We report the observation of defects with fractional topological charges (disclinations) in square and hexagonal patterns as numerical solutions of several generic equations describing many pattern-forming systems: Swift-Hohenberg equation, damped Kuramoto-Sivashinsky equation, as well as nonlinear evolution equations describing large-scale Rayleigh-Benard and Marangoni convection in systems with thermally nearly insulated boundaries. It is found that disclinations in square and hexagonal patterns can be stable when nucleated from special initial conditions. The structure of the disclinations is analyzed by means of generalized Cross-Newell equations.

We investigate the nonlinear dynamics of long-wave Marangoni convection in a 2D binary-liquid layer heated from below. Free surface deformations and the Soret effect are taken into account. We employ the set of evolution equations derived in earlier work in the case of small Galileo and Lewis numbers and solve it numerically with periodic boundary conditions. We validate our numerical solution by comparison between the results obtained via two different numerical methods, as well as by comparison with the prior analytical results. We study the transitions between the nonlinear regimes emerging at finite supercriticality values and find a rich variety of patterns. In a sufficiently large computational domain, we observe multistability of waves chaotic in time and spatially replicated periodic and quasiperiodic solutions. For sufficiently high values of the Marangoni number, we also observe a breakdown of model equations.

Linear stability theory is developed for an activator–inhibitor model where fractional derivative operators of generally different exponents act both on diffusion and reaction terms. It is shown that in the short wave limit the growth rate is a power law of the wave number with decoupled time scales for distinct anomaly exponents of the different species. With equal anomaly exponents an exact formula for the anomalous critical value of reactants diffusion coefficients' ratio is obtained.

In a binary solution of lithium bromide–water, even a small disturbance in the initial homogeneous mass fraction at the absorbing interface has profound effects on the entire system dynamics. This perturbation of absorption disrupts the equilibrium, leading to the formation of surface tension gradients and subsequently, Marangoni flows. While these flows are relatively weak, they result in a non-uniform distribution of density within the bulk, initiating buoyant convection. We investigate complexities of the Marangoni, solutal, and buoyant convection caused by localized disruptions in uniform absorption, all in the absence of any surfactants. We have conducted numerical simulations to explore fluid dynamics and heat and mass transfer, revealing three different regimes. Initially, shortly after disturbance, variations in mass fraction and flow within the cell are primarily governed by the Marangoni force. After a finite period, the emergence of buoyant convection leads to the strong growth of velocity and significant changes in temperature and mass fraction. Finally, the destabilization of the boundary layer becomes so significant that the emission of plumes is observed. At later times, the parallel existence of two types of patterns takes on a spatially fixed form. The central part, occupied by bands (visible on space-time maps), exhibits minimal changes in time, while a periodic structure is established near the wall. This behavior can be characterized as a relaxation–oscillation mode of instability.

We investigate the onset of thermosolutal instabilities in a moderately dense nanoparticle suspension layer with a deformable interface. The suspension is deposited on a solid substrate subjected to a specified constant heat flux. The Soret effect and the action of gravity are taken into account. A mathematical model for the system considered with nanoparticle concentration-dependent density, viscosity, thermal conductivity and the Soret coefficient is presented in dimensional and non-dimensional forms. Linear stability analysis of the obtained base state is carried out using disturbances in the normal mode, and the corresponding eigenvalue problem is derived and numerically investigated. The onset of various instabilities is investigated for cases of both heating and cooling at the substrate. The monotonic solutocapillary instability is found in the case of cooling at the substrate, which exhibits two competing mechanisms that belong to two different disturbance wavelength domains. We identify the occurrence of both monotonic and oscillatory thermocapillary instabilities when the system is heated at the substrate. Furthermore, we show the emergence of the solutal buoyancy instability due to density variation which is promoted by the Soret effect adding nanoparticles heavier than the carrier fluid in the proximity of the layer interface. Transitions from the monotonic to oscillatory thermocapillary instability are found with variation in the gravity- and solutocapillarity-related parameters. Notably, we identify a previously unknown transition from monotonic to the oscillatory thermocapillary instability due to the variation in the strength of the thermal-conductivity stratification coupled with the Soret effect.

We investigate the evolution of convective instability in a LiBr–water binary mixture, driven by thermal and solutal Marangoni stresses, through numerical simulations. A small perturbation in absorption at the surface disturbs the equilibrium, generating surface tension gradients that drive Marangoni flows. To isolate and better understand the interplay between the Marangoni effect and absorption, we extended the previous study by investigating the LiBr–water binary system in the absence of gravity. For the first time, we observed the formation of a stable rim in an absorbing binary mixture, which underwent a slight contraction followed by rapid Marangoni spreading. This behavior shows similarities with the flow patterns seen in the “coffee-ring” and Marangoni spreading phenomena in evaporating binary mixtures. On the subsurface, convective motion breaks into several vortices, accompanied by the formation of plumes with reduced mass fraction. As the system evolves, the symmetry of the flow pattern around the cell center breaks down. The absence of buoyancy-driven forces eliminates a key counterforce to Marangoni flows, transforming the previously ordered patterns into non-periodic oscillations, followed by the development of non-stationary but regular patterns. These results complement our earlier findings [P. F. Arroiabe et al., Phys. Fluids 36, 022119 (2024)] where gravitational forces obscured these phenomena.