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The critical modes of the instabilities of viscoelastic Taylor-Couette flow are investigated using both experiments and linear stability analysis when only one cylinder rotates and the other is fixed. A viscoelastic Rayleigh circulation criterion highlights that the elasticity of the polymer solution can induce a flow instability even if the Newtonian counterpart is stable. When the inner cylinder solely rotates, experimental results show three critical modes: stationary axisymmetric vortices or Taylor vortices for small elasticity, standing waves, also called ribbons for intermediate values of elasticity, and disordered vortices (DV) for large elasticity values. When the outer cylinder rotates and the inner cylinder is fixed and for large values of elasticity, the critical modes appear in the form of DV. There is a good agreement between experimental and theoretical results provided that the elasticity of the polymer solution is accurately determined. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (Part 2)'.

Viscoelastic liquid transfer from one surface to another is a process that finds applications in many technologies, primarily in printing. Here, cylindrical-shaped capillary bridges pinned between two parallel disks are considered. Specifically, the effects of polymer mass fraction, solution viscosity, disk diameter, initial aspect ratio, final aspect ratio, stretching velocity, and filling fraction (alike contact angle) are experimentally investigated in uniaxial extensional flow. Both Newtonian and viscoelastic polymer solutions are prepared using polyethylene glycol and polyethylene oxide, with a wide variety of mass fractions. The results show that the increase in polymer mass fraction and solvent viscosity reduces the liquid transfer to the top surface. Moreover, the increase in the initial and final stretching heights of the capillary bridge also decreases the liquid transfer for both Newtonian and viscoelastic solutions. Finally, the shape of the capillary bridge is varied by changing the liquid volume. Now, Newtonian and viscoelastic solutions exhibit opposite behaviors for the liquid transfer. These findings are discussed in terms of interfacial shape instability and gravitational drainage.

A thermal turbulent Taylor-Couette facility has been designed to investigate turbulent flows generated by differential rotation and radial temperature gradient. It consists of a cylindrical annulus with a rotating inner cylinder and a fixed outer cylinder. The electric heating system is installed inside the inner cylinder, and the annulus is immersed in a large cylindrical container filled with cooling fluid. Temperature regulators independently control the temperature of the inner surface of the inner cylinder and that of the cooling fluid. The facility allows us to reach values of the Reynolds number (Re ∼ 5 × 10 5 ) and of the Rayleigh number (Ra ∼ 3 × 10 6 ) for water as the working fluid. The facility provides torque measurements, a full optical access at the side and from the bottom for velocity measurements using particle image velocimetry (2D, stereoscopic, and tomographic). Temperature measurements in the flow can be performed by thermochromic liquid crystals or laser induced fluorescence.

Transition to defect-mediated turbulence in the ribbon patterns observed in a viscoelastic Taylor-Couette flow is investigated when the rotation rate of the inner cylinder is increased while the outer cylinder is fixed. In four polymer solutions with different values of the elasticity number, the defects appear just above the onset of the ribbon pattern and trigger the appearance of disordered oscillations when the rotation rate is increased. The flow structure around the defects is determined and the statistical properties of these defects are analyzed in the framework of the complex Ginzburg-Landau equation.

A linear stability analysis and an experimental study of a viscoelastic Taylor-Couette flow corotating in the Keplerian ratio allow us to elucidate the analogy between the viscoelastic instability and the magnetorotational instability (MRI). A generalized Rayleigh criterion allows us to determine the potentially unstable zone to pure-elasticity-driven perturbations. Experiments with a viscoelastic polymer solution yield four modes: one pure-elasticity mode and three elastorotational instability (ERI) modes that represent the MRI-analog modes. The destabilization by the polymer viscosity is evidenced for the ERI modes.

