Thermal Convection in Viscoelastic Fluids

Thermal convection in viscoelastic fluids arises when heat-driven buoyancy forces interact with fluid elasticity, leading to rich and often counterintuitive flow behaviours. Unlike Newtonian fluids, viscoelastic liquids can store and release elastic energy, which modifies the threshold for convective onset and alters the morphology of emerging flow patterns. A key feature is the competition among thermal diffusion, viscous dissipation and fluid relaxation time, which gives rise to oscillatory and steady multicellular states as parameters such as the Rayleigh and Prandtl numbers are varied. In cavities and layers subject to temperature gradients, viscoelasticity can either stabilise or destabilise the base flow, depending on the relative magnitude of elastic and viscous effects. External perturbations—such as vibrations or electric field modulation—further enrich the dynamics by introducing additional time scales, leading to synchronous, subharmonic or chaotic responses. These phenomena are of global significance for polymer processing, microfluidic heat exchangers and geophysical flows, where controlling heat transfer and flow stability is essential. Advances in numerical modelling and experimental diagnostics have begun to unravel the interplay between elasticity and buoyancy, opening pathways to optimise transport processes in engineering and natural settings.

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Thermal Convection in Viscoelastic Fluids publication trend

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Technical terms

Viscoelastic fluid: A liquid exhibiting both viscous flow and elastic deformation, characterised by a relaxation time over which stored elastic energy decays.

Rayleigh number: A dimensionless group expressing the ratio of buoyancy forces to viscous and thermal diffusion effects; it governs the onset of convection.

Prandtl number: The ratio of momentum diffusivity (viscosity) to thermal diffusivity; it indicates the relative thickness of velocity and temperature boundary layers.

FENE–CR model: A constitutive description for polymer solutions that accounts for finite extensibility of elastic molecules and non-linear stress responses.

Vibrational Rayleigh number: A modified Rayleigh number incorporating the amplitude and frequency of external vibrations, used to predict thermovibrational instability.

Dielectrophoretic force: A body force on a dielectric fluid induced by spatial gradients of an electric field, which can enhance or suppress convective motion.

References

1. Symmetry properties and bifurcations of viscoelastic thermovibrational convection in a square cavity. Physical Review E (2023).
2. Multicellular states of viscoelastic thermovibrational convection in a square cavity. Physics of Fluids (2021).
3. Effect of time-dependent sinusoidal electric field on the onset of electroconvection in a viscoelastic fluid layer. Condensed Matter Physics (2024).