instability [W. Luo et al., Phys. Rev. Lett. 82, 4134 (1999)]. As model system a composite cylinder with inner heating is considered which reflects the symmetry of the experimentally setup. The general condition for the existence of a potentially unstable stratification in the magnetic fluid is derived. Within a linear stability analysis the critical external induction for the onset of thermomagnetic convection is determined for dilute and nondilute magnetic fluids. The difference between both thresholds allows to test experimentally whether a test sample is a dilute fluid or not.Comment: 18 pages, 5 figure

Tweeting television between innovation and normalization: How Lebanese television and audiences are making use of Twitter in political talk shows

Traditional media have progressively integrated newer media practices, with the constant emergence of new digital technologies, without abandoning their former ones. The adoption of Twitter by TV channels and by other social actors during political talk shows is a case in point. This article aims to assess whether the hybridization of TV talk shows and Twitter has innovated or normalized existing patterns of communication. In the former case, by enabling more interaction between different actors and space for audience deliberation, or in the latter case, by reproducing a traditional one-way communication and a centralized network of information that remains controlled and oriented by the elite (journalists and politicians). The incorporation of older and emergent media logic has an impact on the construction and distribution of political information as well as on the power relationships between journalists, politicians, and TV audiences. Besides allowing political talk shows to expand their flow of information, and to promote their news online, hybridized practices have not only altered the way citizens consume and engage with political information but also how they counter-frame traditional political media content by producing new ones. The research methodology consists of descriptive, content, and network analyses of tweets collected from three Lebanese local TV political talk show “Sarelwa2et” (MTV), “Btefro’ aa Watan” (Al Jadeed), and “Vision 2030” (LBCI) between February and March 2022. Results revealed that TV talk shows are making use of Twitter as a top-down transmitter of information and resorting poorly to its interactive potential. Some newer media practices of Twitter, such as @mention and replies are being applied but only to interact with politicians and journalists, failing to engage with a larger array of voices and thus, leading to an elite-centric discourse within the network. Also, tweets are mostly used to inform audiences and promote TV programs. In addition, network analyses of talk shows via hashtags demonstrated the central and not monopolized role of politicians and journalists as influencers, bridges, and quick spreaders of information. Finally, content analysis of dual screeners’ tweets (n=6000) indicated very little space in a Habermasian public sphere. The total of subjective opinions, irony, and attack/insult tweets are still higher than the total of the introduction of new issues and counter-frames tweets

Solutocapillary Convection in Spherical Shells with a Receding and Deforming Interface

A theoretical and computational study of solutocapillary driven Marangoni instabilities in small spherical shells is presented. The shells contain a binary fluid with an evaporating solvent. The viscosity is a strong function of the solvent concentration, the inner surface of the shell is assumed impermeable and stress free, while non-linear boundary conditions are modeled and prescribed at the receding outer boundary. A time-dependent diffusive state is possible and may lose stability through the Marangoni mechanism due to surface tension dependence on solvent concentration (buoyant forces are negligible in this micro-scale problem). The Capillary number (Ca) provides a measure of the deviation from sphericity and to leading order in the limit Ca → 0 the outer surface evolves with time in a convective state as it does in the diffusive state. We model the motion in this limit and compute supercritical, nonlinear, time-dependent, axisymmetric and three-dimensional, infinite Schmidt number solutocapillary convection. The normal stress balance imposes compatibility restrictions and allows two admissible states: axisymmetric hemispherical convection and three-dimensional solutions exhibiting cubic symmetry. We employ global mass conservation to compute upper bounds on the companion O(Ca) free surface deformations

Oscillatory Thermocapillary Convection

Stability analysis of thermocapillary convection in rectangular cavities is performed using direct numerical simulation. The influence of the Reynolds number (Re), the fluid Prandtl number (Pr) and cavity aspect ratio (Ar) on the motion is investigated. Neutral stability curves for transition to time-dependent convection are delineated in the Re-Ar plane for fluids with Pr=1.0, 4.4, 6.78, and 10. Several interesting features of these diagrams are discussed. One important conclusion is that Ar(epsilon tau) increases as Pr decreases. Thus large values of both Ar and Re are necessary to induce thermocapillary oscillations for small Pr fluids such as liquid metals and semiconductor melts. Energy analysis is also performed for the oscillatory flow in the neighborhood of critical points in order to gain insight into the mechanisms leading to instability

Stabilization of Curcumin by Complexation with Divalent Cations in Glycerol/Water System

The purpose of present study was to stabilize curcumin food pigment by its complexation with divalent ions like (Zn2+, Cu2+, Mg2+, Se2+), in “green media” and evaluate its stability in vitro compared to curcumin alone. The curcumin complexes were prepared by mechanical mixture of curcumin and sulfate salts of each metal (metal : curcumin 1/1mol) into unconventional and nontoxic glycerol/water solvent. Two stoichiometry of complex were obtained, 1 : 1 and 1 : 2 (metal/curcumin), respectively. On evaluation of in vitro stability, all complexes were found to provide a higher stability from curcumin alone

Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined

Oscillatory thermocapillary convection

We study thermocapillary and buoyant thermocapillary convection in rectangular cavities with aspect ratio A = 4 and Pr = 0.015. Two separate problems are considered. The first is combined buoyant thermocapillary convection with a nondeforming interface. We establish neutral curves for transition to oscillatory convection in the Re-Gr plane. It is shown that while pure buoyant convection exhibits oscillatory behavior for Gr is greater than Gr(sub cr) (where Gr(sub cr) is defined for the pure buoyant problem), pure thermocapillary convection is steady within the range of parameters tested. In the second problem, we consider the influence of surface deformation on the pure thermocapillary problem. For the range of parameters considered, thermocapillary convection remained steady