An asymptotic theory is developed to investigate the interaction of surface water waves and a compressible muddy seabed in water of intermediate depth. The water column is treated as inviscid outside a thin bottom boundary layer, the thickness of which is assumed to be of the same order of magnitude as the wave amplitude. The seabed is modelled as an isotropic and homogeneous poro-viscoelastic layer with an incompressible solid skeleton and a compressible pore fluid. The thickness of the seabed is assumed to be comparable to the wave amplitude. Using a perturbation approach, the leading-order analytical solutions for the wave and mud flow are derived, while the evolution of the wave envelope, the mean Eulerian velocity and the mass transport velocity beneath progressive waves are obtained at the second order. Based on the present solution, the wave motion and the induced mass transport are analysed and compared with previous solutions that ignore the compressibility of the seabed. The results demonstrate that the compressibility of the seabed plays a critical role in modulating the flows within both the seabed and the overlying bottom boundary layer. Neglecting compressibility may lead to an underestimation of the interface vertical displacement in highly elastic beds and an overestimation in viscous-dominated cases. Consequently, the Reynolds stress distributions in these regions deviate significantly from predictions based on incompressible seabed theory. This inaccuracy further propagates to the prediction of second-order steady currents and mass transport velocities.

Electrohydrodynamic (EHD) instabilities at polymer–porous interfaces play a pivotal role in determining interfacial morphology, wettability and pattern formation, with implications for energy storage, diagnostics and flexible electronics. This study presents a comprehensive general linear stability analysis to examine electric-field-induced instabilities at a confined interface between a viscoelastic polymer gel and a saturated porous medium. By coupling Maxwell stresses with a modified Darcy–Brinkman–Kelvin–Voigt framework, the model captures how porous medium-moderated EHD instabilities influence both the onset and dominant instability modes. Key parameters – including the electric Rayleigh number, Darcy number, dielectric contrast and geometric filling ratio – govern the spatio-temporal features of emerging patterns. The analysis reveals a sigmoidal dependence of characteristic length and time scales on permeability, i.e. Darcy number, establishing three regimes: impermeable, transitional and highly permeable, with a shift toward shorter wavelengths. The length and time scale transitions, triggered by the solid-saturated porous medium, are further moderated by the dielectric contrast – instabilities are suppressed when the contrast is low and amplified when it is high, enabling sub-micron patterning. Geometric confinement, i.e. increasing filling ratio, further intensifies pattern length scales, suggesting the feasibility of fabricating complex ultra-fine nanoscale encapsulated porous patterns. The elasticity of the viscoelastic layer imposes a threshold for instability onset and is critical for identifying wettability transitions at the interface. This framework offers predictive insight into tuning instability modes through permeability–viscoelasticity–electrostatics interplay, laying the foundation for wettability-controlled interfaces and self-organised interfacial patterns in next-generation EHD-driven systems.

We experimentally study a scallop-like swimmer with reciprocally flapping wings in a nearly frictionless, cohesive granular medium consisting of hydrogel spheres. Significant locomotion is found when the swimmer’s flapping frequency matches the inverse relaxation time of the material. Remarkably, the swimmer moves in the opposite direction compared with its motion in a cohesion-free granular material of hard plastic spheres. At higher or lower frequencies, we observe no motion of the swimmer, apart from a short initial transient phase. X-ray radiograms reveal that the wing motions create low-density zones, which in turn give rise to a hysteresis in drag and propulsion forces. This time-dependent effect, combined with the swimmer’s inertia, accounts for locomotion at intermediate frequencies.

