We derive an ab initio equilibrium statistical mechanics of the gas-liquid-solid contact angle on planar periodic, monodisperse, textured surfaces subject to electrowetting. To that end, we extend an earlier theory that predicts how advance or recession of the contact line amount to distinct first-order phase transitions of the filling state in the ensemble of nearby surface cavities. Upon calculating the individual capacitance of a cavity subject to the influence of its near neighbors, we show how hysteresis, which is manifested by different advancing and receding contact angles, is affected by electrowetting. The analysis reveals nine distinct regimes characterizing contact angle behavior, three of which arise only when a voltage is applied to the conductive liquid drop. As the square voltage is progressively increased, the theory elucidates how the drop occasionally undergoes regime transitions triggering jumps in the contact angle, possibly changing its hysteresis, or saturating it at a value weakly dependent on further voltage growth. To illustrate these phenomena and validate the theory, we confront its predictions with four data sets. A benefit of the theory is to forsake trial-and-error when designing textured surfaces with specific contact angle behavior.

The paper argues that universal approaches to infiltration and drainage in permeable media that pivot around capillarity and that led to dual porosity, non-equilibrium, or preferential flow need to be replaced by a dual process approach. One process has to account for relatively fast infiltration and drainage based on Newton's shear flow, while the other one is responsible for storage and relatively slow redistribution of soil water by focusing on capillarity. Already Schumacher (1864) postulated two separate processes. However, Buckingham's (1907) and Richards' (1931) apparent universal capillary-based approach to flow and storage of water in soils dominated. The paper introduces the basics of Newton's shear flow in permeable media. It presents experimental support for the four presumptions of (i) sharp wetting shock fronts; (ii) that move with constant velocities; (iii) atmospheric pressure prevails behind the wetting shock front; (iv) laminar flow. It further discusses the scale tolerance of the approach, its relationship to Darcy's (1856) law, and its extension to solute transport.

Rising humidity in old and historical buildings is a current issue that affects their structure, due to water capillarity and its propagation inside the walls, a key factor in heritage preserving and its functionality. It is also responsible for materials degradation exposed to frost and defrost cycles, biodegradation and salt crystallization. Moisture also increases the heating costs of the affected buildings, due to high thermal conductivity of the moist masonries. The paper presents an unconventional method for humidity removal or stabilisation due to infiltration of capillary water into the masonries, using electromagnetic waves systems that result in changing the water polarity inside the affected walls and pushing it out of the construction. The system consist of a small box, connected to the power supply, installed inside the building, remaining on the same location throughout the entire life of the construction. By means of this procedure, not only do the walls of the structure stay moisture-free, but also the foundations and the surrounding soil. Through this process, not only the walls of the construction remains dry, but also the foundations and the soil around them. The electromagnetic wave method was applied on five different historical buildings, located in Romania, Cluj Napoca’s historical centre, in the vicinity of Somes river, with rising damp due to water capillarity. Measurements were conducted at every six months after the system installation, for a period of minimum 24 months, using the same marked locations, at a depth of 5 cm in the walls. All buildings studied are made of stone and stone with plain brick, with different chemical, type, pore direction and porosity characteristics. The measured values show in most cases, a clear decrease of wall humidity levels or a stagnation of the capillarity rise in the monitored walls, after a minimum of 24 months after the system installation. The electromagnetic wave system, as a non-destructive method, can be applied to cases with no accidental water source or high raised groundwater, for historical buildings where no exterior works are possible or interior invasive interventions.