Bioconvection is the prototypical active matter system for hydrodynamic instabilities and pattern formation in suspensions of biased swimming microorganisms, particularly at the dilute end of the concentration spectrum where direct cell–cell interactions are less relevant. Confinement is an inherent characteristic of such systems, including those that are naturally occurring or industrially exploited, so it is important to understand the impact of boundaries on the hydrodynamic instabilities. Despite recent interest in this area, we note that commonly adopted symmetry assumptions in the literature, such as for a vertical channel or pipe, are uncorroborated and potentially unjustified. Therefore, by employing a combination of analytical and numerical techniques, we investigate whether confinement itself can drive asymmetric plume formation in a suspension of bottom-heavy swimming microorganisms (gyrotactic cells). For a class of solutions in a vertical channel, we establish the existence of a first integral of motion, and reveal that asymptotic asymmetry is plausible. Furthermore, numerical simulations from both Lagrangian and Eulerian perspectives demonstrate with remarkable agreement that asymmetric solutions can indeed be more stable than symmetric; asymmetric solutions are, in fact, dominant for a large, practically important region of parameter space. In addition, we verify the presence of blip and varicose instabilities for an experimentally accessible parameter range. Finally, we extend our study to a vertical Hele-Shaw geometry to explore whether a simple linear drag approximation can be justified. We find that although two-dimensional bioconvective structures and associated bulk properties have some similarities with experimental observations, approximating near-wall physics in even the simplest confined systems remains challenging.

Vesicles are important surrogate structures made up of multiple phospholipids and cholesterol distributed in the form of a lipid bilayer. Tubular vesicles can undergo pearling – i.e. formation of beads on the liquid thread akin to the Rayleigh–Plateau instability. Previous studies have inspected the effects of surface tension on the pearling instabilities of single-component vesicles. In this study, we perform a linear stability analysis on a multicomponent cylindrical vesicle. We solve the Stokes equations along with the Cahn–Hilliard equation to develop the linearized dynamic equations governing the vesicle shape and surface concentration fields. This helps us to show that multicomponent vesicles can undergo pearling, buckling and wrinkling even in the absence of surface tension, which is a significantly different result from studies on single-component vesicles. This behaviour arises due to the competition between the free energies of phase separation, line tension and bending for this multi-phospholipid system. We determine the conditions under which axisymmetric and non-axisymmetric modes are dominant, and supplement our results with an energy analysis that shows the sources for these instabilities. Lastly, we delve into a weakly nonlinear analysis where we solve the nonlinear Cahn–Hilliard equation in the weak deformation limit to understand how mode-mixing alters the late time dynamics of coarsening. We show that in many situations, the trends from our simulations qualitatively match recent experiments (Yanagisawa et al., Phys. Rev. E, vol. 82, 2010, p. 051928).

Even though liquid foams are ubiquitous in everyday life and industrial processes, their ageing and eventual destruction remain a puzzling problem. Soap films are known to drain through marginal regeneration, which depends upon periodic patterns of film thickness along the rim of the film. The origin of these patterns in horizontal films (i.e. neglecting gravity) still resists theoretical modelling. In this work, we theoretically address the case of a flat horizontal film with a thickness perturbation, either positive (a bump) or negative (a groove), which is initially invariant under translation along one direction. This pattern relaxes towards a flat film by capillarity. By performing a linear stability analysis on this evolving pattern, we demonstrate that the invariance is spontaneously broken, causing the elongated thickness perturbation pattern to destabilise into a necklace of circular spots. The unstable and stable modes are derived analytically in well-defined limits, and the full evolution of the thickness profile is characterised. The original destabilisation process we identify may be relevant to explain the appearance of the marginal regeneration patterns near a meniscus and thus shed new light on soap-film drainage.

A phenomenological description is presented to explain the intermediate and low-frequency/large-scale contributions to the wall-shear-stress (${\tau }_w$) and wall-pressure ($\,{p}_w$) spectra of canonical turbulent boundary layers, both of which are well known to increase with Reynolds number, albeit in a distinct manner. The explanation is based on the concept of active and inactive motions (Townsend, J. Fluid Mech., vol. 11, issue 1, 1961, pp. 97–120) associated with the attached-eddy hypothesis. Unique data sets of simultaneously acquired ${\tau }_w$, ${p}_w$ and velocity-fluctuation time series in the log region are considered, across a friction-Reynolds-number ($Re_{\tau }$) range of $ {O}(10^3) \lesssim Re_{\tau } \lesssim {O}(10^6)$. A recently proposed energy-decomposition methodology (Deshpande et al., J. Fluid Mech., vol. 914, 2021, A5) is implemented to reveal the active and inactive contributions to the ${\tau }_w$- and $p_w$-spectra. Empirical evidence is provided in support of Bradshaw's (J. Fluid Mech., vol. 30, issue 2, 1967, pp. 241–258) hypothesis that the inactive motions are responsible for the non-local wall-ward transport of the large-scale inertia-dominated energy, which is produced in the log region by active motions. This explains the large-scale signatures in the ${\tau }_w$-spectrum, which grow with $Re_{\tau }$ despite the statistically weak signature of large-scale turbulence production, in the near-wall region. For wall pressure, active and inactive motions respectively contribute to the intermediate and large scales of the $p_w$-spectrum. Both these contributions are found to increase with increasing $Re_{\tau }$ owing to the broadening and energization of the wall-scaled (attached) eddy hierarchy. This potentially explains the rapid $Re_{\tau }$-growth of the $p_w$-spectra relative to ${\tau }_w$, given the dependence of the latter only on the inactive contributions.