We examine elastic travelling-wave (‘arrowhead’) solutions in a viscoelastic, unidirectionally body-forced flow, focusing on their existence and morphological changes as the Weissenberg number ${\textit{Wi}}$ and streamwise duct length $L$ are varied. We find that, First, branch topology varies from an isola at low $L$ through a two-sided reconnection at intermediate $L$ to a branch that exists at asymptotically large ${\textit{Wi}}$ for larger $L$. At intermediate $L$, more than two arrowhead solutions can coexist at a given $({\textit{Wi}},L)$ choice due to extra saddle–node bifurcations. Second, the canonical arrowhead consists of two legs joined by an arched head that blocks throughflow and traps a counter-rotating vortex pair, while a polymer strand can emerge as a by-product of a strong extensional region attached to/detached from the arrowhead arch. Third, a minimal domain length $L_{min }$ required to sustain an arrowhead is found to vary non-monotonically with ${\textit{Wi}}$; for ${{\textit{Wi}}}\geqslant 20$, detached-strand states control $L_{min }$ with a relation $L_{min }\approx 0.125\,{{\textit{Wi}}}+1.5$. And fourth, in sufficiently long domains, the upper branch becomes a localised single arrowhead whose streamwise extent depends on ${\textit{Wi}}$, whereas the lower branch can proliferate into a train of arrowheads at high ${\textit{Wi}}$, a phenomenon not previously reported.

Spatial linear instability analysis is employed to investigate the instability of a viscoelastic liquid jet in a co-flowing gas stream. The theoretical model incorporates a non-uniform axial base profile represented by a hyperbolic tangent, capturing the shear layer. The Oldroyd-B model discretised with Chebyshev polynomials is employed, and energy budget analysis is used to interpret underlying mechanisms. At low Weber numbers, the jet evolves axisymmetrically and the instability is governed by interfacial gas-pressure fluctuations; as the Weber number increases, the growing inertia drives a transition of the predominant mode from axisymmetric to helical. At weak elasticity, the instability is also primarily governed by gas-pressure fluctuations. As elasticity increases, the predominant mode transitions from axisymmetric to helical. This transition is accompanied by a migration of disturbance structures from the interface toward the jet interior and an enhanced coupling between velocity perturbation and the basic flow. These trends reveal a new predominant instability mechanism – the elasticity-enhanced shear-driven instability – which is distinct from capillary or Kelvin–Helmholtz instabilities in Newtonian jets. A $\textit{We}$–$El$ phase diagram delineates the boundary between predominant modes and experimental results obtained in a flow-focusing configuration validate the theoretical predictions. Compared with temporal stability results, the spatial framework – by directly resolving the convective downstream amplification of disturbances – achieves quantitative agreement with experiments and highlights the superiority of spatial instability analysis in capturing the dynamics of strongly convective, non-parallel jet flows. These findings provide mechanistic insight into viscoelastic jet instabilities and offer guidance for applications involving droplet and fibre formation in co-flow systems.

Camassa et al. (J. Fluid Mech. 745, 2014, 682–715) demonstrated excellent agreement between the theoretical predictions using the longwave equation and experimental observations for the absolute instability-induced plug formation in the gravity-driven flow of a liquid coating the inner surface of a tube. A similar flow of airway surface liquid (ASL) exists in the proximal airways, driven by the turbulent airflow in addition to gravity. Motivated by the conclusions of previous studies, we probe for the existence of absolute instability in the proximal airways in the present study to determine plug formation and subsequent airway closure by considering ASL elasticity, cylindrical flow geometry and the effect of inhaled air temperature. To accomplish this, we derive a longwave evolution equation, which is then used to obtain the dispersion relation. In contradistinction to the distal airways, the analysis predicts the absence of absolute instability-induced airway closure in the proximal airways for a healthy lung. However, an increased ASL thickness and/or elasticity due to excessive secretion of mucus and mucins in a diseased lung could lead to airway closure due to ASL plugs. Furthermore, inhaling colder air (than body temperature) enhances the absolute instability region, and the opposite is true for inhaling warmer air (than body temperature). For lungs with increased ASL thickness (due to diseases), plug formation is aggravated by colder air inhalation, thus demonstrating that inhaling colder (warmer) air is detrimental (beneficial) for diseased lungs. The predictions of the present analysis are in agreement with clinical observations.

