arXiv subjects

Cláudio P. Fonte

Publications and source records attributed to Cláudio P. Fonte.

8 recordsLinked to original sources

arXiv2026

Yielded-region connectivity governs the onset of gravity-driven spreading in elastoviscoplastic drops

The physical mechanisms controlling the onset of gravity-driven spreading of elastoviscoplastic drops remain unclear because yielding, elastic deformation, and viscous dissipation can occur simultaneously in different regions of the material. To isolate these mechanisms, we perform direct numerical simulations of large axisymmetric drops resting on a thin precursor layer of the same material. Each drop is first equilibrated under gravity, $g$, before being subjected to an additional constant downward acceleration of varying magnitude. The drop rheology is described by the Saramito--Herschel--Bulkley model. Once the rate of deformation becomes negligible under the enhanced forcing, the additional acceleration is removed and the drop is allowed to relax again under gravity alone, enabling the global deformation to be separated into recoverable and unrecoverable components. We find that spreading does not occur simply because some portion of the material yields locally. At low imposed accelerations, yielded regions remain confined within a predominantly solid-like viscoelastic matrix, and the resulting deformation is mostly recoverable. Appreciable spreading is observed when these yielded regions connect to form a continuous fluidised pathway from the drop interior to the free surface, allowing radial material transport. The acceleration required for this transition is governed primarily by the yield stress, whereas elasticity controls the partition between recoverable deformation and spreading by regulating the extent and spatial distribution of yielded regions.

physics.flu-dyn↗

arXiv2026

Network modelling of yield-stress fluid flow in randomly disordered porous media

Yield-stress fluid flow through porous media is governed by a strong coupling between rheology and pore-scale geometry, leading to nonlinear, non-Darcy transport and pronounced channelisation near yielding. We develop a pore-network model for Herschel-Bulkley flow in two-dimensional disordered porous media, including optional wall slip. The network is closed by a physics-based pressure-flow relation for a converging-diverging throat, so that yielding and post-yield transport emerge directly from the pore-scale fluid mechanics without fitted resistance parameters. Benchmarking against direct numerical simulations shows that the model captures both the bulk pressure drop and the evolution of the flow topology from spatially distributed transport to strongly channelised flow. The framework also captures the leading effect of wall slip, which lowers the pressure gradient required for transport and reactivates pathways that remain blocked in the no-slip case. Using the model across different porous geometries, we show that near-yield pressure losses are governed by constriction statistics rather than by an obstacle-scale length. In particular, rescaling with the domain-averaged minimum throat width collapses the plastic-dominated response across porosities, identifying the dissipation-relevant geometric scale for viscoplastic transport in this regime.

physics.flu-dyn↗

arXiv2026

Sub-Yield Dynamics in Yield-Stress Materials

The mechanical response of yield-stress materials below the yield point remains a subject of debate. Two of the most widely used constitutive models for these materials offer fundamentally conflicting views: one permits plastic flow at all stress levels, the other assumes entirely recoverable viscoelasticity below yield. Using parallel superposition rheometry, we test the sub-yield behaviour of a microgel and an emulsion. When residual slip effects are properly accounted for, both fluids exhibit bounded, periodic strain responses, offering compelling evidence that they do not flow in the studied regime. Our results indicate that the sub-yield regime is underpinned by nonlinear viscoelasticity and underscore the need for improved constitutive relations that capture such effects without treating yielding as a precursor for nonlinearity.

physics.flu-dyn↗

arXiv2025

Predicting the distribution of yield-stress fluids in branched pipe manifolds

We develop a one-dimensional network model to predict the steady-state distribution of yield-stress fluids in branched pipe manifolds under wall-slip conditions. The model accounts for major friction losses between junctions and incorporates wall slip through a power-law relation calibrated independently via capillary rheometry. Predictions from the model are validated against both bench-scale experiments and fully resolved computational fluid dynamics simulations, showing excellent agreement across a range of flow conditions. Our results demonstrate that wall slip strongly influences the uniformity of fluid distribution by modifying the relative resistance between outlet branches. Furthermore, we show that the problem can be inverted: measured distribution profiles can be used to estimate slip parameters, offering a practical method for slip characterisation without pressure measurement. This modelling framework is computationally inexpensive, robust, and adaptable to various network configurations, making it a valuable tool for the design and analysis of industrial manifold systems involving viscoplastic fluids.

