COMPUTATIONAL STUDIES OF FILM CONDENSATION, BOILING AND EQUILIBRIUM SHAPE OF A LIQUID FILM SUBJECTED TO THERMOCAPILLARITY

Author

• Ayush Kumar, Southern Illinois University CarbondaleFollow

Date of Award

5-1-2026

Degree Name

Doctor of Philosophy

Department

Engineering Science

First Advisor

Esmaeeli, Asghar

Abstract

This dissertation presents direct numerical simulations (DNS) of three interfacial flow phenomena: thermocapillary-driven film deformation (without phase change), film condensation on a horizontal plate, and film boiling on a heated surface. The conservation equations are formulated using the “one-fluid” approach, which serves as the foundation for several modern multiphase numerical methods. Within this framework, a front tracking technique is coupled with a finite-difference solver to accurately resolve interface dynamics, heat transfer, and topological evolution in liquid–vapor systems. The goal of this work is to advance the fundamental understanding of these processes and to provide validated numerical tools applicable to high performance cooling, microfluidics, and thermal management technologies. In the thermocapillary study, two immiscible liquid layers subjected to a horizontal temperature gradient develop interfacial motion through surface tension variation. The Marangoni number ($Ma$) is a key nondimensional parameter defined as the ratio of advective transport driven by surface-tension gradients to diffusive transport of the thermal source term. Increasing $Ma$ enhances interfacial circulation and deformation until a critical threshold is reached, beyond which the interface stabilizes and long-wavelength disturbances are suppressed. At intermediate $Ma$, localized hot spots drive the interface into traveling-wave motion that alternately propagates from left to right or vice versa, demonstrating nonlinear oscillatory behavior beyond classical theory. The simulations reveal a neutral boundary that separates concave-up and concave-down equilibrium interface shapes. This transition is governed primarily by the depth ratio and viscosity ratio of the two fluids. The condensation analysis focuses on film condensation beneath a cooled, downward-facing horizontal plate, which is a configuration inherently unstable to Rayleigh–Taylor modes. DNS results capture the full evolution from smooth film to pendant-drop formation and periodic detachment. Model accuracy is confirmed through comparison with Stefan’s analytical solution for one-dimensional transient phase change and Gerstmann’s experimentally derived condensation heat transfer correlations. The resulting mean Nusselt number follows the scaling $Nu \propto Gr^{0.23}$, and the simulations further show localized heat-flux intensification at droplet pinch-off locations behavior not predicted by classical laminar-film theory. The film-boiling study extends the same numerical approach to three dimensions, enabling the fully resolved visualization of multiple bubble pinch-off cycles on a horizontal heated surface. Three-dimensional simulations reveal out-of-plane instabilities, lateral entrainment, and vortex stretching that are absent in 2-D or axisymmetric approximations. The computed temporal Nusselt number exhibits oscillatory peaks synchronized with successive bubble detachment and rewetting cycles. Parametric variations of the Jakob number ($Ja = c_p\Delta T / h_{fg}$, ratio of sensible heating to latent heat) and the Grashof number ($Gr = g\,\beta\,\Delta T\,L^3 / \nu^2$, measure of buoyancy strength) reproduce classical boiling trends: thicker, less stable vapor films at higher $Ja$, and faster detachment at larger $Gr$, while capturing the full three-dimensional flow topology. Together, these studies demonstrate a versatile DNS framework capable of predicting phase-change heat transfer across condensation, boiling, and thermocapillary regimes. The results provide validated scaling behavior, reveal new nonlinear dynamics such as traveling-wave motion and repeated vapor pinch-off, and offer a physics-based foundation for designing advanced two-phase cooling systems and microscale thermal devices.