Taylor dispersion of a solute in a pulsatile flow of a viscoelastic fluid, whose constitutive equation follows the Maxwell model, through an eccentric annulus is investigated in this work. To determine the effective dispersion coefficient, $\mathscr{D}_{\textit{eff}}$, we have used the multiple-scale analysis in conjunction with the homogenization method. The governing equation describing this dispersive phenomenon for solute concentration is the advection-diffusion equation, which depends on the velocity profile. Therefore, the momentum equation must be solved in advance. A hyperbolic partial differential equation in a bipolar coordinate system was derived by combining the Cauchy momentum equation with Maxwell’s constitutive equation. Parameters such as the Womersley number, ${\textit{Wo}}$, and the Deborah number, ${\textit{De}}$, control the time-dependent flow and viscoelasticity, respectively. For low Womersley numbers, i.e. for low frequencies, an increase in the Deborah number, the eccentricity, $\phi$, and gap width, $\gamma$, leads to an enhancement of the effective dispersion coefficient. For instance, a fluid with ${\textit{De}} = 5$ could increase $\mathscr{D}_{\textit{eff}}$ by two orders of magnitude compared with a Newtonian fluid with the same settings ($\phi = 0.3$ and ${\textit{Wo}} = 0.1$). However, this enhancement due to the viscoelastic effect is only significant at low frequencies. An advection-diffusion equation for the mean concentration in the cross-section was also derived and evaluated in the same low-frequency limit. It was concluded that pulsatile flow maximises the axial dispersion compared with steady and purely oscillatory flows.

While studying soap film bursting to validate their opening velocity, i.e. the Taylor–Culick velocity, Mysels and co-workers discovered fifty years ago a compression region propagating in front of the hole that they called the aureole. In the wake of such a discovery, a series of papers ‘Bursting of soap films’ focused on the study of such peculiar Marangoni flow resulting from the rapid surfactant compression. Their pioneering theory postulates that surfactants remain insoluble at the interface, leading to a self-similar process that has been verified on small films. In the present study, by using films large enough to allow the surfactant to relax, we reveal a previously unexplored regime of aureole development. The surfactants forming the aureole initially behave as if they were insoluble, with an aureole front propagating at a constant speed. After a few milliseconds, however, the front slows down until it matches the hole-opening velocity, and the aureole length then becomes constant. In this steady regime, a model taking into account surfactant advection/diffusion in the film is developed. Our theory accurately captures the thickness and velocity exponential profiles observed in experiments, demonstrating that the observed deviations arise from a balance between the surfactant rapid compression and a desorption flux. Furthermore, measurements of the characteristic aureole lengths provide estimates of physico-chemical properties of the monolayer, which are discussed in the light of predictions based on adsorption laws. The present study highlights the transition from the insoluble limit to the soluble limit, and paves the way for measurement of out-of-equilibrium dynamics of surfactants.

We investigated the influence of the slip velocity on particle migration in viscoelastic microchannel flows using a hybrid computational approach that coupled the lattice Boltzmann method with coarse-grained molecular dynamics. Our results demonstrate that the slip velocity changes lateral migration mechanisms by affecting the balance of inertial and elastic lift forces. In Newtonian fluids, forward slip drives particles toward the channel walls due to dominant inertial lift, while backward slip promotes migration toward the channel centreline. In viscoelastic fluids, however, slip-induced elastic lift forces arising from asymmetric polymer deformation around particles exceed inertial effects by an order of magnitude. This leads to a complete reversal of migration behaviour. We established that elastic lift scales linearly with the slip velocity and the block ratio, consistent with theoretical predictions, while polymer chain length influences elastic lift through a power-law dependence ($F_{e,s}^*\sim M^{1.66}$). These findings reveal that viscoelasticity-mediated slip effects provide a robust mechanism for particle manipulation in complex fluids. By connecting the microscopic polymer dynamics to macroscopic transport phenomena, our work offers new design principles for particle sorting and focusing applications in microfluidic systems.

