The viscoelastic fluids are usually the blends of a polymeric solute and a Newtonian solvent. In the presence of a temperature gradient, stratification of these solutes can take place via the Soret effect. Here, we investigate the classical Marangoni instability problem for a thin viscoelastic film considering this binary aspect of the fluid. The film, bounded above by a deformable free surface, is subjected to heating from below by a solid substrate. Linear stability analysis performed numerically for perturbations of finite wavelength (short-wave perturbations) reveals that both monotonic and oscillatory instabilities can emerge in this system. The interaction between the thermocapillary and solutocapillary forces in the presence of Soret diffusion is found to give rise to two different oscillatory instabilities, of which one mode was overlooked previously, even for the Newtonian binary mixtures. As a principal result of this work, we provide a complete picture of the susceptibility to different instability modes based on the model parameter values. Finally, an approximate model is developed under the framework of long-wave analysis, which can qualitatively depict the stability behaviour of the system without numerically solving the problem.
We study the Marangoni instability in a thin polymeric liquid film heated from the free surface. Polymeric solutions are usually the binary mixture of a Newtonian solvent with polymeric solute and exhibit viscoelastic behaviour. In the presence of a temperature gradient, stratification of these polymeric solutes can take place via the Soret effect, which may give rise to the solutocapillary effect at the free surface. Considering the Soret effect and incorporating the effects of gravity, here we analyse the stability characteristics of this polymeric thin film bounded between its deformable fr…
We present a theory for the self-propulsion of symmetric, half spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air-water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion-advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary cond…
We derive a general integrodifferential equation for the transient behaviour of small-amplitude capillary waves on the planar surface of a viscous fluid in the presence of the Marangoni effect. The equation is solved for an insoluble surfactant solution in concentration below the critical micelle concentration (cmc) undergoing convective-diffusive surface transport. The special case of a diffusion-driven surfactant is considered near the the critical damping wavelength. The Marangoni effect is shown to contribute to the overall damping mechanism and a first-order term correction to the critica…
We present a thermodynamically based approach to the design of models for viscoelastic fluids with stress diffusion effect. In particular, we show how to add a stress diffusion term to some standard viscoelastic rate-type models (Giesekus, FENE-P, Johnson--Segalman, Phan-Thien--Tanner and Bautista--Manero--Puig) so that the resulting models with the added stress diffusion term are thermodynamically consistent in the sense that they obey the first and the second law of thermodynamics. We point out the potential applications of the provided thermodynamical background in the study of flows of flu…
Spreading on the free surface of a complex fluid is ubiquitous in nature and industry, owing to the wide existence of complex fluids. Here we report on a fingering instability that develops during Marangoni spreading on a deep layer of polymer solution. In particular, the wavelength depends on molecular weight and concentration of the polymer solution. We use the Transmission Lattice Method to characterize the finger height at the micron scale. We model the evolution of spreading radius, involving viscoelastic and shear thinning effects, to suggest a more generalized law than the spreading of …
We study the effect of surfactant on the dynamics of a bubble bursting through an interface. We perform fully three-dimensional direct numerical simulations using a hybrid interface-tracking/level-set method accounting for surfactant-induced Marangoni stresses, sorption kinetics, and diffusive effects. We select an initial bubble shape corresponding to a large Laplace number and a vanishingly small Bond number in order to neglect gravity, and isolate the effects of surfactant on the flow. Our results demonstrate that the presence of surfactant affects the dynamics of the system through Marango…
A thermal colloid suspended in a liquid will transition from a short time ballistic motion to a long time diffusive motion. However, the transition between ballistic and diffusive motion is highly dependent on the properties and structure of the particular liquid. We directly observe a free floating tracer particle's ballistic motion and its transition to the long time regime in both a Newtonian fluid and a viscoelastic Maxwell fluid. We examine the motion of the free particle in a Newtonian fluid and demonstrate a high degree of agreement with the accepted Clercx-Schram model for motion in a …
We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in Part I [U. Thiele, S. Madruga and L. Frastia, Phys. Fluids 19, 122106 (2007)]. To this aim, the linearized bulk equations and boundary equations are solved using continuation techniques for several different cases of energetic bias at the surfaces, corresponding to linear and quadratic solutal Marangoni effects. For purely diffusive transport, an increase i…
Projection-Based Solver for Viscoelastic Stokes Flow using FFTs
Institute for Computational Physics, Universität Stuttgart（斯图加特大学计算物理研究所）；Institute for Theoretical Physics, Utrecht University（乌得勒支大学理论物理研究所）；Department of Information and Computing Sciences, Utrecht University（乌得勒支大学信息与计算科学系）
Active droplets can swim spontaneously in viscous flows as a result of the non-linear convective transport of a chemical solute produced at their surface by the Marangoni and/or phoretic flows generated by this solute's inhomogeneous distribution, provided the ratio of convective-to-diffusive solute transport, or Péclet number $\mbox{Pe}$ is large enough. As the result of their net buoyancy, active drops typically evolve at a small finite distance $d$ from rigid boundaries. Yet, existing models systematically focus on unbounded flows, ignoring the effect of the wall proximity on the intrisical…
