A gas bubble sitting at a liquid-gas interface can burst following the rupture of the thin liquid film separating it from the ambient, owing to the large surface energy of the resultant cavity. This bursting bubble forms capillary waves, a Worthington jet and subsequent droplets for a Newtonian liquid medium. However, rheological properties of the liquid medium like elastoviscoplasticity can greatly affect these dynamics. Using direct numerical simulations, this study exemplifies how the complex interplay between elasticity (in terms of elastic stress relaxation) and yield stress influences the transient interfacial phenomenon of bursting bubbles. We investigate how bursting dynamics depends on capillary, elastic and yield stresses by exploring the parameter space of the Deborah number ${{\textit {De}}}$ (dimensionless relaxation time of elastic stresses) and the plastocapillary number $\mathcal {J}$ (dimensionless yield-stress of the medium), delineating four distinct characteristic behaviours. Overall, we observe a non-monotonic effect of elastic stress relaxation on the jet development while plasticity of the elastoviscoplastic (EVP) medium is shown to affect primarily the jet evolution only at faster relaxation times (low ${{\textit {De}}}$). The role of elastic stresses on jet development is elucidated with the support of energy budgets identifying different modes of energy transfer within the EVP medium. The effects of elasticity on the initial progression of capillary waves and droplet formation are also studied. In passing, we study the effects of solvent-polymer viscosity ratio on bursting dynamics and show that polymer viscosity can increase the jet thickness apart from reducing the maximum height of the jet.

When a highly elastic drop of a polymer solution hits a superhydrophobic surface at a high speed, a growing tail-like filament emerges vertically from the impact spot as the contact line recedes. Notably, the ligament transitions into a balloon-like shape before detaching completely from the surface (Balloon regime). The ligament formation is attributed to liquid impalement upon impact into the surface protrusion spacing, and elastic forces due to polymers prevent ligament breakup. The detachment of the ligament happens when polymeric stresses balance or overcome the adhesion at the surface. This study shows that tuning droplet rheology and surface roughess enables droplets to rebound completely and without splashing at high impact speeds. 

 When water droplets impact solid surfaces at high velocity, they often develop radial protrusions—known as fingering instabilities—that subsequently break up during spreading and retraction, a process termed splashing. Here, we investigate the fingering dynamics of shear‑thinning viscoelastic droplets impacting superhydrophobic surfaces. At low polymer concentrations, liquid elasticity sustains the emergence of elongated fingers, while simultaneously stabilizing them against breakup, thereby suppressing splashing. In contrast, increasing polymer concentration enhances viscous damping, reducing the number of fingers and ultimately suppressing the fingering instability. Our results indicate that the onset of fingering is governed by the interplay of inertia, surface tension, and viscous stresses, while the number of fingers scales robustly with the Weber number. This highlights the dominance of inertia-capillary dynamics in our range of Weber number once the instability is triggered. Remarkably, all impact outcomes resulted in complete rebound, in contrast to previous observation for viscoelastic droplets. Finally, we employ a theoretical framework to predict the temporal evolution of the mean ligament length across polymer concentrations, providing quantitative insight into how elasticity modifies drop retraction dynamics.

Neural network models have been employed to predict the instantaneous flow close to the wall in a viscoelastic turbulent channel flow. Numerical simulation data at the wall are used to predict the instantaneous velocity fluctuations and polymeric-stress fluctuations at three different wall-normal positions in the buffer region. Such an ability of non-intrusive predictions has not been previously investigated in non-Newtonian turbulence. Our comparative analysis with reference simulation data shows that velocity fluctuations are predicted reasonably well from wall measurements in viscoelastic turbulence. The network models exhibit relatively improved accuracy in predicting quantities of interest during the hibernation intervals, facilitating a deeper understanding of the underlying physics during low-drag events. This method could be used in flow control or when only wall information is available from experiments (for example, in opaque fluids). More importantly, only velocity and pressure information can be measured experimentally, while polymeric elongation and orientation cannot be directly measured despite their importance for turbulent dynamics. We therefore study the possibility to reconstruct the polymeric-stress fields from velocity or pressure measurements in viscoelastic turbulent flows. The neural network models demonstrate a reasonably good accuracy in predicting polymeric shear stress and the trace of the polymeric stress at a given wall-normal location. The results are promising, but also underline that a lack of small scales in the input velocity fields can alter the rate of energy transfer from flow to polymers, affecting the prediction of the polymeric-stress fluctuations.

Elasto-inertial turbulence (EIT) offers a mechanism to tune fundamental flow processes using elastic instabilities by the addition of polymer to the fluid. Here, we extend this emerging paradigm to elastoviscoplastic (EVP) materials, where the interplay of elasticity and a yield stress dictates the flow dynamics. Through direct numerical simulations of channel flow, we demonstrate that a yield stress does not suppress EIT but rather reorganizes it, with the flow maintaining an EIT-like characteristic even when most of the domain is nominally unyielded. Plasticity promotes the formation of solid-like plugs and patches, weakens near-wall streaks, and non-monotonically modifies drag, while elastic stresses continue to drive fluctuations in yielded shear layers. Detailed analysis of solid-fraction statistics, first-normal-stress fields, turbulent kinetic energy spectra and budgets jointly reveal a robust elastic turbulent core where EVP stresses transition from net sinks to net sources of turbulent kinetic energy as elasticity of the material increases. The turbulent kinetic energy spectra retain inertial and elastic scaling ranges, and flow topology collapses towards quasi-two-dimensional, sheet-like structures for large elasticity of the EVP material. Together the present results identify EIT in EVP fluids as an elastic turbulent state  modified by plasticity, bridging the gap between viscoelastic EIT and high–Reynolds-number EVP turbulence and providing mechanistic insight directly relevant to controlling drag, mixing and transport in yield-stress fluids.

Accurate estimation of near-wall turbulence from limited surface measurements is critical for various practical and experimental applications; however, it remains challenging due to the complex and multiscale characteristics inherent to turbulent flows. Recent developments in data-driven methods have improved performance over traditional linear approaches, but are often limited by loss functions that primarily penalize point-wise errors. In this study, we consider a composite, spectrally informed loss function that augments the conventional mean-squared error with terms that explicitly promote statistical consistency of fluctuation levels and spectral energy distributions. This loss function is evaluated using a baseline convolutional network model, applied to direct numerical simulation datasets of turbulent open-channel flow at friction Reynolds numbers, Re_τ =180 and 550. We show that considered loss function substantially reduces reconstruction errors of near-wall fluctuation velocity fields obtained from the network model using wall-shear stress and wall-pressure data as inputs. The proposed method recovers up to a threefold improvement in reconstruction accuracy relative to baseline employing mean-squared loss, and retains energy content at small-scale structures. We further show that reconstruction accuracy is only mildly affected when the input wall signals are contaminated with 5-100% Gaussian noise, and retains energy content in small flow structures when predicting from coarse wall inputs, indicating that the trained models generalize robustly to noisy, experimentally relevant conditions. Our results demonstrate that properly designed loss functions can improve reconstruction accuracy, highlighting the importance of training strategy in achieving efficient, high-performance neural-network models for practical non-intrusive sensing applications. The present study also provides a foundation for future extensions with advanced architectures, such as generative or diffusion-based models to further improve reconstruction of turbulent flow fields in complex settings.