Dynamics of spheroidal particle migration within the elasto-inertial square duct flow of Giesekus viscoelastic fluids were studied by using the direct forcing/fictitious domain method. The results show rich migration behaviours, a spheroidal particle gradually transitions from the corner (CO), channel centreline (CC), inertial rotational (IR), diagonal line and cross-section midline equilibrium positions with a decrease in the elastic number, depending on the initial particle position, initial particle orientation and fluid elasticity. From the effect of secondary flow, the IR equilibrium position is reported when the fluid inertia is relatively strong. Six (five) kinds of rotational behaviours are observed for the elasto-inertial migration of prolate (oblate) spheroids. Moreover, the critical elastic number is determined for the migration of spheroidal particles in Giesekus fluids. Near the critical elastic number, oblate and prolate spheroids can simultaneously maintain the CC, CO and IR equilibrium positions, and the initial orientation of particles affects their final rotational modes and equilibrium positions. Through comprehensive analysis, empirical formulas governing the ability of oblate and prolate spheroids to maintain the CC equilibrium position are proposed as $\textit{Wi} = 0.055\,\textit{Re}{-0.1}$ and Wi = 0.045 Re−0.35 when n = 0.5, 0.01 ≤ Wi ≤ 1. Due to the different directions of the pressure forces acting on the particles and the forces from the first normal stress difference and the second normal stress difference, the equilibrium position in Giesekus fluids is rapidly increased by increasing the secondary flow at higher elastic numbers, which is contrary to the phenomenon observed in the Oldroyd-B fluid.

We investigate the influence of shear-thinning and viscoelasticity on turbulent drag reduction in lubricated channel flow – a configuration where a thin lubricating layer of non-Newtonian fluid facilitates the transport of a primary Newtonian fluid. Direct numerical simulations are performed in a channel flow driven by a constant mean pressure gradient at a reference shear Reynolds number $\textit{Re}_\tau = 300$. The interface between the two fluid layers is characterised by Weber number $\textit{We} = 0.5$. The fluids are assumed to have matched densities. In addition to a single-phase reference case, we analyse four configurations: a Newtonian lubrication layer, a shear-thinning Carreau fluid layer, a shear-thinning and viscoelastic FENE-P fluid layer, and a purely viscoelastic FENE-CR fluid layer. Consistent with previous findings (Roccon et al. 2019, J. Fluid Mech., vol. 863, R1), surface tension is found to induce significant drag reduction across all cases. Surprisingly, variations in the lubricating layer viscosity do not yield noticeable drag-reducing effects: the Carreau fluid, despite its lower apparent viscosity, behaves similarly to the Newtonian case. In contrast, viscoelastic effects lead to a further reduction in drag, with both the FENE-P and FENE-CR fluids demonstrating enhanced drag-reducing capabilities.

The coalescence and breakup of drops are classic examples of flows that feature singularities. The behaviour of viscoelastic fluids near these singularities is particularly intriguing – not only because of their added complexity, but also due to the unexpected responses they often exhibit. In particular, experiments have shown that the coalescence of viscoelastic sessile drops can differ significantly from that of their Newtonian counterparts, sometimes resulting in a sharply distorted interface. However, the mechanisms driving these differences in dynamics, as well as the potential influence of the contact angle are not fully known. Here, we study two different flow regimes effectively induced by varying the contact angle and demonstrate how that leads to markedly different coalescence behaviours. We show that the coalescence dynamics is effectively unaltered by viscoelasticity at small contact angles. The Deborah number, which is the ratio of the relaxation time of the polymer to the time scale of the background flow, scales as $\theta ^3$ for $\theta \ll 1$, thus rationalising the near-Newtonian response. On the other hand, it has been shown previously that viscoelasticity dramatically alters the shape of the interface during coalescence at large contact angles. We study this large contact angle limit using two-dimensional numerical simulations of the equation of motion. We show that the departure of the coalescence dynamics from the Newtonian case is a function of the Deborah number and the elastocapillary number, which is the ratio between the shear modulus of the polymer solution and the characteristic stress in the fluid.

