Molecular Dynamics Simulations of Sessile and Pendant Droplets Shape on Inclined and Curved Surfaces (original) (raw)
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Molecular dynamics simulations of the contact angle between water droplets and graphite surfaces
Fluid Phase Equilibria, 2012
Wetting is a widespread phenomenon, most prominent in a number of cases, both in nature and technology. Droplets of pure water with initial radius ranging from 20 to 80 [Å] spreading on graphitic surfaces are studied by molecular dynamics simulations. The equilibrium contact angle is determined and the transition to the macroscopic limit is discussed using Young equation in its modified form. While the largest droplets are almost perfectly spherical, the profiles of the smallest ones are no more properly described by a circle. For the sake of accuracy, we employ a more general fitting procedure based on local averages. Furthermore, our results reveal that there is a possible transition to the macroscopic limit. The modified Young equation is particularly precise for characteristic lengths (radii and contact-line curvatures) around 40 [Å].
Simulation of Sliding of Liquid Droplets
Numerical simulations of sliding behavior of liquid droplets on flat and periodic microgrooved surfaces with a range of groove geometry are conducted. A numerical model is developed which is capable of predicting the critical sliding angle of the drop by comparing the advancing and the receding angles obtained from numerical and experimental findings. The effect of microgroove topography, droplet size and inclination angle on the droplet sliding characteristics is analysed. Using an open-source platform (Surface Evolver), a 3D drop-shape model is developed to numerically determine the drop stability and contact angle hysteresis on tilted surfaces. In this numerical model, the three phase contact line of the drop is obtained by numerically calculating the vertex force and local contact angle at each vertex of the base contour. Several numerical models are developed based on various assumptions of base contour shape (circular or elliptical) and implementation of gravitational force to the droplet. Droplet shapes and critical sliding angles, obtained from these numerical models, are compared with those of experimental results and are found to be in very good agreement.
Journal of the Iranian Chemical Society
In this paper, we analyze the shape of two-dimensional and three-dimensional drops on flat and curved substrates by minimizing free energy with the variational approach. The process initiated from the flat substrate and has proved the drop shape equation. Then, the drop shape equation for these models has been determined by extending the method to curved substrates. The constraints in 2D and 3D models are constant surface area and volume, respectively. The Euler–Lagrange differential equation can be solved analytically in the two-dimensional case and the drop height as a function of x has been driven which is the equation of a circle. In the 3D model, a fundamental partial differential equation (PDE) has been obtained but it cannot be solved analytically and has been solved through a numerical method. This PDE becomes a first-order ordinary differential equation (ODE) after two reduction steps and is solved by the Euler explicit method. Six different systems are simulated and a logical algorithm is introduced to compare the results of the simulation, numerical, and analytical. The simulation results determined there is an iso-density curve or surface that is closest to the analytical result. It has revealed the solution of the three-dimensional case is not a sphere. The spherical cap approximation (SCA) has been widely used in many wettability studies. Comparison of numerical and SCA results have determined this assumption is valid only for contact angles far from 90 degrees. The present results are determined all the drops on each surface can be described by only one equation if the contact angle is measured for the line (in the case of a 2D drop) or the passing plate (in the case of a 3D drop) from the drop edges. The substrate characteristics at the three-phase contact point (TPCP) and the three-phase contact line (TPCL) are the only factors determining the drop shape. The other points and areas away from TPCP and TPCL have not influenced the drop shape.
Langmuir, 2015
correspondingly. The values of the static receding, r θ , and static advancing, a θ , contact angles in cylindrical capillaries were calculated earlier, based on the shape of disjoining/conjoining pressure isotherm. It is shown now that both advancing and receding contact angles of a droplet on a on smooth, homogeneous solid substrate (i) can be calculated based on shape of disjoining/conjoining pressure isotherm, (ii) both advancing and receding contact angles depend on the drop volume and are not unique characteristics of the liquid-solid system. The latter is different from advancing/receding contact angles in thin capillaries. It is shown also that the receding contact angle is much closer to equilibrium contact angle than the advancing contact angle. The latter conclusion is unexpected and is in a contradiction with commonly accepted view that the advancing contact angle can be taken as the first approximation for the equilibrium contact angle. The dependency of hysteresis contact angles on the drop volume has a direct experimental confirmation.
