[00118] On mathematical modeling and simulation of droplets
Session Date & Time :
00118 (1/3) : 1C (Aug.21, 13:20-15:00)
00118 (2/3) : 1D (Aug.21, 15:30-17:10)
00118 (3/3) : 1E (Aug.21, 17:40-19:20)
Type : Proposal of Minisymposium
Abstract : The mathematical modeling and simulation of droplets is a basic and fundamental problem in the history of fluid mechanics. Droplets can undergo a variety of interesting nonlinear dynamics such as droplet coalescence/break up, electro-wetting, and traveling waves, etc, due to surface tension effects, substrate geometry and material, as well as external physical forces. This minisymposium will present recent advances in the modeling and simulation of droplets and focus on the mathematical challenges arising from different real-world applications.
Organizer(s) : Hangjie Ji, Pejman Sanaei
Sponsor : This session is sponsored by the SIAM Activity Group on Computational Science and Engineering.
Michael Booty (New Jersey Institute of Technology)
Radu Cimpeanu (University of Warwick)
Marina Chugunova (Claremont Graduate University)
Pejman Sanaei (Georgia State University)
Mark Bowen (Waseda University)
Shixin Xu (Duke Kunshan University)
Enkeleida Lushi (New Jersey Institute of Technology)
Talks in Minisymposium :
[01260] A phase field model for a drop suspended in viscous liquids under the influence of electric fields
Author(s) :
Shixin Xu (Duke Kunshan Univeristy)
Yuzhe Qin (Shanxi University)
Huangxiong Huang (Beijing Normal University)
Abstract : In this talk, we consider modeling the deformation of a droplet under an electric field. Firstly, we derive the Poisson-Nernst-Planck-Navier-Stokes phase field model based on the energy variational method, and then we obtain a general phase-field leaky dielectric model taking into account the capacitance according to the electroneutrality. Then a detailed asymptotic analysis confirms that the sharp interface limit of our proposed diffusive-interface model is consistent with the sharp interface model. We take a series of numerical experiments to validate the correctness and effectiveness of our model. The numerical result shows the validity of the asymptotic analysis by comparing the diffuse interface method and existing immersed boundary method results. Finally, we compare the deformations for the interface with and without the capacitance. It shows that the capacitance will weak the formation of droplets.
[01510] Motion of Liquid Droplets in Gas Channels
Author(s) :
Marina Chugunova (Claremont Graduate University )
Abstract : Understanding of liquid droplets dynamics in gas channels is critical for improvement of performance and durability of the catalysts made of a dense porous material. We derive a mathematical model to study how different surface properties and operating conditions affect the dynamics of liquid droplets. We present multiple numerical simulations of a single droplet dynamics for different sizes of droplets and different choices of contact angles. We show the influence of an air flow to a thin liquid film and analyze traveling wave type solutions.
Joint work with A. Nadim, Y Ruan, and R Taranets
[01886] Hybrid Asymptotic-Numerical Methods for Two-Phase Flow With Soluble Surfactant
Author(s) :
Michael Booty (New Jersey Institute of Technology)
Abstract : Surfactant molecules diffuse slowly in bulk flows because of their size, so that the Peclet number of surfactant diffusion is large, and transfer between a stretched drop interface and bulk flow occurs in a thin layer adjacent to the interface that is about one thousandth of the drop radius. Analytical and numerical results of asymptotic, boundary integral, and conformal mapping techniques are presented. This is joint work with Michael Siegel, Ryan Atwater and Samantha Evans.
[02422] Thermally-driven coalescence in thin liquid film flowing down a fiber
Author(s) :
Hangjie Ji (North Carolina State University)
Claudia Falcon (Wake Forest University)
Erfan Sedighi (University of California, Los Angeles)
Abolfazl Sadeghpour (University of California, Los Angeles)
Y. Sungtaek Ju (University of California, Los Angeles)
Andrea L. Bertozzi (University of California, Los Angeles)
Abstract : This paper presents a study on the dynamics of a thin liquid film flowing down a vertical cylindrical fibre under a streamwise thermal gradient. Previous works on isothermal flows have shown that the inlet flow and fibre geometry are the main factors that determine a transition from the absolute to the convective instability flow regimes. Our experiments demonstrate that an irregular wavy pattern and bead coalescence, which are commonly seen in the convective regime, can also be triggered by applying a thermal gradient along the fibre. We develop a lubrication model that accounts for gravity, temperature-dependent viscosity and surface tension to describe the thermal effects on downstream bead dynamics. Numerical simulations of the model show good agreement between the predicted droplet coalescence dynamics and the experimental data.
[02884] Capillary rebound of droplets impacting onto a liquid bath
Author(s) :
Radu Cimpeanu (University of Warwick)
Luke F.L. Alventosa (Brown University)
Daniel M. Harris (Brown University)
Abstract : We study millimetric drops impacting onto the free surface of a quiescent bath, a canonical scenario which provides excellent opportunities to co-develop experimental, analytical and computational techniques in a rich multi-scale context. We find that increases in gravitational forces or viscosity lead to a decrease in the coefficient of restitution and an increase in the contact time. The inertio-capillary limit defines an upper bound on the coefficient of restitution, depending only on the Weber number.
