ICAMS / Interdisciplinary Centre for Advanced Materials Simulation


Dynamic of droplets on flat substrates: lattice Boltzmann method versus analytic models

Date: 08.08.2011
Place: 20th International Conference on Discrete Simulation of Fluid Dynamics (DSFS 2011), Fargo, USA

Nasrollah Moradi
Fathollah Varnik
Ingo Steinbach

Recently, controlling droplet motion have attracted considerable interests due to their promising applications ranging from microfluidic devices to fuel cells and inkjet printing [1-4]. In this contribution, we concentrate on the steady state motion of cylindrical drops under the action of body force on a perfectly flat substrate. Despite the apparent simplicity of the problem, several issues, such as dependence of the center-of-mass velocity and the dissipation loss on the material parameters and external forcing as well as the role of droplet deformation are still not fully understood [5]. Driving a simple analytic relation, we show that as long as droplet deformation is negligible, droplet's center-of-mass velocity linearly scales with force density and is proportional to the square of the droplet radius. A variation of viscosity, on the other hand, has no influence on the shape of droplet. Consequently, center-of-mass velocity is directly proportional to the inverse of viscosity regardless of the deformation state of droplet. We employ a free-energy based lattice Boltzmann model [6-8] to investigate all these issues. In addition, a detailed study of the local dissipation loss inside droplet is also provided. A result of these investigations is that dissipation mainly occurs within a region below the droplet's center-of-mass. Using the latter observation, we propose a simple analytic expression accounting for the dependence of droplet velocity on the equilibrium contact angle. Results of computer simulations confirm the validity of this simple model [9].

[1] P. G. de Gennes, F. Brochard-Wyart and D. Quere, Capillarity andWetting Phenomena, (Springer 2004).
[2] F. Varnik et. al., J. Phys.: Condens. Matter 23(2011) 184112.
[3] M. Gross , F. Varnik and D. Rabbe , EPL 88 (2009) 26002.
[4] N. Moradi, F. Varnik and I. Steinbach, EPL 89 (2010) 26006.
[5] J. Servantie and M. Muller, J. Chem. Phys. 128 (2008) 014709.
[6] T. Lee and P. F. Fischer, Phys. Rev. E 74 (2006) 046709.
[7] T. Lee and L. Liu, Phys. Rev. E 78 (2008) 017702.
[6] M. Gross, N. Moradi, G. Zikos and F. Varnik., Phys. Rev. E 83 (2010) 017701.
[9] N. Moradi, F. Varnik and I. Steinbach,EPL 95 (2011) 44003.

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