Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session G11: Drops: Wetting and Spreading II |
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Chair: Pengtao Yue, Virginia Polytechnic Institute Room: Georgia World Congress Center B216 |
Monday, November 19, 2018 10:35AM - 10:48AM |
G11.00001: An interface-preserving level-set method for interfacial flows with moving contact lines Jiaqi Zhang, Pengtao Yue It is well-known that the level-set methods have poor mass conservation properties, mostly due to the shift of the zero level set during the reinitialization process. In this talk, we present an interface-preserving discontinuous Galerkin method to solve the Hamilton-Jacobi equation for the level-set reinitialization. This reinitialization method essentially causes no mass loss as long as the interface curvature can be resolved by the computational mesh. More importantly, it allows for an easy implementation of the artificial boundary conditions that arise when the interfaces intersect the domain boundaries at non-90 degree angles. We solve the level-set and flow equations by finite element methods based on the finite-element library deal.II. A generalized Navier condition is adopted to relax the moving contact line singularity. We first compute a rising bubble for code validation as well as an illustration of the mass conservation performance. We then compute the advancing menisci in a Poiseuille flow, which are validated against Cox’s hydrodynamic theory. We will also present some preliminary results on a non-iterative model for contact-angle hysteresis. |
Monday, November 19, 2018 10:48AM - 11:01AM |
G11.00002: Phase-field simulations of contact angle hysteresis Pengtao Yue When a fluid interface slides on a solid substrate, the advancing and receding contact angles may differ, which is known as contact angle hysteresis. We will present a novel boundary condition for contact angle hysteresis based on a simple modification of the phase-field wall energy relaxation model. By exploring the surface potential resulted from the mixing and wall energies, the advancing, receding, and pinning of contact line can be directly identified without the explicit knowledge of contact angle or contact-line velocity. Our boundary condition pins the contact line automatically if the microscopic contact angle falls between the advancing and receding values. Once the contact line moves, the correct microscopic contact angle is picked up and the contact-line dynamics with a single-valued static contact angle is recovered. For a 2D drop adhering to a wall under a pressure-driven creeping flow, our phase-field results agree very well with the boundary-integral results in literature. Based on the simulations of advancing menisci between parallel plates, we come up with guidelines on the choice of relaxation parameter to achieve desired pinning effect and slip length. In the end we will present 3D simulations on sliding drops on an inclined plane. |
Monday, November 19, 2018 11:01AM - 11:14AM |
G11.00003: A sub-grid-scale viscous force model for simulating moving contact lines Sheng Wang, Olivier Desjardins Simulations of two-phase flows with moving contact lines are often reported to be mesh-dependent [Afkhami et al., 2009] due to the diverging viscous stress at the contact line [Huh and Scriven, 1971]. Strategies such as the Navier-slip boundary condition and the Cox-Voinov dynamic contact-angle model have been proposed to alleviate this issue. However, the Navier-slip boundary condition requires an unrealistically large slip-length to achieve better mesh-independency, and no clear reason justifies the improved mesh-independency of the Cox-Voinov dynamic model [Legendre and Maglio, 2015]. In this talk, we volume-filter the Navier-Stokes equations for two-phase flows with moving contact lines, and identify two unclosed terms: a sub-grid scale (SGS) surface tension force and a SGS viscous force. The SGS surface tension force is closed by the uncompensated Young’s force model [Wang and Desjardins, 2017], and a new physics-based closure is derived for the SGS viscous force. Both models are flexible and easily implementable in any numerical framework. Simulations using both SGS models are verified to be mesh-independent, and the utility of the model is demonstrated across a number of examples, including drop spreading on a plane and drop sliding down an inclined plane. |
Monday, November 19, 2018 11:14AM - 11:27AM |
G11.00004: Vortex Shedding and Depinning of Wind-Forced Liquid Drops Roger Simon, Edward White Water drops adhere to solid substrates but can depin when wind forcing exceeds the adhesion force provided by surface tension. Schmucker and White (2012.DFD.M4.6) measured critical wind forcing limits for high-Reynolds-number airflow forcing and found a critical constant Weber number, Wecrit = 8.0 for a range of drop Bond numbers. This work seeks to identify what behavior is associated with Wecrit = 8.0 and why wind-forced drops depin when they do. One hypothesis suggests that, at high Reynolds numbers, drops depin when their interface natural frequency matches the frequency of air vortex shedding in the separated drop wake. We investigate whether a resonance between vortex shedding and drop interface oscillations is involved with depinning. We measure the shedding frequencies behind solid protuberances of the same size as typical drops and, separately, water-drop interface frequencies. We compare our measured values under different flow conditions to establish whether shedding and interface resonance are related to depinning. |
Monday, November 19, 2018 11:27AM - 11:40AM |
G11.00005: Dissipation by oscillatory contact-lines Yi Xia, Paul H Steen Contact-line (CL) effects influence the extent of energy dissipation when a liquid moves across a solid support, as when a liquid undergoes rapid spreading. For sufficiently rapid spreading, inertia competes with capillarity to influence the interface shape near the support. A traditional approach to evaluate CL dissipation calculates the mechanical work associated with the deformed interface based on measurements local to the CL. These measurements are achievable with our set-up where we use resonant-mode plane-normal support oscillations to drive lateral contact-line motion of droplets in the inertial-capillary regime (Re high and Ca low). In contrast to the traditional approach, by tuning the driving frequency near resonance, we obtain the scaled peak height (amplification factor) and phase difference to yield a non-dimensional characterization of dissipation (damping ratio). This approach requires only the displacements of the drop peak and the driving platform as inputs, independent of measurements local to the CL. CL dissipation is isolated from other modes of dissipation and partitioning of dissipation between CL and bulk sources is discussed. |