physics.flu-dyn↗

arXiv2025

Uncertainty in Elastic Turbulence

Elastic turbulence can lead to to increased flow resistance, mixing and heat transfer. Its control -- either suppression or promotion -- has significant potential, and there is a concerted ongoing effort by the community to improve our understanding. Here we explore the dynamics of uncertainty in elastic turbulence, inspired by an approach recently applied to inertial turbulence in Ge et al. (2023) \textit{J. Fluid Mech.} 977:A17. We derive equations for the evolution of uncertainty measures, yielding insight on uncertainty growth mechanisms. Through numerical experiments, we identify four regimes of uncertainty evolution, characterised by I) rapid transfer to large scales, with large scale growth rates of $τ^{6}$ (where $τ$ represents time), II) a dissipative reduction of uncertainty, III) exponential growth at all scales, and IV) saturation. These regimes are governed by the interplay between advective and polymeric contributions (which tend to increase uncertainty), viscous, relaxation and dissipation effects (which reduce uncertainty), and inertial contributions. In elastic turbulence, reducing Reynolds number increases uncertainty at short times, but does not significantly influence the growth of uncertainty at later times. At late times, the growth of uncertainty increases with Weissenberg number, with decreasing polymeric diffusivity, and with the logarithm of the maximum length scale, as large flow features adjust the balance of advective and relaxation effects. These findings provide insight into the dynamics of elastic turbulence, offering a new approach for the analysis of viscoelastic flow instabilities.

physics.flu-dyn↗

arXiv2025

Large Amplitude Oscillatory Extension (LAOE) of dilute polymer solutions

This study presents an experimental framework for large amplitude oscillatory extension (LAOE) to investigate nonlinear material properties of complex fluids. Using a microfluidic optimized shape cross-slot extensional rheometer, we generate approximately homogeneous planar extensional flows driven by programmable syringe pumps operating in oscillatory or pulsatile sinusoidal modes. Micro-particle image velocimetry and simultaneous pressure drop measurements are employed to analyze the time-dependent flow field and elastic stress response. For Newtonian fluids, a linear relationship between the applied strain rate and pressure drop is observed across a wide range of oscillation amplitudes and frequencies. In contrast, dilute polymer solutions exhibit significant deviations, with excess pressure drops and divergence between average strain rates along extension and compression axes during the LAOE cycle. By spanning a broad range of Weissenberg and Deborah numbers, we identify unique Lissajous curves and critical conditions for the onset of nonlinearities under oscillatory extension. Numerical simulations, assuming homogeneous flow, underpin the experimental findings, validating the robustness of our microfluidic approach. This study demonstrates the utility of oscillatory extensional flows for probing the nonlinear rheological behavior of soft materials, offering quantitative insights into their extensional properties under nonlinear flow conditions.

physics.flu-dyn↗

arXiv2025

A new complex fluid flow phenomenon: Bubbles-on-a-String

A liquid jet plunging into a quiescent bath of the same liquid is a fundamental fluid mechanical problem underpinning a range of processes in industry and the natural world. Significant attention has been given to the study of plunging laminar Newtonian jets and the associated air entrainment that can occur. However, there have been very few (if any) studies devoted to the equivalent case for non-Newtonian viscoelastic liquids. Here we consider the laminar plunging and associated air entrainment of a shear thinning viscoelastic jet into a still bath of the same liquid. We describe a previously unreported phenomenon, that we call ``bubbles-on-a-string'' (BUoaS), consisting of multiple stable toroidal bubbles rising co-axially around the submerged jet. In a qualitative sense, this new observation is akin to an inverse version of the well-known rheological phenomenon ``beads-on-a-string''. The BUoaS phenomenon is stable and repeatable and can be reproduced to a lesser extent in Newtonian surfactant solutions, indicating that low surface tension is key, but non-Newtonian rheology seems likely to provide the most favourable conditions for the onset of the phenomenon. A full characterisation and detailed study of this behaviour with accompanying numerical simulation is to follow in an upcoming publication.

physics.flu-dyn↗

arXiv2024

Modern, Efficient, and Differentiable Transport Equation Models using JAX: Applications to Population Balance Equations

Population balance equation (PBE) models have potential to automate many engineering processes with far-reaching implications. In the pharmaceutical sector, crystallization model-based design can contribute to shortening excessive drug development timelines. Even so, two major barriers, typical of most transport equations, not just PBEs, have limited this potential. Notably, the time taken to compute a solution to these models with representative accuracy is frequently limiting. Likewise, the model construction process is often tedious and wastes valuable time, owing to the reliance on human expertise to guess constituent models from empirical data. Hybrid models promise to overcome both barriers through tight integration of neural networks with physical PBE models. Towards eliminating experimental guesswork, hybrid models facilitate determining physical relationships from data, also known as 'discovering physics'. Here, we aim to prepare for planned Scientific Machine Learning (SciML) integration through a contemporary implementation of an existing PBE algorithm, one with computational efficiency and differentiability at the forefront. To accomplish this, we utilized JAX, a cutting-edge library for accelerated computing. We showcase the speed benefits of this modern take on PBE modelling by benchmarking our solver to others we prepared using older, more widespread software. Primarily among these software tools is the ubiquitous NumPy, where we show JAX achieves up to 300x relative acceleration in PBE simulations. Our solver is also fully differentiable, which we demonstrate is the only feasible option for integrating learnable data-driven models at scale. We show that differentiability can be 40x faster for optimizing larger models than conventional approaches, which represents the key to neural network integration for physics discovery in later work.

cs.CE↗