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Hypothesis: Understanding contact angle hysteresis on rough surfaces isimportant as most industrially relevant and naturally occurring surfacespossess some form of random or structured roughness. We hypothesise thathysteresis originates from the energy dissipation during the$\textit{stick-slip}$ motion of the contact line and that this energydissipation is key to developing a predictive equation for hysteresis.  Experiments: We measured hysteresis on surfaces with randomly distributed andperiodically arranged microscopic cylindrical pillars for a variety ofdifferent liquids in air. The inherent (flat surface) contact angles testedrange from lyophilic ($\theta_{\rm{e}}=33.8^{\circ}$) to lyophobic($\theta_{\rm{e}} = 112.0^{\circ}$).  Findings: A new methodology for calculating the average advancing andreceding contact angles on random surfaces is presented. Also, the correlationsfor roughness-induced energy dissipation were derived, and a predictiveequation for the advancing and receding contact angles during homogeneous(Wenzel) wetting on random surfaces is presented. Significantly, equations thatpredict the onset of the alternate wetting conditions of hemiwicking,split-advancing, split-receding and heterogeneous (Cassie) wetting are alsoderived, thus defining the range of validity for the derived homogeneouswetting equation. A novel feature 'cluster' concept is introduced whichexplains the measurably higher hysteresis exhibited by structured surfacescompared to random surfaces observed experimentally.

Predicting Contact Angle Hysteresis on Surfaces with Randomly and Periodically Distributed Cylindrical Pillars via Energy Dissipation