11 research outputs found
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
The electrospreading behavior of a liquid drop on a solid surface is of fundamental interest in many technological processes. Here we study the effect of the solid topography as well as the dielectric thickness on the dynamics of electrostatically-induced spreading by performing experiments and simulations. In particular, we use an efficient continuum-level modeling approach which accounts for the solid substrate and the electric field distribution coupled with the liquid interfacial shape. Although spreading dynamics depend on the solid surface topography, when voltage is applied electrospreading is independent of the geometric details of the substrate but highly depends on the solid dielectric thickness. In particular, electrospreading dynamics are accelerated with thicker dielectrics. The latter comes to be added to our recent work by Kavousanakis et al., Langmuir, 2018, which also highlights the key role of the dielectric thickness on electrowetting-related phenomena
Connection of Intrinsic Wettability and Surface Topography with the Apparent Wetting Behavior and Adhesion Properties
The need for connecting the intrinsic
material wettability with
surface geometry, adhesion to liquids, and the apparent wettability
is of primary importance when aiming to design advanced functional
materials. Here, by solving the Young−Laplace equation, augmented
with a Derjaguin pressure, we tackle the necessity for implementing
the Young angle boundary condition at the contact line, and thus we
are able to compute multiple and reconfigurable three-phase contact
lines in equilibrium. Using the finite element method and special
parameter continuation techniques, we highlight the highly nonlinear
dependence of the apparent contact angle on the Young angle, which
quantifies the material wettability. By computing equilibrium shapes
of entire droplets, we find multiple Cassie and Wenzel type states
in certain wettability regimes. We, for the first time, find a material
wettability regime where Cassie, Wenzel, and partially impregnated
states are (meta)stable. The energy barriers for transitions between
these states are computed, and their dependence on certain surface
geometric features is shown. The “rose petal effect”
as well as the “lotus effect” are illuminated through
free and adhesion energy computations, and certain geometries are
suggested that favor one state or the other
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