Miguel Angel Herrada

We study the stability of the bubble rising in the presence of a soluble surfactant numerically and experimentally. For the range of surfactant concentrations considered, the Marangoni stress almost immobilises the interface. However, the non-zero surface velocity is crucial to understanding the surfactant behaviour. Global linear stability analysis predicts the transition to an oblique path above the threshold of the Galilei number (the bubble radius). This transition is followed by the coexistence of stationary and oscillatory instabilities as the Galilei number increases. These predictions agree with the experimental observations without any fitting parameters. We evaluate the bubble deformation, hydrostatic pressure variation and perturbed viscous stress. The perturbation of the velocity field causes a destabilising vortex in the rear of the bubble, while the perturbed viscous stress produces a torque opposing this vortex. We found that the torque significantly decreases above the critical Galilei number, which may constitute the origin of instability. The linear stability analysis and the experiments were conducted for Surfynol, which can be regarded as a fast (fast-kinetics) surfactant. Our experiments show the considerable differences between the rising of bubbles in the presence of a fast and a non-fast surfactant.

Steady tip streaming in the limit of vanishing flow rate has been experimentally and numerically documented, yet theoretical solutions describing local conical Stokes flows have remained elusive. Here, we derive approximate analytical solutions for local conical flows in liquid–liquid flow focusing scenarios, addressing the limit of negligible emitted flow rate. Our analysis demonstrates the existence of a universal relationship between the inner-to-outer liquid viscosity ratio and the cone angle, establishing the theoretical underpinning for precise control of microscopic jet formation. A posteriori comparison with previously published experiments reveals that digitised cusp-like meniscus profiles collapse quantitatively onto the predicted slender-body similarity solution. These findings pave the way for technologies that require exact manipulation of fluid flows at nearly molecular dimensions.

The breakup of viscous liquid threads is governed by a complex interplay of inertial, viscous and capillary stresses. Theoretical predictions near the point of breakup suggest the emergence of a finite-time singularity, leading to universal power laws describing the breakup, characterised by a universal prefactor. Recent stability analyses indicate that, due to the presence of complex eigenvalues, achieving similarity may only be possible through time-damped oscillations, making it unclear when and how self-similar regimes are reached for both visco-inertial and viscous regimes. In this paper, we combine experiments with unprecedented spatio-temporal resolution and highly resolved numerical simulations to investigate the evolution of the liquid free surface during the pinching of a viscous capillary bridge. We experimentally show for the first time that, for viscous fluids the approach to the self-similar solution is composed of a large overshoot of the instantaneous shrinking speed before the system converges to the nonlinear pinch-off similarity solution. In the visco-inertial case, the convergence to the stable solution is oscillatory, whereas in the viscous case, the approach to singularity is monotonic. While our experimental and numerical results are in good agreement in the viscous regime, systematic differences emerge in the visco-inertial regime, potentially because of effects such as polymer polydispersity, which are not incorporated into our numerical model.

The linear stability of an elongated axisymmetric gas bubble transported by a liquid in a capillary tube is analyzed through the use of numerical simulations. The study focuses on the influence of inertia, characterized by the Reynolds number ( Re ) and the imposed flow rate, characterized by a capillary number ( Ca l ), on the stability of the bubble tail, which exhibits ripples at high Re. The numerical approach utilizes a boundary-fitted method in a reference frame anchored to the bubble, combined with a mixed spatial discretization based on spectral collocation in the radial direction and finite differences in the axial direction. This framework enables the computation of steady nonlinear solutions through a Newton iteration scheme and facilitates the linear stability analysis of these solutions. Direct numerical simulations using the volume of fluid method in OpenFOAM are also performed to corroborate the results of the stability analysis. We perform systematic simulations for Ca l = 0.005 − 0.04 and observe that the system becomes unstable, with the emergence of oscillations at the rear of the bubble, when the Reynolds number grows above a critical value, designated as Re * ; this critical value is dependent on the capillary number. The instability is due to the increased inertia of the recirculating flow in the liquid behind the bubble, which impinges its rear meniscus. A modified Weber number We p , based on the relative velocity between the external flow and the bubble, is introduced to describe the competition between the destabilizing pressure force acting on the bubble rear and surface tension. Our results show that the bubble dynamics become unstable for a critical value, We p * ≈ 3.65 , which remains quite uniform across the range of capillary numbers tested, and divides the Ca l − Re diagram into stable and unstable regimes. Our findings offer insights into the behavior of bubbles in microfluidic applications, with implications for heat transfer, mass transfer, and cleaning processes in microchannels. Published by the American Physical Society 2025

We consider flow through a finite-length flexible-walled channel formed by removing a portion from one wall of a wide rigid channel and replacing by a pre-tensioned hyperelastic sheet of finite thickness. The flow is driven by a prescribed upstream flow rate which is uniform along the channel inlet, and so with periodic boundary conditions in the transverse direction the system admits a steady state with a wall profile which is deformed in the streamwise direction but spatially uniform in the spanwise direction. Identical to the planar case, this system exhibits two stable static configurations: an upper branch where the flexible wall is mostly inflated and a lower branch where the wall is highly collapsed. We consider the stability of these steady states to spanwise perturbations, showing that both can become unstable to distinct families of self-excited oscillations. In particular, for large spanwise wavenumbers, these steady states are unstable to oscillatory normal modes where the perturbation wall profile has a single oscillating hump in the streamwise direction, not previously seen in collapsible channel flows driven by fixed upstream flux. Furthermore, for sufficiently large wavenumbers and no wall pre-tension in the spanwise direction, this system is always unstable to a new spanwise non-uniform static configuration, which arises due to the merging of a pair of unstable oscillatory normal modes. However, with non-zero spanwise wall pre-tension, there is always a region of parameter space where the spanwise uniform steady state is stable for all wavenumbers.