Convection-Induced Patterns in Phase-Separating Polymeric Fluids

Abstract

The process of pattern formation and droplet coarsening has been studied for ternary polymeric fluids in which phase separation was induced by solvent evaporation. For a particular range of solvent evaporation rates and thicknesses of liquid layers, ordered hexagonal patterns were formed at the liquid film-air interface. We ascribe this effect to Bénard-Marangoni convection induced by solvent evaporation and estimate conditions generating periodic two-phase structures in polymeric films. Droplet coarsening rate featured a crossover from R ϳ t 0.89 to R ϳ t 0.67 coinciding with the onset of convection and was explained by convection-induced stabilization of droplets against coalescence.[S0031-9007(98)07184-1] PACS numbers: 61.25.Hq, 47.54. + r, 61.41. + e, Under particular conditions, patterns with a high degree of order and symmetry emerge in phase-separating polymeric fluids on a length scale significantly exceeding molecular dimensions [1,2]. For multicomponent liquids undergoing phase separation due to solvent evaporation, it was suggested that Bénard-Marangoni convection [3] may be a source of ordered patterns. Indeed, cooling of the top surface due to the solvent removal is similar to heating of a fluid film from below in a sense that it generates temperature gradient in a liquid layer. Fluctuations of temperature at the liquid-air interface result in local surface tension variations enhanced by the upward flow of the warmer liquid from the bulk. In a steady state, surface-tension-driven convection arises in the fluid layer.The manner in which the dynamics of phase separation and structure evolution are influenced by convection has not been studied although it is known that hydrodynamic effects play a significant role in droplet coarsening. For the cooperative action of Brownian motion and hydrodynamic interactions on the domain growth, Siggia [4] showed that hydrodynamic effects accelerate coalescence-induced coarsening to R ϳ t l , where R is a droplet mean radius, and t is a coarsening time. Furukawa [5], using coupled Navier-Stokes and Cahn-Hillard equations, predicted for 3D systems with a high Reynolds number two new growth modes that originated from a balance of the inertial forces and interfacial tension, i.e., R ϳ t n with n 1 and n 2 3 . Experimental studies of phase-separation dynamics in a gravity-dominated regime showed that flow can either enhance or suppress droplet growth, depending on a balance of viscous and sedimentation forces [6].It is reasonable to expect that involvement of droplets of a new phase in convection of the intervening liquid would generate coarsening dynamics different from that predicted and observed in a flow-dominated regime.In Bénard-Marangoni convection, pattern formation is governed by a balance of the surface-tension-driven forces and dissipation due to the thermal diffusion and the frictional action of viscosity [3]. The competition of these factors is expressed by a Marangoni numberwhere ͑≠g͞≠T ͒ is the temperature derivative of the surface tension g; DT is the dif...

Robust Self‐Assembly of Highly Ordered Complex Structures by Controlled Evaporation of Confined Microfluids

“…[1][2][3][4][5] The spatial variation of evaporative flux and possible convection mean, however, that these non-equilibrium dissipative structures (e.g., coffee rings, [6] fingering patterns, [7] and polygonal network structures [8] ) are often irregular and stochastically organized. Yet for many applications in microelectronics, data storage devices, and biotechnology, it is highly desirable to achieve surface patterns that have a well-controlled spatial arrangement.…”

Near-Field Optical Microscopy of Defects in Cholesteric Oligomeric Liquid Crystal Films

“…Both Bénard-Marangoni and buoyancy convections depend on the fact that solvent evaporation cools the liquid surface thereby increasing the surface tension as well as the density and leading to a stratification of the mixture [6,8]. Convection-induced regular patterning of PMMA and polystyrene has been obtained with the periodicity $ 3-10 mm [9,10]. Regarding our experiments, we believe, that $ 50-100-mm cellular domains may be the result of a convective motion.…”

Self-organized patterns of microparticles in polymer films

“…It is reasonable to assume that the formation of the patterns is a direct consequence of the instability driven by the evaporation of the solvent. To explain the formation of patterns under such conditions, Rayleigh-Bénard and Marangoni convection have been invoked [19,20]. Alternative mechanisms have been proposed to explain the formation of mesoscopically scaled patterns in polymer solution systems [21][22][23][24].…”