Spreading and bistability of droplets on differentially heated substrates

AbstractAn axisymmetric drop spreads on a radially heated, partially wetting solid substrate in a rotating geometry. The lubrication approximation is applied to the field equations for this thin viscous drop to yield an evolution equation that captures the dependence of viscosity, surface tension, gravity, centrifugal forces and thermocapillarity. We study the quasi-static spreading regime, whereby droplet motion is controlled by a constitutive law that relates the contact angle to the contact-line speed. Non-uniform heating of the substrate can generate both vertical and radial temperature gradients along the drop interface, which produce distinct thermocapillary forces and equivalently flows that affect the spreading process. For the non-rotating system, competition between surface chemistry (wetting) and thermocapillary flows induced by the thermal gradients gives rise to bistability in certain regions of parameter space in which the droplets converge to an equilibrium shape. The centrifugal forces that develop in a rotating geometry enlarge the bistability regions. Parameter regimes in which the droplet spreads indefinitely are identified and spreading laws are computed to compare with experimental results from the literature.

Download Full-text

Effect of Surface Nano-Texturing on Wetting Properties: Molecular Dynamics Study

Ukrainian Journal of Physics ◽

10.15407/ujpe65.9.817 ◽

2020 ◽

Vol 65 (9) ◽

pp. 817

Author(s):

M. Aleksandrovych ◽

G. Castanet ◽

S. Burian ◽

F. Lemoine ◽

D. Lacroix ◽

...

Keyword(s):

Molecular Dynamics ◽

Smooth Surface ◽

Substrate Surface ◽

Equilibrium Shape ◽

Solid Substrate ◽

Silicon Substrates ◽

Wetting Properties ◽

Flat Substrate ◽

Dynamics Simulations ◽

Effect Of Surface

Molecular dynamics simulations describing the equilibrium shape of a nanodroplet located on the solid substrate are presented for the cases of a “cylindrical water droplet” on silicon substrates. Several examples of the structuration of the solid substrate surface are simulated, i.e.: atomistic flat substrate and substrates with ordered nanopillars and nanopores. The adhesives forces between molecules of the substrate and the fluid are modified to change the wettability. Three wetting configurations are considered in this work for the smooth surface: (i) hydrophilic (0 = 30∘), (ii) hydrophobic (0 = 136∘), and (iii) an intermediate regime (0 = 80∘). Further, the dependence of the wetting angle as a function of the surface state is studied in details for the above-mentioned configurations.

Download Full-text

Gliding on a layer of air: impact of a large-viscosity drop on a liquid film

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.682 ◽

2019 ◽

Vol 878 ◽

Cited By ~ 6

Author(s):

K. R. Langley ◽

S. T. Thoroddsen

Keyword(s):

Liquid Film ◽

Impact Velocity ◽

Solid Surface ◽

High Speed ◽

Solid Substrate ◽

Compliant Surfaces ◽

Theoretical Predictions ◽

Viscous Drop ◽

Water Drops ◽

Air Film

In this paper we contrast the early impact stage of a highly viscous drop onto a liquid versus a solid substrate. Water drops impacting at low velocities can rebound from a solid surface without contact. This dynamic is mediated through lubrication of a thin air layer between the liquid and solid. Drops can also rebound from a liquid surface, but only for low Weber numbers. Impacts at higher velocities in both cases lead to circular contacts which entrap an air disc under the centre of the drop. Increasing the drop viscosity produces extended air films for impacts on a smooth solid surface even for much larger velocities. These air films eventually break through random wetting contacts with the solid. Herein we use high-speed interferometry to study the extent and thickness profile of the air film for a large-viscosity drop impacting onto a viscous film of the same liquid. We demonstrate a unified scaling of the centreline height of the air film for impacts on both solid and liquid, when using the effective impact velocity. On the other hand, we show that the large-viscosity liquid film promotes air films of larger extent. Furthermore, the rupture behaviour becomes fundamentally different, with the air film between the two compliant surfaces being more stable, lacking the random wetting patches seen on the solid. We map the parameter range where these air films occur and explore the transition from gliding to ring contact at the edge of the drop dimple. After the air film ruptures, the initial contraction occurs very rapidly and for viscosities greater than 100 cSt the retraction velocity of the air film is ${\sim}0.3~\text{m}~\text{s}^{-1}$, independent of the liquid viscosity and impact velocity, in sharp contrast with theoretical predictions.

