Multi-scale roughness and the Lotus effect: Discontinuous liquid air interfaces

Significance Statement

The interest in super-hydrophobic surfaces has risen in the past few years as witnessed in the high number of studies done on this research topic. The capacity to generate a super-hydrophobic surface is important for a number of applications. In view of these developments, in-depth understanding of the mechanism behind super-hydrophobicity is necessary for generating durable, super-hydrophobic surfaces. One of the first hypotheses advanced that multi-scale roughness is necessary for super-hydrophobicity. This hypothesis has recently been tested using a theoretical model. It has been demonstrated that multi-scale roughness is actually not essential for super-hydrophobicity per se but improves the mechanical stability of the rough layer that makes a surface super-hydrophobic.

Roughness grooves are not always identical; therefore an important question arises concerning the position of the liquid-air interface within them. A simple way to handle this would be to assume that the liquid-air interface penetrates into the grooves uniformly and is continuous. This procedure of computation can be referred to as the uniform penetration method.

Unfortunately, while it might seem proper, in the case of single roughness, to adopt the assumption of uniform liquid penetration, it may not be appropriate for multiscale roughness. The possibility of non-uniform penetration into the roughness grooves is a critical aspect that can affect the way the drop interacts with the surface.

Professor Abraham Marmur and Dr. Svetlana Kojevnikova at Technion – Israel Institute of Technology investigated effect of assuming non-uniform penetration into a simple multiscale roughness structure. They measured the quantitative difference between two approaches by the difference between the predicted contact angles. Their research work is published in Colloids and Surfaces A: Physicochemical and Engineering Aspects.

The authors considered surface topographies of one, two, and three roughness scales. The proposed theoretical model was 2-dimensional. This implies that the solid surface extends to infinity perpendicularly to the plane of the page, and so is the cylindrical drop. Previous studies indicate that 2-dimensional models result in identical qualitative conclusions as complicated, 3-dimensional models. Therefore, the authors adopted the 2-dimensional model.

The researchers used a simple model for roughness that was composed of rectangular grooves configured in up to three scales of roughness. They considered the penetration of liquid into each groove independently. They presented the quantitative results by the apparent contact angle, which was associated with the most stable state of the drop. In addition, they expressed the qualitative results in the forms of wetting regime; the roughness scales that were penetrated by the liquid.

Marmur and Kojevnikova also observed that the difference in the most stable contact angles computed by the uniform or non-uniform penetration approach is a complex function of the Young contact angle as well as the geometric attributes of the model solid surface. Computation based on the non-uniform penetration in their study led to a more stable contact angle that was up to 15% different from the value computed by the uniform penetration method. The difference between results of the two methods was more pronounced for roughness scale of higher orders.

Multi-scale roughness and the Lotus effect: Discontinuous liquid air interfaces-Advances in Engineering

About the author

Svetlana Kojevnikova received her Ph.D. degree from Technion – Israel Institute of Technology in 2005. In her thesis works, she investigated mechanism of aerosol collection by sprays of electrically charged droplets.  Since graduation, she has been involved in various academic and industrial projects. Among her research interests are theoretical modeling and numerical simulation of micro- and macro- scale continuous and dispersed multiphase flows, particle dynamics, and adhesion.  She is currently studying various aspects of the phenomenon of super-hydrophobicity with Prof. Abraham Marmur.

About the author

Abraham (Avi) Marmur received his D.Sc. in 1974 at the chemical engineering department, Technion – Israel Institute of Technology, then spent two years in Buffalo, NY as a postdoc with Eli Ruckenstein. He returned to Technion in 1976 as a faculty member and is now a Professor Emeritus. During this period, he spent two Sabbatical years, one at the University of Wisconsin, Madison, and another at the IBM Almaden Research Center. Prof. Marmur has worked and published extensively in the field of interfacial phenomena for more than forty years and has been consulting for major companies. He has also participated in many international conferences and has been active in lecturing in universities and industrial sites in many countries.

His goal is to study the fundamentals of interfacial phenomena, such as the definition of surface tension, correlations for interfacial tensions, correct ways of measuring contact angles, super-hydrophobicity, unexplored cases in nucleation, etc. In addition, he was an editor of Reviews in Chemical Engineering, and was on the advisory committee of Journal of Colloid and Interface Science, Journal of Adhesion Science and Technology, Advances in Colloid and Interface Science, Colloids and surfaces A, Scientific Reports, and Surface Innovations. At Technion, professor Marmur received awards for excellence in research and in teaching, and in 2017 he received the International Association of Advanced Materials Medal.

Selected publications:

Michal Yarom and Abraham Marmur. Capillary Condensation with a Grain of Salt. Langmuir, 2017, 33 (46), pp 13444–13450.

Michal Yarom and Abraham Marmur. Stabilization of Boiling Nuclei by Insoluble Gas: Can a Nanobubble Cloud Exist? Langmuir, 2015, 31 (28), pp 7792–7798

Abraham Marmur. Surface Tension and Adsorption without a Dividing Surface. Langmuir, 2015, 31 (46), pp 12653–12657

Yael Katsir, Gal Goldstein, Abraham Marmur. Bubble the wave or waive the bubble:Why seawater waves foam and freshwater waves do not? Colloids and Interface Science Communications, Volume 6, May 2015, Pages 9-12.


Svetlana Kojevnikova, and Abraham Marmur. Multi-scale roughness and the Lotus effect: Discontinuous liquid air interfaces. Colloids and Surfaces A: Physicochemical. Eng. Aspects, volume 521 (2017), pages 78–85.

Go To Colloids and Surfaces A: Physicochemical. Eng. Aspects,


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