Simulation of a Water Droplet on Horizontally Smooth Surface Using Quasi-Molecular Modelling
masterorg.wu.ac.th
We developed a method based on quasi-molecular modelling to simulate the fall of water drops. Each quasimolecule was a group of particles that interacted in a fashion entirely analogous to classical Newtonian molecular interactions. When a falling water droplet was simulated at low impact velocity, the droplets moved periodically (i.e. the droplets moved up and down for a certain period, then stopped moving and reached a steady state), spreading and recoiling without splash or break-up. Spreading rates of falling water droplets increased rapidly as time increased until the spreading rate reached its steady state at time t ~ 0.4 s after the impact. The droplet height above the surface decreased as time increased, remained constant after the droplet diameter attained a maximum value and reached its steady state at time t ~ 0.4 s after the impact. When impact velocities were varied by changing the setting of the vertical height (i.e. at 0.25, 1.25 and 6.00 cm), spreading rates increased with increasing impact velocity. However, the droplet height above the surface was not affected by increasing impact velocity.
Simulation of Pendant Droplet Behavior on Plain and Patterned Surfaces using Surface Evolver
2021
In this work, pendant droplets of different liquids (i.e. water, ethylene glycol, methanol, and acetone) on a plain aluminum surface and a three-stripe patterned surface were simulated using the Surface Evolver (SE) software. The critical droplet volume before detachment from a surface and droplet properties such as diameter, height, and surface energy were measured. Surface Evolver is a program that models liquid surfaces shaped by different forces and constraints. The program works by modifying a surface toward minimal thermodynamic energy by a gradient descent method. The initial input to Surface Evolver is a script file containing all the pertinent information about the droplet to be simulated including the gravitational constant, volume, density, and contact angle. For these simulations, the gravitational constant was set to-1 for all liquids (i.e. 9.81 m s-2), and the values of density and contact angle were based on the simulated liquid type. As part of this study, droplet contact angles were measured on an aluminum surface at room temperature (~20°C), and these values were used as inputs in the simulation. The measured static contact angle for water, ethylene glycol, methanol, and acetone were found to be 88.2 ,°61.0 ,°20.9°, and 13.0°, respectively. For each simulation, more than 100 iterations were performed before the droplet geometry converged and was ready for measurement. The surface energy was taken directly after each iteration, while the droplet height and diameter were calculated from simulation pictures using a pixel counting method. The critical pendant droplet volumes for water, ethylene glycol, methanol, and acetone on a plain aluminum surface were found to be 17.9, 21, 19.03, and 14 µL, respectively. For the purposes of this study, the critical volume (i.e. when the droplet starts detaching) was defined when the surface energy was found to be in the range of-0.15 J to 0.15 J. Besides critical volumes, droplet data associated with smaller volumes (i.e. 5, 8, 10, 12, and 15 µL) were also measured and compared among liquids. Patterned surfaces were also studied in this work. These surfaces consisted of a central hydrophilic stripe varying from 1 mm to 5 mm in width sandwiched between two outer hydrophobic regions. Critical droplet volumes on these surfaces are also discussed.