Download Full-text

On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics

International Journal of Modern Physics D ◽

10.1142/s0218271816400162 ◽

2016 ◽

Vol 25 (11) ◽

pp. 1640016 ◽

Cited By ~ 13

Author(s):

Friedrich W. Hehl ◽

Yakov Itin ◽

Yuri N. Obukhov

Keyword(s):

General Relativity ◽

Gravitational Potential ◽

Linear Response ◽

Maxwell Equations ◽

Constitutive Law ◽

Classical Electrodynamics ◽

Field Equations ◽

Origin And Evolution ◽

Fundamental Equations

In 1922, Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible. He successfully applied this idea to Newton’s gravitostatics and to Maxwell’s electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law. We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes. We show that classical electrodynamics can be developed without a metric quite straightforwardly: the Maxwell equations, together with a local and linear response law for electromagnetic media, admit a consistent premetric formulation. Kottler’s program succeeds here without provisos. In Kottler’s approach to gravity, making the theory relativistic, two premetric quasi-Maxwellian field equations arise, but their field variables, if interpreted in terms of general relativity, do depend on the metric. However, one can hope to bring the Kottler idea to work by using the teleparallelism equivalent of general relativity, where the gravitational potential, the coframe, can be chosen in a premetric way.

Download Full-text

Finite Element and Experimental Analysis of an Axisymmetric Electromechanical Converter with a Magnetostrictive Rod

Energies ◽

10.3390/en13051230 ◽

2020 ◽

Vol 13 (5) ◽

pp. 1230 ◽

Cited By ~ 1

Author(s):

Dorota Stachowiak ◽

Andrzej Demenko

Keyword(s):

Finite Element ◽

Constitutive Law ◽

Experimental Investigations ◽

Field Equations ◽

Displacement Fields ◽

Applied Model ◽

Measurement Results ◽

Proper Definition ◽

Definition Of ◽

Electromechanical Converter

The paper presents the numerical and experimental investigations of the axisymmetric magnetostrictive actuator with a Terfenol-D rod. The applied model consists of equations that describe the magnetic and mechanical displacement fields. The equations of both fields are coupled through a nonlinear magneto-mechanical constitutive law. The model is considered as 2D axisymmetric. The finite element method is used to solve the field equations. Special attention is paid to the proper definition of magneto-mechanical relations. These relations are formed from measurements. A unique test stand is designed for the experimental investigation. The selected results of the simulation are compared with the measurement results. The comparison shows that the applied numerical model is sufficiently accurate.

Download Full-text

On Saint-Venant's problem for an elastic strip

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500024938 ◽

1988 ◽

Vol 110 (1-2) ◽

pp. 161-181 ◽

Cited By ~ 15

Author(s):

Alexander Mielke

Keyword(s):

Constitutive Relations ◽

Solution Space ◽

Elliptic Systems ◽

Constitutive Law ◽

Whole Body ◽

Infinite Strip ◽

Dimensional Manifold ◽

Field Equations ◽

Equilibrium Equations ◽

Dimensional Solution

SynopsisThe equilibrium equations for elastic deformations of an infinite strip are considered. Under the assumption of sufficiently small strains along the whole body, it is shown that all solutions lie on a six-dimensional manifold. This is achieved by rewriting the field equations as a differential equation in a function spaceover the cross-section, the axial variable taken as time. Then the theory of centre manifolds for elliptic systems applies. Thus the local Saint-Venant's problem is solved. Moreover, the structure of the finite-dimensional solution space is analysed to reveal exactly the two-dimensional rod equations of Kirchhoff. The constitutive relations for this rod model are calculated in a mathematically rigorous way out of the constitutive law of the material forming the strip.

Download Full-text