Interfacial flow

Interfacial flow

Nano- and microparticles at fluid interfaces

Particles driven along and across fluid interfaces

Micro- and nanoparticles readily attach to interfaces between two immiscible fluids where they minimize their free energy compared to being suspended in one of the bulk phases. The dynamics of such adsorbed particles is very different from bulk particle dynamics. For example, when a small spherical particle is driven along the interface between two fluids with high viscosity contrast, the interface becomes deformed if the three-phase contact line at the particle surface is pinned. The corresponding interface shape is displayed in the figure below. Owing to this deformation, close-by particles experience a pairwise capillary attraction.

Furthermore, a particle driven along a fluid interface experiences a drag force that depends on its contact angle (determining the degree of immersion in the two fluids) and the viscosity of the fluids. The corresponding generalization of the classical Stokes drag formula can be derived based on geometric perturbation expansions.

A small particle driven across the interface between two immiscible liquids shows a characteristic dynamics which – for small enough capillary numbers – is dominated by the wetting forces at the interface. The figure below shows a series of snapshots of a microsphere crossing a liquid-liquid interface. During that process, the particle “snaps in” to the interface, and a finite force is needed to detach it from there.

Key publications

A. Dörr and S. Hardt, Driven particles at fluid interfaces acting as capillary dipoles, J. Fluid Mech. 77 (2015), 5–26.

A. Sinha, A. K. Mollah, S. Hardt and R. Ganguly, Particle dynamics and separation at liquid–liquid interfaces, Soft Matter 9 (2013), 5438-5447.

Optically controlled Marangoni tweezers

Light is a powerful tool for the manipulation of particles on the microscale. Commonly employed optical techniques for particle manipulation are based on optical tweezers, relying on forces due to gradients in the electromagnetic field strength. In the Rayleigh regime these forces scale as the particle volume and therefore rapidly diminish with decreasing particle diameter. For this reason, the trapping and manipulation of nanoscale objects with light remains a challenge.

In that context, we propose a novel technique for the optical manipulation of particles adsorbed at a gas-liquid interface based on optically induced Marangoni flow. The method relies on photoswitchable surfactants that can be reversibly switched between two isomeric states, cis and trans. The surface tension of liquid covered with cis molecules is higher than that of a surface covered with trans molecules. When a water surface covered with the trans form of the surfactant is locally illuminated with 325 nm light, the surface tension in the illuminated region increases. The gradient in surface tension induces a Marangoni flow directed radially inward in a coordinate frame centered at the focal spot, as depicted in the figure below. The left part of the figure shows a schematic of the physical principle, while the right part shows a visualization of the resulting flow based on particle streakline velocimetry. It has been experimentally demonstrated that the optically induced Marangoni flow can be utilized to trap and manipulate microparticles adsorbed to the interface at lower light intensity than with conventional optical tweezers. The favorable force scaling with the particle diameter makes this a promising principle for the manipulation of nanoscale objects.

Key publications

S. N. Varanakkottu, S. D. George, T. Baier, S. Hardt, M. Ewald and M. Biesalski, Particle manipulation based on optically controlled free surface hydrodynamics, Angew. Chem. Int. Ed. 52 (2013), 7291-7295.

Coupled instabilities of liquid films

It is well known that liquid surfaces or liquid-liquid interfaces may become unstable, e. g. if a temperature gradient normal to the surface or a shear stress is applied. Prominent examples are the Bénard–Marangoni and the Kelvin Helmholtz instability. The corresponding phenomena may be classified as “pattern formation via self-organization”, i.e. a pattern spontaneously forms whose spatio-temporal structure is determined by intrinsic properties of the system, but not by externally imposed templates. In that context the question arises how the instabilities and the corresponding patterns are modified through the interaction between two self-organizing systems. It suggests itself that such interactions are ubiquitious in nature, and also play a role in a number of technological applications. Nevertheless, the body of research in that area appears to be relatively sparse.

We have shown that the interaction between two self-organizing systems may change the nature of the instability patterns. The figure below depicts two thermally coupled liquid films, i.e. the dynamics is governed by the heat flux between two solid surfaces at different temperatures coated by the films. The right part of the figure shows an example of a computed deformation pattern. While in the uncoupled system the individual films exhibit a stationary deformation pattern, in the thermally coupled system travelling waves can appear at the film surfaces. This demonstrates that when coupling two unstable fluid systems, qualitatively new instability modes may emerge.

Key publications

M. Vécsei, M. Dietzel and S. Hardt, Coupled self-organization: Thermal interaction between two liquid films undergoing long-wavelength instabilities, Phys. Rev. E 89 (2014), 053018.