My published research was inspired by my intellectual curiosity and passion for applied mathematics! As a graduate student, I studied a classical problem in pattern formation (Faraday waves) by combining experiments, theory, and numerics. Then, for postdoctoral research, I applied theory and numerics to predict novel liquid film dynamical phenomena. Below are links to my publications and informal abstracts. Continue further below from some image and video highlights.
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(8) W. Batson, L.J. Cummings, D. Shirokoff, L. Kondic. "Oscillatory thermocapillary instability of a film heated by a thick substrate." J. Fluid Mech., 2019, 872, pp 928-962.
This work presents a formal theory for the emergence of oscillatory dynamics in liquid films heated by thick substrates. Such dynamics arise strictly in physical systems governed by at least two distinct time scales. Here, oscillatory dynamics are found for cases when the time scale of the film deflection coincides with one of the (infinitely many) time scales associated with substrate thermal diffusion. Mathematical rigor, computational precision, and physical insight are used to classify all possible stability configurations and pinpoint oscillatory regimes with respect to the input parameter space.
(7) W. Batson, Y. Agnon, A. Oron. "Thermocapillary modulation of self-rewetting films." J. Fluid Mech., 2017, 819, pp 562-591.
This work considered 'self-rewetting' liquids whose surface tension depends nonlinearly on temperature. Such liquids tend to increase heat transfer rates because they wet heated surfaces instead of receding (dry-out) like most liquids do. Motivated by applications to humid-vapor thermoacoustic engines, this work showed that thermal modulation of a bounding vapor may lead to thermocapillary destabilization of a flat, self-rewetting film to a wavy state. After deriving a nonlinear partial differential equation for the film evolution, linear analysis is used to describe underlying physics. Numerical integration of the nonlinear evolution equation is also used to show saturation to different wavy films that may travel or pulsate quasiperiodically.
(6) W. Batson, Y. Agnon, A. Oron. "Mass variation of a thin liquid film driven by an acoustic wave." Phys. Fluids, 2015, 27, 062106.
If a thermoacoustic engine is operated with a condensible vapor, then a situation arises where condensed liquid films are bounded by and interact with a vapor-phase acoustic wave. This work showed for wavy, nonlinear films that time-periodic mass transfer with the the bounding acoustic wave promotes non-conservative film mass loss or gain. These results were demonstrated and explained via linear analysis and nonlinear simulation of a reduced-order, nonlinear partial differential equation for the film evolution.
(5) W. Batson, F. Zoueshtiagh, R. Narayanan. "Two-frequency excitation of single-mode Faraday waves" J. Fluid Mech., 2015, 764, pp 538-571.
Extending the work of (3), this manuscript investigates the effect of two-frequency excitation on the dynamics of Faraday waves in small cells. Linear analysis is presented, and experimental agreement is found to mirror that seen for single-frequency excitation. Other experimental features that are reported include bifurcation of periodic flows, dynamics near a co-dimension 2 point, and a pronounced effect of the excitation phase angle on the instability threshold when the second frequency is twice the primary frequency. I am especially grateful to Professor Ranga Narayanan for his continued support following graduation that enabled me to conduct the experiments for this work.
(4) W. Batson, F. Zoueshtiagh, R. Narayanan. "Dual role of gravity on the Faraday threshold for immiscible viscous layers," Phys. Rev. E., 2013, 88, 063002.
In zero-gravity, the dispersion relation for Faraday waves tells us that the natural frequency of a given wavenumber is decreased relative to settings with gravity. Accordingly, for a fixed excitation frequency, the resonant wavenumber and corresponding viscous effects increase when gravity is removed. In this work we show that, although gravity destabilizes the system at low excitation frequencies, stabilization is encountered at large frequencies due to the increased effect of viscosity.
(3) W. Batson, F. Zoueshtiagh, R. Narayanan. "The Faraday threshold in small cylinders and the sidewall non-ideality." J. Fluid Mech., 2013, 729, pp 496-523.
Faraday waves arise at fluid interfaces that are subjected to a periodic modulation of gravity, e.g. vertical container vibrations. Because laterally-large systems have access to a continuous spectrum of wavenumbers, the observed wavelength normally corresponds to that whose natural frequency is half the modulational frequency. In contrast, laterally small systems are subject to a discretized wavenumber spectrum, and, as a result, the same wavenumber is observed for continuous bands of vibrational frequencies. In this paper, we studied a discretized system experimentally and compared the threshold behavior to a viscous theory for horizontally infinite layers. To strike agreement, experimental fluids were carefully chosen to approximate stress-free sidewalls. In doing so, remarkable agreement was observed and finer nuances in the experimental threshold behavior were examined.
(2) W. R. Batson, L. E. Johns, R. Narayanan. "Effect of domain perturbations on the critical condition for steady-state thermal explosions." Ind. Eng. Chem. Res., 2011, 50 (23), pp 13244-13249.
For steady-state heat conduction with heat generation, there exist critical conditions beyond which solutions do not exist. Physically, criticality marks the division between domains that can and those that can not support the heat generation. In this work, the effect of domain perturbations on criticality is investigated for two-dimensional cylindrical and annular domains for different boundary conditions and heating sources. Depending on these conditions, it is determined that criticality may become more or less severe for the problem on a perturbed domain. My role in this work was to numerically solve eigenvalue problems and track solution branches, which was done in MATLAB using a Chebyshev Spectral method.
(1) H. H. Nguyen, J. H. McAliley, W. R. Batson III, D. A. Bruce, "Molecular design of functionalized m-poly(phenylene ethynylene) foldamers: from simulation to synthesis." Macromolecules. 2010, 43 (14), pp 5932-5942.
In this work, the folding dynamics of helical polymers are investigated using molecular dynamics simulations. I contributed to this project as an undergraduate by conducting organic synthesis and performing molecular dynamics simulations.
Summer 2010: Professor Farzam Zoueshtiagh and I posing with the mechanical shaker, experimental cell, and high speed camera used for our Faraday wave experiemnts. I spent about 18 months in Lille, France over several trips to advance these experiments.
Spring 2013: photo from the Japanese space agency, JAXA. Here, I participated in the early stages of work on electrodynamically-driven Faraday instability. My Ph.D advisors worked with JAXA (and ESA) towards conducting experiments in space, hence the paper (4) we published on the instability in zero-gravity.
Summer 2013: Image from publication (3) chosen for cover of JFM volume 729.
Spring 2014: View of Haifa Bay from the Baháʼí Gardens in Haifa, Israel. For two and a half years at the Technion, I developed models of liquid film dynamics. In 2016, I continued this work with another two-year position at the New Jersey Institute of Technology.
Winter 2015: From (5), time series of (top) centerline deviation of the fundamental axisymmetric Faraday instability, (middle) sidewall contact line, (bottom) digitized input vibrational excitation.
Winter 2015: From (5), time series of (top) centerline deviation of the fundamental axisymmetric Faraday instability, (middle) sidewall contact line, (bottom) digitized input vibrational excitation.
Summer 2016: Quasiperiodic flows detected in the self-rewetting liquid film model of (7)
Summer 2016: Quasiperiodic flows detected in the self-rewetting liquid film model of (7)
Summer 2019: Contour plots from (8) generated using numerical continuation and optimization to track solutions to an implicitly-defined transcendental dispersion relation with respect to the parameters S and B.
Summer 2019: Contour plots from (8) generated using numerical continuation and optimization to track solutions to an implicitly-defined transcendental dispersion relation with respect to the parameters S and B.
Fall 2013: APS DFD - Gallery of Fluid Motion submission for publication (3).
Summer 2018: Animation of the collisions I studied in publication (8).
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