ORIGINAL CONTRIBUTION Numerical study of energetics and wetting stability of liquid droplets on microtextured surfaces Anjan Goswami 1 & Md. Ashiqur Rahman 1 Received: 2 June 2017 /Revised: 3 July 2017 /Accepted: 10 July 2017 /Published online: 21 July 2017 # Springer-Verlag GmbH Germany 2017 Abstract The suspended wetting state (Cassie-Baxter state) on a microstructured surface tends to collapse to a wetted state (Wenzel state) if the liquid-air interface is perturbed. Multiple metastable Cassie-Baxter (CB) wet- ting states, separated by an energy barrier from Wenzel state, may also exist. In this study, numerical method is applied to study the wetting properties of liquid droplets on a variety of microtextured surfaces with a particular focus on the stability of the CB wetting state. A dimen- sionless form of droplet energy is used to compare the relative stabilities of multiple metastable states. The se- quence of stable drop configurations with increasing droplet volume on a particular substrate is analyzed for both isotropic and anisotropic cases. Applying di- mensional variation, characterized by the pillar spacing and pillar width, on surface microtexture, the key pa- rameter which plays dominant role in the stability of droplet is explored. The solid-fraction that the droplet avails at the drop-base is observed to be the most vital parameter for the droplet stability. Spreading of droplet from one isotropic wetting configuration to an aniso- tropic configuration is not favorable unless the spread- ing of the droplet is restricted to be unidirectional. Keywords Interfaces . Wettability . Wetting Stability . Surface Evolver . Energetics Introduction Wettability, i.e., the hydrophobic or hydrophilic properties of a surface is characterized by the static contact angle or simply the contact angle made between the droplet’ s edge and the surface underneath it. Smooth flat surfaces with appropriate surface chemistries are found to show maximum Bintrinsic hydrophobicity^ of 120 ° [1]. By introducing roughness features (e.g., micropillars, microgrooves) on these hydrophobic surfaces, superhydrophobicity can be attained with a contact angle of greater than 150 ° [2–4]. Superhydrophobic surface has attracted significant attention due to its some noble properties, such as self- cleaning [4], anti-corrosion [5], and condensate retention capac- ity [4, 6] which facilitates many engineering applications. Wetting on rough surfaces are typically of two distinct states: Wenzel wetting state [7] and Cassie-Baxter (CB) wetting state [8]. In Wenzel wetting state, a homogeneous contact be- tween the droplet and substrate exists and the droplet enters into the asperities of the surface. CB wetting state is also known as the Bfakir state^ [9] as the droplet does not enter into the asper- ities of rough surface; rather, it sits comfortably on the top of the peaks of the surface roughness as fakirs are supposed to do on the bed of nails. Thus, a composite contact is created be- neath the droplet, i.e., liquid sits on a composite surface of air and solid. The state of superhydrophobicity on a surface is attained by increasing the contribution of CB wetting mode, which reduces the practical contact area between solid and liquid. Moreover, when the scale of the roughness features is much smaller than the deposited droplet, it generally possesses composite wetting state and the classical CB model [8] is con- sidered sufficient to describe wetting behaviors. Generally, a droplet attains equilibrium shape on a substrate by minimizing the total energy of the system and equilibrium shape confirms the wetting configuration with the minimum en- ergy. However, in practice, droplets on rough surface do not * Md. Ashiqur Rahman ashiqurrahman@me.buet.ac.bd 1 Department of Mechanical Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka 1000, Bangladesh Colloid Polym Sci (2017) 295:1787–1796 DOI 10.1007/s00396-017-4158-x