The dispersion of solutes has been extensively studied due to its important applications in microfluidic devices for mixing, separation and other related processes. Solute dispersion in fluids can be analysed over multiple time scales; however, Taylor dispersion specifically addresses long-term behaviour, which is primarily influenced by advective dispersion. This study investigates Taylor–Aris dispersion in a viscoelastic fluid flowing through axisymmetric channels of arbitrary shape. The fluid’s rheology is described using the simplified Phan-Thien–Tanner (sPTT) model. Although the channel walls are axisymmetric, they can adopt any geometry, provided they maintain small axial slopes. Drawing inspiration from the work of Chang & Santiago (2023 J. Fluid Mech. vol. 976, p. A30) on Newtonian fluids, we have developed a governing equation for solute dynamics that accounts for the combined effects of fluid viscoelasticity, molecular diffusivity and channel geometry. This equation is expressed using key dimensionless parameters: the Weissenberg number, the Péclet number and a shape-dependent dimensionless function. Solving this model allows us to analyse the temporal evolution of the solute distribution, including its mean and variance. Our analysis shows that viscoelasticity significantly decreases the effective solute diffusivity compared with that observed in a Newtonian fluid. Additionally, we have identified a specific combination of parameters that results in zero or negative transient growth of the variance. This finding is illustrated in a phase diagram and provides a means for transient control over dispersion. We validated our results against Brownian dynamics simulations and previous literature, highlighting potential applications for the design and optimisation of microfluidic devices.

The effectiveness of polymer drag reduction by targeted injection is studied in comparison with that of a uniform concentration (or polymer ocean) in a turbulent channel flow. Direct numerical simulations are performed using a pseudo-spectral code to solve the coupled equations of a viscoelastic fluid using the finitely extensible nonlinear elastic dumbbell model with the Peterlin approximation. Light and heavy particles are used to carry the polymer in some cases, and polymer is selectively injected into specific flow regions in the other cases. Drag reduction is computed for a polymer ocean at a viscosity ratio of $\beta = 0.9$ for simulation validation, and then various methods of polymer addition at $\beta = 0.95$ are compared for their drag-reduction performance and general effect on the flow. It was found that injecting polymer directly into regions of high axial strain inside and around coherent vortical structures was the most effective at reducing drag, while injecting polymer very close to the walls was the least effective. The targeting methods achieved up to 2.5 % higher drag reduction than an equivalent polymer ocean, offering a moderate performance boost in the low drag-reduction regime.

Asymptotic flow states with limiting drag modification are explored via direct numerical simulations in a moderate-curvature viscoelastic Taylor–Couette flow of the FENE-P fluid. We show that asymptotic drag modification (ADM) states are achieved at different solvent-to-total viscosity ratios ($\beta$) by gradually increasing the Weissenberg number from 10 to 150. As $\beta$ decreases from 0.99 to 0.90, for the first time, a continuous transition pathway is realised from the maximum drag reduction to the maximum drag enhancement, revealing a complete phase diagram of the ADM states. This transition originates from the competition between Reynolds stress reduction and polymer stress development, namely, a mechanistic change in angular momentum transport. Reduced $\beta$ has been found to effectively enhance elastic instability, suppressing large-scale Taylor vortices while promoting the formation of small-scale elastic Görtler vortices. The enhancement and in turn dominance of small-scale structures result in stronger incoherent transport, facilitating efficient mixing and substantial polymer stress development that ultimately drives the AMD state transition. Further analysis of the scale-decomposed transport equation of turbulent kinetic energy reveals an inverse energy cascade in the gap centre, which is attributed to the polymer-induced energy redistribution: polymers extract more energy from large scales than they can dissipate, with the excess energy redirected to smaller scales. However, the energy accumulating at smaller scales cannot be dissipated immediately and is consequently transferred back to larger scales via nonlinear interactions, thereby unravelling a novel polymer-mediated cycle for the reverse energy cascade. Overall, this study unravels the challenging puzzle of the existence of distinct dynamically connected ADM states and paves the way for coordinated experimental, simulation and theoretical studies of transition pathways to desired ADM states.

