Equilibrium of droplets on micro/nano – structured surfaces: reformulating the Young-Laplace equation

50 σ.Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Υπολογιστική Μηχανική”Η συμβατική διατύπωση της εξίσωσης Young-Laplace διέπει το ισοζύγιο δυνάμεων στην ελεύθερη επιφάνεια μιας σταγόνας, και συγκεκριμένα στη διεπιφάνεια υγρού/αέρα. Η επίδραση της διαβρεκτικότητας της στερεής επιφάνειας, στην οποία επικάθεται η σταγόνα, εισάγεται με την εφαρμογή της συνοριακής συνθήκης της γωνίας επαφής Young (θY) στη γραμμή τριπλής επαφής υγρού/στερεού/αέρα. Αν και η μεθοδολογία αυτή έχει εφαρμοστεί με επιτυχία στην ισορροπία σταγόνων σε επίπεδες και λείες στερεές επιφάνειες, στην περίπτωση των μίκρο/νάνο-δομημένων επιφανειών δεν επαρκεί. Εκεί, η σταγόνα μπορεί να σχηματίζει περισσότερες από μία τριπλές γραμμές επαφής με το στερεό, και αέρας να παγιδεύεται μεταξύ του υγρού και της στερεής επιφάνειας. Εμφανίζεται επομένως, το πρόβλημα της εφαρμογής της συνοριακής συνθήκης της γωνίας επαφής Young, σε κάθε μία γραμμή τριπλής επαφής, ο αριθμός και θέση των οποίων είναι άγνωστοι. Στην παρούσα εργασία, για τον υπολογισμό τέτοιων καταστάσεων προτείνεται μια επαναδιατύπωση της εξίσωσης Young-Laplace, η οποία διέπει τόσο τη διεπιφάνεια αέρα/υγρού (όπως γίνεται και στη συμβατική Young-Laplace), όσο και τη διεπιφάνεια υγρού/στερεού ενσωματώνοντας τις σχετικές αλληλεπιδράσεις υγρού/στερεού σε μίκρο-κλίμακα (δυνάμεις van der Waals). Επιπλέον, σε συνδυασμό με μεθόδους παραμετρικής ανάλυσης είναι εφικτός ο υπολογισμός ευσταθών και ασταθών καταστάσεων ισορροπίας καθώς επίσης και των ενεργειακών φραγμάτων που διαχωρίζουν τις ευσταθείς καταστάσεις διαβροχής. Ο υπολογισμός των ενεργειακών φραγμάτων για διάφορες γεωμετρίες μικρο-δομών μπορεί να αποτελέσει ένα σημαντικό εργαλείο για το σχεδιασμό επιφανειών που θα επιτρέπουν ή θα αποτρέπουν τη μετάβαση μεταξύ υπερυδρόφοβων και υπερυδρόφιλων καταστάσεων. Η μεθοδολογία που προτείνεται, μπορεί εύκολα να εφαρμοστεί σε στερεές επιφάνειες με τραχύτητα σύνθετης γεωμετρίας. Το μεγάλο πλεονέκτημα της μεθόδου είναι η υπολογιστική της αποδοτικότητα (σε υπολογιστικό χρόνο και πόρους) σε σύγκριση με μεσοσκοπικές προσομοιώσεις Lattice-Boltzmann ή μοριακές προσομοιώσεις που χρησιμοποιούνται συνήθως σε τέτοιες περιπτώσεις.By solving the Young Laplace equation of capillary hydrostatics one can accurately determine equilibrium shapes of droplets on relatively smooth solid surfaces. The solution, however, of the Young Laplace equation becomes tricky when a droplet is sitting on a geometrically patterned surface and multiple, and unknown a priori, three phase contact lines have to be accounted for, since air pockets are trapped beneath the liquid droplet. In this work, we propose an augmented Young-Laplace equation, in which a unified formulation for the liquid/vapor and liquid/solid interfaces is adopted, incorporating microscale interactions. This way, we bypass the implementation of the Young’s contact angle boundary condition at each three phase contact line. We demonstrate the method’s efficiency by computing equilibrium wetting states of entire droplets sitting on geometrically structured surfaces. The application of well-established parameter continuation techniques enables the tracing of stable and unstable equilibrium solution families, including the well-known Cassie-Baxter and Wenzel states. The computation of unstable solutions is necessary for the determination of energy barriers separating co-existing stable wetting states. Since energy barriers determine whether a surface facilitates or inhibits certain wetting transitions, their computation is important for many technical applications. Our continuum-level analysis can readily be applied to patterned surfaces with increased and unstructured geometric complexity, having a significant computational advantage, compared to the computationally demanding mesoscopic simulations that are usually employed for the same task.Νικόλαος Θ. Χαμάκο

Highlighting the Role of Dielectric Thickness and Surface Topography on Electrospreading Dynamics

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Connection of Intrinsic Wettability and Surface Topography with the Apparent Wetting Behavior and Adhesion Properties

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Neither Lippmann nor Young: Enabling Electrowetting Modeling on Structured Dielectric Surfaces

Aiming to illuminate mechanisms of wetting transitions on geometrically patterned surfaces induced by the electrowetting phenomenon, we present a novel modeling approach that goes beyond the limitations of the Lippmann equation and is even relieved from the implementation of the Young contact angle boundary condition. We employ the equations of the capillary electrohydrostatics augmented by a disjoining pressure term derived from an effective interface potential accounting for solid/liquid interactions. Proper parametrization of the liquid surface profile enables efficient simulation of multiple and reconfigurable three-phase contact lines (TPL) appearing when entire droplets undergo wetting transitions on patterned surfaces. The liquid/ambient and the liquid/solid interfaces are treated in a unified context tackling the assumption that the liquid profile is wedge-shaped at any three-phase contact line. In this way, electric field singularities are bypassed, allowing for accurate electric field and liquid surface profile computation, especially in the vicinity of TPLs. We found that the invariance of the microscopic contact angle in electrowetting systems is valid only for thick dielectrics, supporting published experiments. By applying our methodology to patterned dielectrics, we computed all admissible droplet equilibrium profiles, including Cassie–Baxter, Wenzel, and mixed wetting states. Mixed wetting states are computed for the first time in electrowetting systems, and their relative stability is presented in a clear and instructive way

How to Achieve Reversible Electrowetting on Superhydrophobic Surfaces

Collapse (Cassie to Wenzel) wetting transitions impede the electrostatically induced reversible modification of wettability on superhydrophobic surfaces, unless a strong external actuation (e.g., substrate heating) is applied. Here we show that collapse transitions can be prevented (the droplet remains suspended on the solid roughness protrusions) when the electrostatic force, responsible for the wetting modification, is smoothly distributed along the droplet surface. The above argument is initially established theoretically and then verified experimentally

How to Achieve Reversible Electrowetting on Superhydrophobic Surfaces

Collapse (Cassie to Wenzel) wetting transitions impede the electrostatically induced reversible modification of wettability on superhydrophobic surfaces, unless a strong external actuation (e.g., substrate heating) is applied. Here we show that collapse transitions can be prevented (the droplet remains suspended on the solid roughness protrusions) when the electrostatic force, responsible for the wetting modification, is smoothly distributed along the droplet surface. The above argument is initially established theoretically and then verified experimentally