Viscous fingering, a classic hydrodynamic instability, is governed by the the competition between destabilising viscosity ratios and stabilising surface tension or thermal diffusion. We show that the channel confinement can induce ‘diffusion’-like stabilising effects on viscous fingering even in the absence of interfacial tension and thermal diffusion, when a clear oil invades the mixture of the same oil and non-colloidal particles. The key lies in the generation of long-range dipolar disturbance flows by highly confined particles that form a monolayer inside a Hele-Shaw cell. We develop a coarse-grained model whose results correctly predict universal fingering dynamics that is independent of particle concentrations. This new mechanism offers insights into manipulating and harnessing collective motion in non-equilibrium systems.

We present an experimental study on the effects of polymer additives on the turbulent/non-turbulent interface (TNTI) in a fully developed round water jet. The Reynolds number based on the jet diameter is fixed at $Re=7075$. The Weissenberg number $Wi$ ranges from 24 to 86. We employ time-resolved simultaneous particle image velocimetry and laser-induced fluorescence measurements to investigate the local entrainment and engulfment process along the TNTI in two regimes: entrainment transition and enhancement regimes. In polymer-laden jets, the TNTI fluctuates more intermittently in the radial direction and more ambient fluid can be engulfed into the turbulent region due to the augmented large scale motion. Though the contribution of engulfment to the total flux increases with $Wi$, engulfment is still not the major contribution to the entrainment in polymer-laden jets. We further show that the local entrainment velocity is increased in both regimes compared with the pure water jet, due to two contributions: polymer elastic stress and the more intermittent character of the TNTI. In the entrainment transition regime, we observe smaller fractal dimension and shorter length of TNTI compared with the Newtonian case, consistent with previous numerical simulations (Abreu et al. J. Fluid Mech. vol. 934, 2022, A36); whereas those in the enhancement regime remain largely unchanged. The difference between the two regimes results from the fact that the jet flow decays in the streamwise direction. In the entrainment transition regime, turbulence intensity is strong enough to significantly stretch the polymers, resulting in a smoother TNTI in the inertial range. However, in the entrainment enhancement regime, the polymer’s feedback is not strong enough to alter the fractal dimension due to the low elasticity. The above mentioned differences of entrainment velocity and TNTI in the entrainment reduction/transition and enhancement regimes also explain the reduced and enhanced spreading rate of the viscoelastic jet observed in previous numerical simulations and experiments (Guimarães et al. J. Fluid Mech. 2020,vol. 899, A11; Peng et al. Phys. Fluids, 2023, vol. 35, 045110).

From anthropogenic litter carried by ocean currents to plant stems travelling through the atmosphere, geophysical flows are often seeded with elongated, fibre-like particles. In this study, we used a large-scale laboratory model of a tidal current – representative of a widespread class of geophysical flows – to investigate the tumbling motion of long, slender and floating fibres in the complex turbulence generated by flow interactions with a tidal inlet. Despite the non-stationary, non-homogeneous and anisotropic nature of this turbulence, we find that long fibres statistically rotate at the same frequency as eddies of similar size, a phenomenon called scale selection, which is known to occur in ideal turbulence. Furthermore, we report that the signal of the instantaneous transverse velocity difference between the fibre ends changes significantly from the signal produced by the flow in the fibre surroundings, although the two are statistically equivalent. These observations have twofold implications. On the one hand, they confirm the reliability of using the end-to-end velocity signal of rigid fibres to probe the two-point transverse statistics of the flow, even under realistic conditions: oceanographers could exploit this observation to measure transverse velocity differences through elongated floats in the field, where superdiffusion complicates collecting sufficient data to probe two-point turbulence statistics at a fixed separation effectively. On the other hand, by addressing the dynamics of inertial range particles floating in the coastal zone, these observations are crucial to improving our ability to predict the fate of meso- and macro-litter, a size class that is currently understudied.

We study theoretically and experimentally the propagation of two bubbles in a Hele-Shaw cell under a uniform background flow. We consider the regime where the bubbles are large enough to be flattened by the cell walls into a pancake-like shape, but small enough such that each bubble remains approximately circular when viewed from above. In a system of two bubbles of different radii, if the smaller bubble is in front, it will be overtaken by the larger bubble. Under certain circumstances, the bubbles may avoid collision by rolling over one another while passing. We find that, for a given ratio of the bubble radii, there exists a critical value of a dimensionless parameter (the Bretherton parameter) above which the two bubbles will never collide, regardless of their relative size and initial transverse offset, provided they are initially well separated in the direction of the background flow. Additionally, we determine the corrections to the bubble shape from circular for two bubbles aligned with the flow direction. We find that the front bubble flattens in the flow direction, while the rear bubble elongates. These shape changes are associated with changes in velocity, which allow the rear bubble to catch the bubble in front even when they are of the same size.

