Contact angle hysteresis and pinning at periodic defects in statics

International audienceThis article deals with the theoretical prediction of the wetting hysteresis on nonideal solid surfaces in terms of the surface heterogeneity parameters. The spatially periodical chemical heterogeneity is considered. We propose precise definitions for both the advancing and the receding contact angles for the Wilhelmy plate geometry. It is well known that in such a system, a multitude of metastable states of the liquid meniscus occurs for each different relative position of the defect pattern on the plate with respect to the liquid level. As usual, the static advancing and receding angles are assumed to be a consequence of the preceding contact line motion in the respective direction. It is shown how to select the appropriate states among all metastable states. Their selection is discussed. The proposed definitions are applicable to both the static and the dynamic contact angles on heterogeneous surfaces. The static advancing and receding angles are calculated for two examples of periodic heterogeneity patterns with sharp borders: the horizontal alternating stripes of a different wettability (studied analytically) and the doubly periodic pattern of circular defects on a homogeneous base (studied numerically). The wetting hysteresis is determined as a function of the defect density and the spatial period. A comparison with the existing results is carried out

Exact density profiles for fully asymmetric exclusion process with discrete-time dynamics

Exact density profiles in the steady state of the one-dimensional fully asymmetric simple exclusion process on semi-infinite chains are obtained in the case of forward-ordered sequential dynamics by taking the thermodynamic limit in our recent exact results for a finite chain with open boundaries. The corresponding results for sublattice parallel dynamics follow from the relationship obtained by Rajewsky and Schreckenberg [Physica A 245, 139 (1997)] and for parallel dynamics from the mapping found by Evans, Rajewsky and Speer [J. Stat. Phys. 95, 45 (1999)]. By comparing the asymptotic results appropriate for parallel update with those published in the latter paper, we correct some technical errors in the final results given there.Comment: About 10 pages and 3 figures, new references are added and a comparison is made with the results by de Gier and Nienhuis [Phys. Rev. E 59, 4899(1999)

Определяне на динамичния контактен ъгъл чрез профила на менискуса

Станимир Д. Илиев, Нина Хр. Пешева - Представен е хибриден експериментално-числен метод, работещ в реално време, за определяне на макроскопичния динамичен контактен ъгъл, който менискусът на течност в съд формира с вертикална пластина, която се потапя или издърпва с постоянна скорост от съда с течността. Този метод е приложим, когато системата е в стационарно състояние. Методът се базира на пълния хидродинамичен модел на Войнов. Той позволява да се получи числено с висока точност стационарната форма на профила на динамичния менискус (и от там ъгълът на наклон на менискуса) като се използва като гранично условие експериментално определената височина на менискуса на пластината.We present here a real time hybrid experimental/numerical method for determination of the macroscopic dynamic contact angle which the liquid meniscus forms with a withdrawing/immersing at constant speed vertical solid plate partially immersed in a thank of liquid when the system is in a stationary state. This method is based on the full hydrodynamic model of Voinov. It allows one to obtain numerically with high precision the stationary shape of the dynamic meniscus profile (and from there the angle of the meniscus slope) using as boundary condition the experimentally determined meniscus height. *2000 Mathematics Subject Classification: 76A05, 76B45.S. I. has received financial support from the NSF-Bulgaria under grant number DO 02 75/08

Wetting of doubly periodic rough surfaces in Wenzel’s regime

In this work we present preliminary results from our numerical study of the shapes of a liquid meniscus in contact with doubly sinusoidal rough surfaces in Wenzel’s wetting regime. Using the full capillary model we obtain the advancing and the receding equilibrium meniscus shapes for a broad interval of surface roughness factors. 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 physical defects. We find that depending on the mutual disposition of the contact line and the lattice of periodic defects, different stick-slip behaviors of the contact line depinning mechanism appear, leading to different values of the contact angle hysteresis

Dependence of the contact line roughness exponent on the contact angle on substrates with dilute mesa defects: numerical study

We compute the roughness exponent of the averaged contact line width of a liquid on heterogeneous substrates with randomly distributed dilute defects in statics. We study the case of circular “mesa”-type defects placed on homogeneous base. The shape of the liquid meniscus and the contact line are obtained numerically, using the full capillary model when a vertical solid plate, partially dipped in a tank of liquid, is slowly withdrawing from the liquid. The obtained results imply that the contact line roughness exponent depends on the contact angle $$\theta$$, which the liquid meniscus forms with the solid homogeneous base. The roughness exponent grows when $$|\theta - 90^{\circ } |$$ decreases, and it changes from 0.5 at $$|\theta - 90^{\circ } |= 70^{\circ }$$ to 0.67 at $$|\theta - 90^{\circ } |= 0^{\circ }$$. A wide range of contact angles ($$60^{\circ }$$–$$107.5^{\circ }$$) is present, where the roughness exponent is practically constant, equal to previously obtained experimental results on the magnitude of the roughness exponent and its dependence on $$\theta$$

Wetting of doubly periodic rough surfaces in Wenzel’s regime

In this work we present preliminary results from our numerical study of the shapes of a liquid meniscus in contact with doubly sinusoidal rough surfaces in Wenzel’s wetting regime. Using the full capillary model we obtain the advancing and the receding equilibrium meniscus shapes for a broad interval of surface roughness factors. 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 physical defects. We find that depending on the mutual disposition of the contact line and the lattice of periodic defects, different stick-slip behaviors of the contact line depinning mechanism appear, leading to different values of the contact angle hysteresis