Stanimir Iliev

Wetting Properties of Well-Structured Heterogeneous Substrates

We study numerically the wetting properties of model heterogeneous flat substrates. The shapes of three-dimensional liquid drops in equilibrium with such substrates in the framework of the classical capillary theory are obtained. The numerical method used for minimizing the free energy is based on the local variations approach. It has been extended here to treat chemically heterogeneous substrates with “mesa” defects, i.e., sharp boundaries between surface patches with different surface tensions. The method allows inclusion of the gravity and the line tension of the contact line as well as different constraints, e.g. the constant volume constraint. We discuss the implications for the standard and modified Cassie equations and for the interpretation of the experimental data. Two different situations arise regarding the averaging of the contact angle for the two types of substrates considered:  that with radial symmetry and that without (the dart board substrate).

Iterative method for the shape of static drops

Abstract A numerical method for the computation of equilibrium shapes of liquid drops is presented. The latter are with fixed volume and undergo surface tension and gravity. An iterative procedure to minimize the energy of the system is used. A new scheme, which directly simulates virtual displacements of the considered system is described. The method is tested by studying a sessile drop and is used to analyze the equilibrium of a drop on an inclined plane handing from a square.

Contact angle hysteresis and meniscus corrugation on randomly heterogeneous surfaces with mesa-type defects.

The results of a numerical study of the various characteristics of the static contact of a liquid meniscus with a flat but heterogeneous surface, consisting of two types of homogeneous materials, forming regularly and randomly distributed microscopic defects are presented. The solutions for the meniscus shape are obtained numerically using the full expression of the system free energy functional. The goal is to establish how the magnitude and the limits of the hysteresis interval of the equilibrium contact angle, the Cassies angle, and the contact line (CL) roughness exponent are related to the parameters, characterizing the heterogeneous surface-the equilibrium contact angles on the two materials and their fractions. We compare the results of different ways of determining the averaged contact angle on heterogeneous surfaces. We study the spread of the CL corrugation along the liquid meniscus. We compare our results with the numerical results, obtained using linearized energy functional, and also with experimental results for the CL roughness exponent. The obtained results support the conclusion that some characteristics depends on the type (regular or random) of the heterogeneity pattern.

Quasistatic relaxation of arbitrarily shaped sessile drops.

We study a spontaneous relaxation dynamics of arbitrarily shaped liquid drops on solid surfaces in the partial wetting regime. It is assumed that the energy dissipated near the contact line is much larger than that in the bulk of the fluid. We have shown rigorously in the case of quasi-static relaxation using the standard mechanical description of dissipative system dynamics that the introduction of a dissipation term proportional to the contact line length leads to the well-known local relation between the contact line velocity and the dynamic contact angle at every point of an arbitrary contact line shape. A numerical code is developed for three-dimensional drops to study the dependence of the relaxation dynamics on the initial drop shape. The available asymptotic solutions are tested against the obtained numerical data. We show how the relaxation at a given point of the contact line is influenced by the dynamics of the whole drop which is a manifestation of the nonlocal character of the contact line relaxation.

4D imaging through spray-on optics

Light fields are a powerful concept in computational imaging and a mainstay in image-based rendering; however, so far their acquisition required either carefully designed and calibrated optical systems (micro-lens arrays), or multi-camera/multi-shot settings. Here, we show that fully calibrated light field data can be obtained from a single ordinary photograph taken through a partially wetted window. Each drop of water produces a distorted view on the scene, and the challenge of recovering the unknown mapping from pixel coordinates to refracted rays in space is a severely underconstrained problem. The key idea behind our solution is to combine ray tracing and low-level image analysis techniques (extraction of 2D drop contours and locations of scene features seen through drops) with state-of-the-art drop shape simulation and an iterative refinement scheme to enforce photo-consistency across features that are seen in multiple views. This novel approach not only recovers a dense pixel-to-ray mapping, but also the refractive geometry through which the scene is observed, to high accuracy. We therefore anticipate that our inherently self-calibrating scheme might also find applications in other fields, for instance in materials science where the wetting properties of liquids on surfaces are investigated.

Contact-angle hysteresis on periodic microtextured surfaces: Strongly corrugated liquid interfaces.

We study numerically the shapes of a liquid meniscus in contact with ultrahydrophobic pillar surfaces in Cassies wetting regime, when the surface is covered with identical and periodically distributed micropillars. Using the full capillary model we obtain the advancing and the receding equilibrium meniscus shapes when the cross-sections of the pillars are both of square and circular shapes, for a broad interval of pillar concentrations. The bending of the liquid interface in the area between the pillars is studied in the framework of the full capillary model and compared to the results of the heterogeneous approximation model. The contact angle hysteresis is obtained when the three-phase contact line is located on one row (block case) or several rows (kink case) of pillars. It is found that the contact angle hysteresis is proportional to the line fraction of the contact line on pillars tops in the block case and to the surface fraction for pillar concentrations 0.1-0.5 in the kink case. The contact angle hysteresis does not depend on the shape (circular or square) of the pillars cross-section. The expression for the proportionality of the receding contact angle to the line fraction [Raj et al., Langmuir 28, 15777 (2012)LANGD50743-746310.1021/la303070s] in the case of block depinning is theoretically substantiated through the capillary force, acting on the solid plate at the meniscus contact line.