The inertial migration of neutrally buoyant spherical particles in viscoelastic fluids flowing through square channels is experimentally and numerically studied. In the experiments, using dilute aqueous solutions of polymers with various concentrations that have nearly constant viscosities, we measured the distribution of suspended particles in downstream cross-sections for the Reynolds number ($\textit{Re}$) up to 100 and the elasticity number ($El$) up to 0.07. There are several focusing patterns of the particles, such as four-point focusing near the centre of the channel faces on the midlines for low $\textit{El}$ and/or high $\textit{Re}$, four-point focusing on the diagonals for medium $\textit{El}$, single-point focusing at the channel centre for relatively high $\textit{El}$ and low $\textit{Re}$, and five-point focusing near the four corners and the channel centre for high $\textit{El}$ and very low $\textit{Re}$. Among these focusing patterns, various types of particle distributions suggesting the presence of a new equilibrium position located between the midline and the diagonal, and multistable states of different equilibrium positions were observed. In general, as $\textit{El}$ increases from 0 at a constant $\textit{Re}$, the particle focusing positions shift from the midline to the diagonal in the azimuthal direction first, and then inward in the radial direction to the channel centre. These focusing patterns and their transitions were numerically well reproduced based on a FENE-P model with measured values of viscosity and relaxation time. Using the numerical results, the experimentally observed focusing patterns of particles are elucidated in terms of the fluid elasticity-induced lift and the wall-induced elastic lift.

Experimental studies of natural convection in yield stress fluids have revealed transient behaviours that contradict predictions from viscoplastic models. For example, at a sufficiently large yield stress, these models predict complete motionlessness; below a critical value, yielding and motion onset can be delayed in viscoplastic models. In both cases, however, experiments observe immediate motion onset. We present numerical simulations of the transient natural convection of elastoviscoplastic (EVP) fluids in a square cavity with differentially heated side walls, exploring the role of elasticity in reconciling theoretical predictions with experimental observations. We consider motion onset in EVP fluids under two initial temperature distributions: (i) a linear distribution characteristic of steady pure conduction, and (ii) a uniform distribution representative of experimental conditions. The Saramito EVP model exhibits an asymptotic behaviour similar to the Kelvin-Voigt model as $t\to 0^+$, where material behaviour is primarily governed by elasticity and solvent viscosity. The distinction between motion onset and yielding, a hallmark of EVP models, is the key feature that bridges theoretical predictions with experimental observations. While motion onset is consistently immediate (as seen in experiments), yielding occurs with a delay (as predicted by viscoplastic models). Scaling analysis suggests that this delay varies logarithmically with the yield stress and is inversely proportional to the elastic modulus. The intensity of the initial pre-yield motion increases with higher yield stress and lower elastic modulus. The observed dynamics resemble those of under- and partially over-damped systems, with a power-law fit providing an excellent match for the variation of oscillation frequency with the elastic modulus.

