Evaporation and condensation have been reported to be able to considerably alter the pinch-off profile of nano liquid threads. However, it is still not well understood how evaporation and condensation will impact the instability of nano liquid threads. In this article, we propose a modified stochastic lubrication equation (MSLE) that incorporates both thermal fluctuations and evaporation–condensation. We conduct stability analysis based on the MSLE and show that the curvature-dependent evaporation tends to enhance the growth of perturbations of small wavenumber but impede those with large wavenumber. For realistic fluids, the effect is actually very small. However, in a supersaturated vapour environment, condensation is dominant. Stability analysis and molecular dynamics simulations both show that the growth of the perturbations is considerably impeded by condensation. The spectrum curves of the perturbations shift to smaller wavenumber and lower magnitude. The effect of condensation becomes very significant on short nano liquid threads whose lengths are around the critical length in Rayleigh’s classic theory. Although condensation is usually a slow process, it can completely alter the stability of short liquid threads, rendering an originally unstable thread stable. Our results open up a new avenue to control the instability of nano liquid threads through environmental vapour pressure.

We present a comprehensive experimental and theoretical investigation of the evaporation dynamics of freely levitated water droplets in an upward airstream under varying temperature and relative humidity conditions, using a custom-designed wind tunnel that replicates natural rainfall scenarios. A high-speed imaging system captures the temporal evolution of morphology, shape oscillations and size reduction of the droplet undergoing evaporation. Our observations reveal that larger droplets exhibit persistent shape oscillations due to the interplay between inertia and surface tension in the presence of convective airflow, which significantly alters the evaporation rate compared with that of a stationary spherical droplet in quiescent air. To quantify the effects of air convection, complex morphology and shape oscillations of the levitated droplet at different temperatures and humidity, we develop a modified evaporation model that extends the classical $d^2$ law. This model incorporates (i) a generalised Sherwood number that accounts for the variation in Reynolds number, Schmidt number, temperature and relative humidity; and (ii) a shape factor that captures the time-averaged surface area of oscillating droplets. The model is validated against experimental findings across a wide range of droplet sizes and environmental conditions, showing excellent agreement in predicting the temporal evolution of droplet diameter and total evaporation time. Furthermore, we construct a regime map showing the variation in the lifetime of the droplet in the temperature–humidity space. The present study establishes a framework that integrates convective transport and morphological deformation, offering new insights into the microphysics of raindrop evaporation.

The integration of Artificial Intelligence (AI) into computational science (CS) and computational fluid dynamics (CFD) has raised profound epistemological debates concerning the nature of knowledge and its effectiveness in science. A central question in this discourse is whether AI can rival, or potentially surpass, the effectiveness of traditional mathematical methods in addressing the intricate challenges of CFD. In this work, I examine the concept of effectiveness within this context, highlighting the fundamental epistemological distinctions between AI-driven approaches and classical mathematical techniques. First, this analysis identifies four foundational pillars of effectiveness (PoEs) in scientific methods: (i) symmetries, which impose internal structure and coherence; (ii) scale separation, allowing specific treatments for the different scales and their interactions; (iii) sparsity, which simplifies complexity and enhances explicability; and (iv) semantic significance, which fosters abstraction, reasoning and interpretability. Yet, unlike mathematics where rigour ensures credibility by default, AI methods raise additional concerns of robustness and trust. Therefore, beyond the four PoEs, I also discuss credibility as a complementary pillar essential for the adoption of AI in the CFD community. The next critical step is to assess whether, and to what extent, AI can emulate or even outperform the roles and functions traditionally fulfilled by mathematical models. I therefore systematically review if, and how, these four pillar of effectiveness can be applied to AI-based algorithms. I show that those pillars are actually declined in a succession of technical advances that have shown promising results when using AI in CFD.

Predicting and controlling the transport of colloids in porous media is essential for a broad range of applications, from drug delivery to contaminant remediation. Chemical gradients are ubiquitous in these environments, arising from reactions, precipitation/dissolution or salinity contrasts, and can drive particle motion via diffusiophoresis. Yet our current understanding mostly comes from idealised settings with sharply imposed solute gradients, whereas in porous media, flow disorder enhances solute dispersion, and leads to diffuse solute fronts. This raises a central question: Does front dispersion suppress diffusiophoretic migration of colloids in dead-end pores, rendering the effect negligible at larger scales? We address this question using an idealised one-dimensional dead-end geometry. We derive an analytical model for the spatio-temporal evolution of colloids subjected to slowly varying solute fronts and validate it with numerical simulations and microfluidic experiments. Counterintuitively, we find that diffuseness of the solute front enhances removal from dead-end pores: although smoothing reduces instantaneous gradient magnitude, it extends the temporal extent of phoretic forcing, yielding a larger cumulative drift and higher clearance efficiency than sharp fronts. Our results highlight that solute dispersion does not weaken the phoretic migration of colloids from dead-end pores, pointing to the potential relevance of diffusiophoresis at larger scales, with implications for filtration, remediation and targeted delivery in porous media.

We investigate a nonlinear interaction between viscous fingering (VF) and phase separation (PS) in a binary fluid system within a radial Hele-Shaw cell. Through nonlinear simulations, we analyse displacement under favourable viscosity contrast, in which a more viscous fluid displaces a less viscous one, and PS may induce VF. The system undergoes PS when the concentration lies within the spinodal region, where the second derivative of free energy is negative. In the absence of viscosity contrast, the flow exhibits distinct morphologies, rings under the strongest PS conditions and droplets otherwise. A distinct composition of separated droplets results from uphill and downhill diffusion imbalances. The prominence of PS is characterised by the interfacial tension within the spinodal region, while the extent of pattern rupture is quantified by the interfacial length in the fully separated region. We identify interfacial tension as a reliable and experimentally accessible indicator of PS. It offers a practical alternative to the second derivative of free energy, which is challenging to quantify directly. We find that higher miscibility stabilises the overall pattern, as evidenced by reductions in both interfacial tension and interfacial length. In contrast, viscosity contrast plays a complex role: while a favourable viscosity contrast generally stabilises the flow by reducing interfacial length, there are specific flow conditions under which the interfacial length increases despite a weaker PS condition. Our results reveal instability patterns consistent with experimental observations, reinforcing the reliability of our findings.

This paper examines how in-plane contraction/relaxation waves applied to the walls affect a two-dimensional laminar flow in a channel. Of primary interest is how the application of such waves alters the pressure gradient required to drive a prescribed flow rate. It is shown that the waves generate a pumping effect that acts in the direction opposite to wave propagation. Depending on the exact configuration at hand, this pumping can enhance or reduce the pressure losses in the flow. Waves that propagate against the flow always reduce the pressure losses, while waves that propagate with the flow can only reduce the losses if they are sufficiently slower than the flow. It is demonstrated that a significant increase in pressure losses can be achieved when the properties of the waves align with the natural frequencies of the flow. Finally, it is shown that the pumping effect generates propulsion if one of the walls is allowed to move.