My research interests concern mathematical, scientific, and engineering aspects of fluid interfaces that are excited periodically in time. One of the greatest delights to me, is a mathematical model that can be verified experimentally. This became most clear to me during my work as a graduate student with Professors Ranga Narayanan and Farzam Zoueshtiagh. My dissertation on Faraday waves is a fundamental work in the sense that its principle goal was to design an experiment that agreed with the predictions of linear theory and then investigate nonlinear behaviors. Nevertheless my education in chemical engineering continues to shape the applications I envision for my projects. My ongoing interest in technical application of Faraday waves is to utilize the response on microfluidic scales. Here at NJIT, I am continuing work on Faraday waves with Professor Wooyoung Choi. We are interested in experimental verification of nonlinear models of Faraday waves, for systems with two deflectable surfaces, i.e., immiscible bilayers with an upper free surface.

As a postdoc at the Technion, I started working with Professors Alex Oron and Yehuda Agnon on applications of thin liquid films to condensible vapor thermoacoustics. This work analyzes the nonlinear partial differential equations that arise for the film thickness, when a bounding-phase acoustic wave drives thermal fluctuations in the film. Because these equations are first order in time, resonant responses that are typical of second-order, inertial systems are uncommon. Instead, temporal excitations may induce time-averaged effects that dictate whether or not the film is stable to rupture. Of particular interest is that we have uncovered an oscillatory, deflected film flow that does not rupture in long time. The result is obtained for fluids whose surface tension depends nonlinearly on temperature, notable examples of which include long chain alcohols such as butanol and pentanol. These mixtures have demonstrated enhanced heat transfer performance in a wide variety of microfluidic devices in recent years, and our view is they may have similar effects in thermoacoustic settings.

Here at NJIT, I am also working with Professors Lou Kondic and Linda Cummings on a project motivated by experiments on laser-driven thermocapillary breakup of nanoscopic metal films. Whereas resonant dynamics typically do not arise in the leading order approximation of a thin liquid film, oscillatory responses are possible when the film thickness is coupled to another process that is also first order in time—for example, a second film thickness associated with a bilayer configuration, or, the dynamics of an interfacial surfactant concentration. For these metal films, we find that the film thickness is necessarily coupled to the full, time-dependent heat conduction problem in the substrate, and, as a result, unstable oscillatory responses may be driven in the absence of temporal excitation. This result has been obtained by numerical simulation of a nonlinear model that assumes constant heating is applied to the bottom of the substrate, and ongoing work is being conducted to augment laser irradiation and refine experimental predictions.

- W. Batson, Y. Agnon, A. Oron. “Thermocapillary modulation of self-rewetting films.”
*J. Fluid Mech*, (in production). - W. Batson, F. Zoueshtiagh, R. Narayanan. “Two-frequency excitation of single-mode Faraday waves.”
*J. Fluid Mech*.,**2015**, 764, pp 538-571. - 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. - 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.