A previously developed modelling procedure for large eddy simulations (LESs) is extended to allow physical space implementations for inhomogeneous flows. The method is inspired by the well-established theoretical analyses and numerical investigations of homogeneous isotropic turbulence. A general procedure that focuses on recovering the full subgrid scale (SGS) dissipation from resolved fields is formulated, combining the advantages of both the structural and the functional strategy of SGS modelling. The interscale energy transfer is obtained from the test-filtered velocity field, corresponding to the subfilter scale (SFS) stress, or, equivalently, the similarity model is used to compute the total SGS dissipation. The energy transfer is then cast in the form of eddy viscosity, allowing the method to retain the desired total SGS dissipation in low resolution LES runs. The procedure also exhibits backscatter without causing numerical instabilities. The new approach is general and self-contained, working well for different filtering kernels, Reynolds numbers and grid resolutions.

Complex materials with internal microstructure such as suspensions and emulsions exhibit time-dependent rheology characterised by viscoelasticity and thixotropy. In many large-scale applications such as turbulent pipe flow, the elastic response occurs on a much shorter time scale than the thixotropy, hence these flows are purely thixotropic. The fundamental dynamics of thixotropic turbulence is poorly understood, particularly the interplay between microstructural state, rheology and turbulence structure. To address this gap, we conduct direct numerical simulations (DNS) of fully developed turbulent pipe flow of a model thixotropic (Moore) fluid as a function of the thixoviscous number $\Lambda$, which characterises the thixotropic kinetic rate relative to turbulence eddy turnover time, ranging from slow ($\Lambda \ll 1$) to fast ($\Lambda \gg 1$) kinetics. Analysis of DNS results in the Lagrangian frame shows that, as expected, in the limits of slow and fast kinetics, these time-dependent flows behave as time-independent purely viscous (generalised Newtonian) analogues. For intermediate kinetics ($\Lambda \sim 1$), the rheology is governed by a path integral of the thixotropic fading memory kernel over the distribution of Lagrangian shear history, the latter of which is modelled via a simple stochastic model for the radially non-stationary pipe flow. The DNS computations based on this effective viscosity closure exhibit excellent agreement with the fully thixotropic model for $\Lambda =1$, indicating that the purely viscous (generalised Newtonian) analogue persists for arbitrary values of $\Lambda \in (0,\infty ^+)$ and across nonlinear rheology models. These results significantly simplify our understanding of turbulent thixotropic flow, and provide insights into the structure of these complex time-dependent flows.

Deformation occurs in a thin liquid film when it is subjected to a non-uniform electric field, which is referred to as the electrohydrodynamic patterning. Due to the development of a non-uniform electrical force along the surface, the film would evolve into microstructures/nanostructures. In this work, a linear and a nonlinear model are proposed to thoroughly investigate the steady state (i.e. equilibrium state) of the electrohydrodynamic deformation of thin liquid film. It is found that the deformation is closely dependent on the electric Bond number BoE. Interestingly, when BoE is larger than a critical value, the film would be deformed remarkably and get in contact with the top template. To model the ‘contact’ between the liquid film and the solid template, the disjoining pressure is incorporated into the numerical model. From the nonlinear numerical model, a hysteresis deformation is revealed, i.e. the film may have different equilibrium states depending on whether the voltage is increased or decreased. To analyse the stability of these multiple equilibrium states, the Lyapunov functional is employed to characterise the system’s free energy. According to the Lyapunov functional analysis, at most three equilibrium states can be formed. Among them, one is stable, another is metastable and the third one is unstable. Finally, the model is extended to study the three-dimensional deformation of the electrohydrodynamic patterning.

This study presents a novel approach for constructing turbulence models using the kinetic Fokker–Planck equation. By leveraging the inherent similarities between Brownian motion and turbulent dynamics, we formulate a Fokker–Planck equation tailored for turbulence at the hydrodynamic level. In this model, turbulent energy plays a role analogous to temperature in molecular thermodynamics, and the large-scale structures are characterised by a turbulent relaxation time. This model aligns with the framework of Pope’s generalised Langevin model, with the first moment recovering the Reynolds-averaged Navier–Stokes (RANS) equations, and the second moment yielding a partially modelled Reynolds stress transport equation. Utilising the Chapman–Enskog expansion, we derive asymptotic solutions for this turbulent Fokker–Planck equation. With an appropriate choice of relaxation time, we obtain a linear eddy viscosity model at first order, and a quadratic Reynolds stress constitutive relationship at second order. Comparative analysis of the coefficients of the quadratic expression with typical nonlinear viscosity models reveals qualitative consistency. To further validate this kinetic-based nonlinear viscosity model, we integrate it as a RANS model within computational fluid dynamics codes, and calculate three typical cases. The results demonstrate that this quadratic eddy viscosity model outperforms the linear model and shows comparability to a cubic model for two-dimensional flows, without the introduction of ad hoc parameters in the Reynolds stress constitutive relationship.