Monday, November 19, 2018 11:40AM - 11:53AM |
G11.00006: Control of Droplet Spreading On Ultrasonically Vibrated Hydrophobic Surfaces Matthew A Trapuzzano The way a liquid wets a solid surface depends on chemistry, geometry, and local energy inputs. Low-frequency surface vibration causes wetting changes prompted by contact line oscillations. High-frequency (ultrasonic) surface vibration also causes liquid to wet or spread out on a surface, but governing mechanisms are relatively uncharacterized. This work investigates the wetting effects of high frequency vibration (> 20 kHz). Droplets (10 to 50 µL) on hydrophobic surfaces are imaged as they are vibrated with ultrasonic piezoelectric transducers. Spreading of droplets occurs abruptly when a threshold surface acceleration is exceeded. Droplet volume decreases the threshold acceleration, while frequency and initial contact angle impact the extent of spreading. Experimental results are compared to numerical simulations of vibrating droplets to obtain an accurate model. Wetting changes remain after cessation of vibration, however new droplets wet with the original contact angle except for some cases where vibration of liquid can affect the integrity of the coating. Spreading of droplets can be controlled by tuning vibration frequency and amplitude. This control has various industry applications where droplet manipulation is used. |
Monday, November 19, 2018 11:53AM - 12:06PM |
G11.00007: Motion of drops on highly hydrophobic surfaces Radu Cimpeanu, Alexander W. Wray, Steven Davis, Omar K Matar We analyse the behaviour of droplets resting on hydrophobic substrates. Such systems have been of significant practical interest in recent years due to their involvement in numerous prototypical problems such as post-rupture. From a theoretical point of view, it presents a curious challenge due to the multi-valuedness of the interface, presenting a stumbling block to typical low-order modelling techniques. The equilibrium problem is solved exactly in terms of elliptic functions and via matched asymptotic expansions showing good agreement. The dynamic problem is computed via an energetic approach that is more accurate and with a broader range of applicability than existing solutions, with validation being performed against direct numerical simulations. |
Monday, November 19, 2018 12:06PM - 12:19PM |
G11.00008: Atomistic level study of wettability of hydrogen passivated silicon oxide surface Shyam Badu, Sushanta Mitra In this work, quantum mechanical method is applied to study the wetting phenomenon on hydrogen passivated silicon oxide surface at atomistic level. The wettability parameters, such as cohesion and adhesion energies, contact angle and the spreading coefficient for water on hydrogen passivated silicon oxide surfaces are calculated using density functional theory. The change in cohesion energy and contact angle with change in the number of water layers placed on the silicon oxide surface is also analyzed. Once the number of water monolayers added to the surface become three or more, the cohesion energy and the contact angle become invariant. The computational results for the wettability parameters are compared for two different functionals i.e., B3LYP and M06. This study could open up a new research area in “quantum wetting”. |
Monday, November 19, 2018 12:19PM - 12:32PM |
G11.00009: Wettability of solid DNA nucleobases using density functional theory Sushanta Mitra, Shyam Badu In the present work, we have applied density functional theory to calculate the wettability properties of solid DNA nucleobases and their pairs with water. We have modeled the solid surfaces of the nucleobases thymine, adenine and their pairs using crystallographic information data. Wettability properties such as contact angle, cohesion energy, adhesion energy and the spreading coefficient have been calculated., Furthermore, we have implemented various types of exchange correlation-based density functionals B3LYP, M06, PW91 and PBE0 to test the sensitivity of wettability parameters. The values of the contact angle show the hydrophobicity nature of the surfaces for both the solid nucleobases as well as their pair. We have also studied the effect of dispersion correction on the wettability parameters using the density functionals B97D and B97D3. This computation study provides insight to the self-assembly of DNA strands in the body fluid. |
Monday, November 19, 2018 12:32PM - 12:45PM |
G11.00010: Establishing a novel continuum model of static and dynamic contact angles in a superhydrophobic case study: A water droplet on micrometer-sized patterns of a hybrid hydrophobic/-philic surface Arash Azimi, Chae Rohrs, Ping He, Chun-Wei Yao Modeling the static and dynamic contact angles is a grand challenge in studying the wetting and de-wetting of liquids on solid surfaces. We propose a dynamic slip boundary model based on the Young’s equation, and establish a novel, realistic continuum approach to simulate the 3-D contact line dynamics. In this paper, a water droplet interacting with micrometer-sized patterns of a hybrid hydrophobic/-philic surface is presented as a case study to validate our model with experimental measurements. Good agreements have been observed for all cases: (1) static, advancing and receding conditions, and (2) at four different pillar spacings. Moreover, details of the droplet-surface interaction have been studied: (i) penetrations, (ii) sagging, and (iii) local and global contact angles. Our results show that the spurious interfacial velocity, which is small, does not affect the validity of our model. Note that there is no fitting parameters used in this research. |
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