MSE14: Collapse of elastomeric microposts driven by capillarity

Background

The dynamics of elastocapillary systems has received increasing attention in the last few years [1, 2] because of its relevance in the development of nanotechnologies, MEMS and bio-mimetic smart materials. Many fabrication processes to construct micrometric features on elastic surfaces, e.g. to obtain microchannels and filament carpets, rely on soft lithography techniques, in which a solvent is used to rinse away excess material at the final stages of the micropatterning process. With increasing miniaturisation, capillary and elastic effects become dominant, and the surface tension of the evaporating rinsing agent can induce the collapse of the desired pattern [3].

A theoretical understanding of the interplay between elastic and capillary forces in these systems is desirable as it would help to develop strategies that prevent the spoiling of surfaces with targeted properties. Moreover, due to the ubiquity of elastocapillary systems in biological and technological systems, it would constitute a natural starting point for the longer term goal of investigating the dynamics of liquid fronts on textured elastic surfaces, cilia carpets and plant leaves.

Techniques and Challenges

To tackle this problem, we will develop a 3D lattice-Boltzmann scheme to solve the Navier-Stokes equations coupled to fluid and elastic boundaries.      

The lattice-Boltzmann fluid will be modelled using the widely validated mesoscopic free-energy approach [4, 5], which allows the coexistence of liquid-vapour phases without the need for non-local interface-tracking algorithms. Elastic boundaries will be included using the immersed boundary method [6], which tracks the moving objects off the lattice-Boltzmann grid.

Results

We are currently developing the immersed boundaries in our lattice-Boltzmann model. Fig. 1 shows a drop (blue fluid) sitting between two rigid curved fibres (black lines).  Our next step will be to implement the elasticity on the fibres and the back-coupling to the lattice-Boltzmann fluid.

The Future

The full hydrodynamics simulations will provide a powerful tool to complement and extend the lubrication models currently being developed in our group, MSE10, and allow us to address questions that cannot be addressed using lubrication-type models.

References

[1] Roman, B., Bico, J.: Elasto-capillarity: deforming an elastic structure with a liquid droplet, J. Phys. Cond. Matter., 2010

[2] Liu, J.-L., Feng, X.-Q.: On elastocapillarity: A review, Acta Mech. Sin., 2012

[3] Tanaka, T., Morigami, M., Atoda, N.: Mechanism of resist pattern collapse during development process, Japan. J. Appl. Phys., 1993

[4] Swift, M.R., Osborn, W.R., Yeomans, J.M.: Lattice Boltzmann simulation of nonideal fluids, Phys. Rev. Lett., 1995

[5] Desplata, J.-C., Pagonabarraga, I., Bladon, P.: LUDWIG: A parallel lattice-Boltzmann code for complex fluids, Comput. Phys. Commun., 2001

[6] Peskin, C.S.: The immersed boundary method, Acta Numerica, 2002