Sessile droplets shape response to complex body forces
Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2019
The majority of studies on forced wetting of sessile droplets refers to application of a steadily increasing normal or tangential force or to a specific combination of these forces arising from tilting the substrate. The above constitute well-defined test conditions but are not representative of what is encountered in most industrial applications. To approach realistic industrial conditions and so also expand existing wetting theories, an evaluation of droplet shape deformation under the influence of a complicated evolution of body forces, is performed herein. To this aim, two sets of experiments are carried out in Kerberos device creating force fields by combination of gravitational and centrifugal forces: i) by oscillations of the tilting angle at constant rotation speed and ii) by alternating small step-increases of the rotation speed and the tilting angle, one after the other, so as to trail the symmetric side profile (SSP) curve of a droplet. The latter is done in three or six steps following two different paths: increasing first either the rotation speed or the tilting angle. The aim of the experiments is, on one hand, to explore droplet deformation under cycles of increasing/decreasing tangential forces and, on the other hand, to analyze the effect of residual tangential forces on droplet shape. Several features related to the droplet shape evolution are investigated such as contact angles, side and top contour profiles and droplet 3-dimensional shape. The resulting droplet profiles are analyzed using numerical solutions of the Young-Laplace equation. It is found that the 3-dimensional Young Laplace equation can describe very accurately the experimental profiles.
Advancing and receding wetting behavior of a droplet on a narrow rectangular plane
Colloid and Polymer Science, 2012
The contact angle (CA) measurements are generally performed on a large planar surface of a specific substrate with the width larger than the droplet size. In this study, the contact angle hysteresis on a narrow rectangular plane with a width smaller than the droplet size is experimentally studied through the inflation-deflation process by the needle-syringe method. The inflation process by stepwise addition of the liquid to the droplet leads to the contact line advancing outwardly along the major axis with advancing angle (θ a). Although the droplet width is constrained by the edge of the plane, the CA along the minor axis (θ w) increases and its value is greater than θ a (θ w > θ a). Deflation process by stepwise withdrawal of liquid from the droplet results in the contact line retracting inwardly along the major axis as the CA reduces to receding angle (θ r). In the meantime, the CA along the minor axis decreases as well. Both advancing and receding angles acquired from the narrow rectangular plane are confirmed with those obtained form the typical large surface of acrylic glass. On the basis of free energy minimization and liquidinduced defects model, Surface Evolver simulations are performed to reproduce the behavior of droplet on the narrow rectangular plane during the inflation-deflation process. The results of experiment and simulation agree with each other very well. Keywords Contact angle hysteresis. Needle-syringe method. Free energy minimization. Liquid-induced defects model. Surface Evolver This article is part of the Topical Collection on Contact Angle Hysteresis.
Closed-form expression for the profile of partially wetting two-dimensional droplets under gravity
Physical Review E, 2012
Analytical solutions for the shape of both hanging and sitting droplets under the effects of gravity and surface tension are presented. The modeling also includes the action of molecular forces arising between the liquid and the substrate, which are responsible for the formation of a stable nanometric film in the region close to the droplet contact line. The shape of the droplet is completely described by an analytical solution that also accounts for the pancake-shaped droplets as a limiting case. We find expressions that relate microscopic and nanoscopic aspects, such as the strengths of the molecular forces and the thickness of the nanometric film, to macroscopic quantities, such as the cross-sectional area and the width of the droplet. We study the effect of gravity on the contact angle and find that for small droplets the contact angle follows a power law with the droplet's size. For sitting droplets we find that the there is an upper limit for the value of the gravity.
Molecular dynamics of a liquid drop spreading in a corner formed by two planar substrates
Physical Review E, 1999
Molecular-dynamics simulations were used to investigate the spreading of nonvolatile liquid drops in a solid corner formed by two planar substrates. To understand the effect of the corner on the spreading, liquid drops in a corner with angles of 45°, 90°, and 135°as well as on a flat substrate were examined. Both the solid substrate and the liquid drop were modeled using the Lennard-Jones interaction potential in the present study. Simulation results show that the mass center of the liquid molecules migrated towards the corner as time evolved and the spreading rate increased as the corner angle decreased. It is found that the variation of the mean spreading area with time can be described by a general relation of A(t)ϳt, which is in agreement with results obtained by other investigators. The distribution of liquid atoms per unit normalized corner degree shows a similar trend for different corner angles. ͓S1063-651X͑99͒02311-9͔