The Weissenberg effect, or rod-climbing phenomenon, occurs in non-Newtonian fluids where the fluid interface ascends along a rotating rod. Despite its prominence, theoretical insights into this phenomenon remain limited. In earlier work, Joseph & Fosdick (1973, Arch. Rat. Mech. Anal. vol. 49, pp. 321–380) employed domain perturbation methods for second-order fluids to determine the equilibrium interface height by expanding solutions based on the rotation speed. In this work, we investigate the time-dependent interface height through asymptotic analysis with dimensionless variables and equations using the Giesekus model. We begin by neglecting inertia to focus on the interaction between gravity, viscoelasticity and surface tension. In the small-deformation scenario, the governing equations indicate the presence of a boundary layer in time, where the interface rises rapidly over a short time scale before gradually approaching a steady state. By employing a stretched time variable, we derive the transient velocity field and corresponding interface shape on this short time scale, and recover the steady-state shape on a longer time scale. In contrast to the work of Joseph and Fosdick, which used the method of successive approximations to determine the steady shape of the interface, we explicitly derive the interface shape for both steady and transient cases. Subsequently, we reintroduce small but finite inertial effects to investigate their interaction with viscoelasticity, and propose a criterion for determining the conditions under which rod climbing occurs. Through numerical computations, we obtain the transient interface shapes, highlighting the interplay between time-dependent viscoelastic and inertial effects.

Investigations into the effects of polymers on small-scale statistics and flow patterns were conducted in a turbulent von Kármán swirling (VKS) flow. We employed the tomographic particle image velocimetry technique to obtain full information on three-dimensional velocity data, allowing us to effectively resolve dissipation scales. Under varying Reynolds numbers ($R_\lambda =168{-}235$) and polymer concentrations ($\phi =0{-}25\ {\textrm{ppm}}$), we measured the velocity gradient tensor (VGT) and related quantities. Our findings reveal that the ensemble average and probability density function (PDF) of VGT invariants, which represent turbulent dissipation and enstrophy along with their generation terms, are suppressed as polymer concentration increases. Notably, the joint PDFs of the invariants of VGT, which characterise local flow patterns, exhibited significant changes. Specifically, the third-order invariants, especially the local vortex stretching, are greatly suppressed, and strong events of dissipation and enstrophy coexist in space. The local flow pattern tends to be two-dimensional, where the eigenvalues of the rate-of-strain tensor satisfy a ratio $1:0:-1$, and the vorticity aligns with the intermediate eigenvector of the rate-of-strain tensor, while it is perpendicular to the other two. We find that these statistics observations can be well described by the vortex sheet model. Moreover, we find that these vortex sheet structures align with the symmetry axis of the VKS system, and orient randomly in the horizontal plane. Further investigation, including flow visualisation and conditional statistics on vorticity, confirms the presence of vortex sheet structures in turbulent flows with polymer additions. Our results establish a link between single-point statistics and small-scale flow topology, shedding light on the previously overlooked small-scale structures in polymeric turbulence.

We investigate theoretically the breakup dynamics of an elasto-visco-plastic filament surrounded by an inert gas. The filament is initially placed between two coaxial disks, and the upper disk is suddenly pulled away, inducing deformation due to both constant stretching and capillary forces. We model the rheological response of the material with the Saramito–Herschel–Bulkley (SHB) model. Assuming axial symmetry, the mass and momentum balance equations, along with the constitutive equation, are solved using the finite element framework PEGAFEM-V, enhanced with adaptive mesh refinement with an underlying elliptic mesh generation algorithm. As the minimum radius decreases, the breakup dynamics accelerates significantly. We demonstrate that the evolution of the minimum radius, velocity and axial stress follow a power-law scaling, with the corresponding exponent depending on the SHB shear-thinning parameter, $n$. The scaling exponents obtained from our axisymmetric simulations under creeping flow are verified through asymptotic analysis of the slender filament equations. Our findings reveal three distinct breakup regimes: (a) elasto-plastic, (b) elasto-plasto-capillary, both with finite-time breakup for $n\lt 1$, and (c) elasto-plasto-capillary with no finite-time breakup for $n=1$. We show that self-similar solutions close to filament breakup can be achieved by appropriate rescaling of length, velocity and stress. Notably, the effect of the yield stress becomes negligible in the late stages of breakup due to the local dominance of high elastic stresses. Moreover, the scaling exponents are independent of elasticity, resembling the breakup behaviour of finite extensible viscoelastic materials.