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.
[03374] Plug formation in models of falling viscous films inside tubes
Format : Online Talk on Zoom
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
Format : Talk at Waseda University
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.
[02884] Capillary rebound of droplets impacting onto a liquid bath
Format : Talk at Waseda University
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.
[02422] Thermally-driven coalescence in thin liquid film flowing down a fiber
Format : Talk at Waseda University
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.
00118 (2/3) : 1D @D402 [Chair: Hangjie Ji, Pejman Sanaei]
[01886] Hybrid Asymptotic-Numerical Methods for Two-Phase Flow With Soluble Surfactant
Format : Talk at Waseda University
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.
[01260] A phase field model for a drop suspended in viscous liquids under the influence of electric fields
Format : Talk at Waseda University
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.
[05478] Phase-field modeling of colloid-polymer mixtures in microgravity
Format : Talk at Waseda University
Author(s) :
Anand Oza (New Jersey Institute of Technology)
Abstract : We present a theoretical model for colloid-polymer mixtures in a microgravity environment. The addition of polymer to a colloidal suspension induces weakly attractive forces between the colloids and leads to a three-phase coexistence region, wherein liquid phase "droplets" coexist with a low-density gas phase and a high-density crystal phase. Colloid-polymer mixtures are thus an archetype for modeling phase transition processes, but the details of the observed colloidal structures remain poorly understood. We construct, analyze and numerically simulate a phase-field model for structure evolution in colloid-polymer mixtures. The model consists of the Cahn-Hilliard equation, which describes phase separation processes in multicomponent mixtures, coupled with the Stokes equation for viscous fluid flow. The results of the model are compared against experiments performed on the International Space Station, using data available on the NASA Physical Sciences Informatics system.
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
[02886] On the immersed boundary method in simulating liquid-gas interfaces
Format : Talk at Waseda University
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.