The stability of the circular Couette flow of a dielectric fluid is analyzed by a linear perturbation theory. The fluid is confined between two concentric cylindrical electrodes of infinite length with only the inner one rotating. A temperature difference and an alternating electric tension are applied to the electrodes to produce a radial dielectrophoretic body force that can induce convection in the fluid. We examine the effects of superposition of this thermoelectric force with the centrifugal force including its thermal variation. The Earth's gravity is neglected to focus on the situations of a vanishing Grashof number such as microgravity conditions. Depending on the electric field strength and of the temperature difference, critical modes are either axisymmetric or nonaxisymmetric, occurring in either stationary or oscillatory states. An energetic analysis is performed to determine the dominant destabilizing mechanism. When the inner cylinder is hotter than the outer one, the circular Couette flow is destabilized by the centrifugal force for weak and moderate electric fields. The critical mode is steady axisymmetric, except for weak fields within a certain range of the Prandtl number and of the radius ratio of the cylinders, where the mode is oscillatory and axisymmetric. The frequency of this oscillatory mode is correlated with a Brunt-Väisälä frequency due to the stratification of both the density and the electric permittivity of the fluid. Under strong electric fields, the destabilization by the dielectrophoretic force is dominant, leading to oscillatory nonaxisymmetric critical modes with a frequency scaled by the frequency of the inner-cylinder rotation. When the outer cylinder is hotter than the inner one, the instability is again driven by the centrifugal force. The critical mode is axisymmetric and either steady under weak electric fields or oscillatory under strong electric fields. The frequency of the oscillatory mode is also correlated with the Brunt-Väisälä frequency.

This article deals with the thermal convection in a dielectric fluid confined in a finite-length plane capacitor with a temperature gradient under microgravity conditions. The dielectrophoretic force resulting from differential polarization of the fluid plays the role of buoyancy force associated with an electric effective gravity. It induces the convection when the Rayleigh number based on this electric gravity exceeds a critical value. Two-dimensional numerical simulation for a geometry with a large aspect ratio is used to determine the convective flow in the saturated state. The Nusselt number Nu is computed for a wide range of Prandtl number (0.01 ≤ Pr ≤ 10(3)) and its dependence on the distance from the critical condition is determined. A correlation between Nu and Pr in the vicinity of criticality is obtained and compared with that of the Rayleigh-Bénard convection. The behavior of the convection is analyzed in detail from an energetic viewpoint: electrostatic energy, power inputs by different components of the electric gravity and viscous and thermal dissipations are computed.

Thermal convection in a dielectric fluid layer between two parallel plates subjected to an alternating electric field and a temperature gradient is investigated under microgravity conditions. A thermoelectric coupling resulting from the thermal variation of the electric permittivity of the fluid produces the dielectrophoretic (DEP) body force, which can be regarded as thermal buoyancy due to an effective gravity. This electric gravity can destabilize a stationary conductive state of the fluid to develop convection. The similarity of the DEP thermal convection with the Rayleigh-Bénard (RB) convection is examined by considering its behavior in detail by a linear stability theory and a two-dimensional direct numerical simulation. The results are analyzed from an energetic viewpoint and in the framework of the Ginzburg-Landau (GL) equation. The stabilizing effects of a thermoelectric feedback make the critical parameters different from those in the RB instability. The nonuniformity of the electric gravity arising from the finite variation of permittivity also affects the critical parameters. The characteristic constants of the GL equation are comparable with those for the RB convection. The heat transfer in the DEP convection is weaker than in the RB convection as a consequence of the feedback that impedes the convection.

Spiral vortex flow in the counter-rotating Couette-Taylor system with a large aspect ratio and an intermediate gap has been investigated using Particle Image Velocimetry (PIV). From data of velocity components, we have determined nonlinear properties (anharmonicity, mirror symmetry, axial and radial flow rates) of spiral vortices and compared them to those of Taylor vortices. The velocity field around a spatio-temporal defect has been measured. There is a good agreement between these experimental results with available results from numerical simulations.

The transition to turbulence in a flow of semidilute shear-thinning viscoelastic solution with a moderate elasticity was investigated in the Taylor-Couette system with a fixed outer cylinder. As the cylinder rotation frequency increases, the base flow bifurcates to a pattern of ribbons and then to disordered oscillations (DOs). Within these DOs, we have identified two particular regimes of turbulence: spatiotemporal intermittency (STI) followed by inertioelastic turbulence (IET) with a net transition between them. This transition is evidenced by a sharp peak of a diffusion velocity and a Weissenberg number.