Planform selection in Bénard-Marangoni convection: l hexagons versus g hexagons

Self-Organization Regimes Induced by Ultrafast Laser on Surfaces in the Tens of Nanometer Scales

A laser-irradiated surface is the paradigm of a self-organizing system, as coherent, aligned, chaotic, and complex patterns emerge at the microscale and even the nanoscale. A spectacular manifestation of dissipative structures consists of different types of randomly and periodically distributed nanostructures that arise from a homogeneous metal surface. The noninstantaneous response of the material reorganizes local surface topography down to tens of nanometers scale modifying long-range surface morphology on the impact scale. Under ultrafast laser irradiation with a regulated energy dose, the formation of nanopeaks, nanobumps, nanohumps and nanocavities patterns with 20–80 nm transverse size unit and up to 100 nm height are reported. We show that the use of crossed-polarized double laser pulse adds an extra dimension to the nanostructuring process as laser energy dose and multi-pulse feedback tune the energy gradient distribution, crossing critical values for surface self-organization regimes. The tiny dimensions of complex patterns are defined by the competition between the evolution of transient liquid structures generated in a cavitation process and the rapid resolidification of the surface region. Strongly influencing the light coupling, we reveal that initial surface roughness and type of roughness both play a crucial role in controlling the transient emergence of nanostructures during laser irradiation.

Sub-100 nm 2D nanopatterning on a large scale by ultrafast laser energy regulation

Coupling ultrafast light irradiation to surface nanoreliefs leads to periodic patterns, achieving record processing scales down to tens of nanometers. Driven by near-field interactions, the promising potential of the spontaneous pattern formation relies on the scaling up of one-step manufacturing processes. Here, we report the self-assembly of unconventional arrays of nanocavities of 20 nm diameter with a periodicity down to 60 nm upon ultrafast laser irradiation of a nickel surface. In stark contrast to laser-induced surface ripples, which are stochastic and suffer from a lack of regularity, the 2D patterns present an unprecedented uniformity on extreme scales. The onset of nanocavity arrays ordered in a honeycomb lattice is achieved by overcoming the anisotropic polarization response of the surface by a delayed action of cross-polarized laser pulses. The origin of this self-arrangement is identified as a manifestation of Marangoni convection instability in a nanoscale melt layer, destabilized by the laser-induced rarefaction wave.

Thermal convection in a cylinder and the problem of planform selection in an internally heated fluid layer

The paper deals with the hexagonal convective flow near the stability threshold in an internally heated fluid layer. In our previous numerical study of convection near the stability threshold in a square box with internal heat generation [Phys. Lett. A 377, 2111 (2013)]PYLAAG0375-960110.1016/j.physleta.2013.06.013 for a region of large horizontal extent, it has been shown that at small values of Prandtl number (Pr), convection sets in as a pattern of hexagonal cells with upward motion in the center (up-hexagons), whereas at large Pr, a stable flow pattern is formed by hexagonal cells with a downward motion in the center (down-hexagons). Here, we study axisymmetric convection in a cylinder as a model of motion in a single hexagonal cell. The radius of the cylinder matches the size of hexagons observed in our three-dimensional simulation. The lateral boundary of the cylinder is free and heat insulated. Horizontal bounding surfaces are rigid. The upper boundary is maintained at a constant temperature; the lower one is insulated. Two stable, steady-state motions with the upward and downward flow at the cylinder axis have been attained in calculations, irrespective of Pr. Cylindrical motion with the same direction of circulation as in the stable hexagons has a maximum temperature drop measured along the radius at the bottom of the cell. We suggest maximization of the temperature drop as a selection criterion, which determines the preferred state of motion in an internally heated fluid layer. This new selection principle is validated by the comparative analysis of the dominant nonlinear effects in low- and high-Prandtl number convection.

Stability of hexagonal patterns in Bénard-Marangoni convection

Hexagonal patterns in Bénard-Marangoni (BM) convection are studied within the framework of amplitude equations. Near threshold they can be described with Ginzburg-Landau equations that include spatial quadratic terms. The planform selection problem between hexagons and rolls is investigated by explicitly calculating the coefficients of the Ginzburg-Landau equations in terms of the parameters of the fluid. The results are compared with previous studies and with recent experiments. In particular, steady hexagons that arise near onset can become unstable as a result of long-wave instabilities. Within weakly nonlinear theory, a two-dimensional phase equation for long-wave perturbations is derived. This equation allows us to find stability regions for hexagon patterns in BM convection.

Convection in two-layer systems with an anomalous thermocapillary effect

Recently, it was found that the anomalous thermocapillary effect (the interfacial tension increases with temperature) is typical for various liquid-liquid systems. We consider the combined action of buoyancy and thermocapillary instability mechanisms in systems with an anomalous thermocapillary effect on the interface. The problem is solved in both linear and nonlinear formulations. A special type of oscillatory instability has been found and investigated.