[02886] On the immersed boundary method in simulating liquid-gas interfaces
Author(s) :
Pejman Sanaei (Georgia State University)
Michael Y. Li (New York University)
Daniel Chin (New York Universty)
Charles Puelz (Baylor College of Medicine)
Abstract : In this work, we use the immersed boundary method with four extensions to simulate a moving liquid-gas interface on a solid surface. We first define a moving contact line model and implements a static-dynamic friction condition at the
immersed solid boundary. The dynamic contact angle is endogenous instead of prescribed, and the solid boundary
can be non-stationary with respect to time. Second, we simulate both a surface tension force and a Young’s force with one general equation that does not involve estimating local curvature. In the third extension, we splice liquid-gas
interfaces to handle topological changes, such as the coalescence and separation of liquid droplets or gas bubbles.
Finally, we re-sample liquid-gas interface markers to ensure a near-uniform distribution without exerting artificial
forces. We demonstrate empirical convergence of our methods on non-trivial examples and apply them to several
benchmark cases, including a slipping droplet on a wall and a rising bubble.
[03374] Plug formation in models of falling viscous films inside tubes
Author(s) :
H. Reed Ogrosky (Virginia Commonwealth University)
Abstract : Falling viscous liquid films coating the interior of a tube occur in a variety of applications. If the film is thick enough, it may pinch off and form a plug, occluding the tube. In this talk I will discuss recent work examining the impact of surfactant, slip, viscoelasticity, and viscosity stratification on plug formation in a model for film flow. Implications for understanding occlusion in human airways will be discussed.
[03547] Dipole-type solutions to the thin-film equation
Author(s) :
Mark Bowen (Waseda University)
Thomas Witelski (Duke University)
Abstract : We investigate the dynamics of a thin liquid film spreading in a semi-infinite domain $x\ge0$, so that $x=0$ corresponds to an edge over which fluid can drain. In particular, we investigate self-similar solutions of the one-dimensional "thin-film" equation (a fourth order degenerate parabolic equation) on $x\ge0$. We find classes of first- and second-kind similarity solutions and describe how these classes are connected. We also discuss the extension of our results to self-similar solutions featuring sign-changes.
[04721] Exploring diffraction of walking droplets with a pilot-wave model
Author(s) :
Anand Oza (New Jersey Institute of Technology)
Antoine Bellaigue (Universite de Rennes)
Giuseppe Pucci (Consiglio Nazionale delle Ricerche - Istituto di Nanotecnologia (CNR-NANOTEC))
Abstract : The seminal experiments of Yves Couder and Emmanuel Fort demonstrated that a droplet walking on the surface of a fluid bath may exhibit behavior thought to be peculiar to the quantum realm. One of their experiments suggested that single-particle diffraction and interference may be obtained when a walker crosses a single- or a double-aperture between submerged barriers. Later experiments with finer control of experimental parameters yielded different results, thus reopening the question of the extent of the analogy between walkers and quantum particles. Here we use a hydrodynamic pilot-wave model to explore numerically the diffraction of a wave-driven particle by barriers, which are represented as an array of reflecting point sources of waves. The statistical distribution of the particle's deflected position is wavelike and generally exhibits multiple peaks, the number of which depends on the obstacle geometry and the bath's forcing acceleration.
[05145] Deformability Affects Vesicle Migration and Entrapment in Vortical Flows
Author(s) :
Enkeleida Lushi (New Jersey Institute of Technology)
Gokberk Kabacaoglu (Bilkent University )
Abstract : We use numerical simulations to systematically investigate the vesicle dynamics in two-dimensional (2D) Taylor-Green vortex flow in the absence of inertial forces. Vesicles are highly deformable membranes encapsulating an incompressible fluid and they serve as numerical and experimental proxies for biological cells such as red blood cells. Vesicle dynamics has been studied in free-space/bounded shear, Poiseuille and Taylor-Couette flows in 2D and 3D. Taylor-Green vortex are characterized with even more complicated properties than those flows such as non-uniform flow-line curvature, shear gradient. We study the effects of three parameters on the vesicle dynamics: the ratio of the interior fluid viscosity to that of the exterior one, the ratio of the shear forces on the vesicle to the membrane stiffness (characterized by the capillary number) and the vesicle deflation. Vesicle deformability is a nonlinear function of these three parameters. Although the study is in 2D, our findings contribute to the wide spectrum of intriguing vesicle dynamics: vesicles becomes trapped in the vortex by migrating towards the vortex center if they are sufficiently deformable. If not so, they migrate away from the vortex center and travel across the periodic arrays of vortices. In biological cells, vortex flows are frequently observed and found to be responsible for the molecular transport. Our results show that the soft particles migrate towards the vortex center and stay trapped there in vortex flows, whereas, the stiff ones can be transported across.
