Advances in Multiphase Flow Science and Technology: Second Edition

Over the past decade, two key technologies—high-speed imaging (including cameras and lighting) [1,2] and high-speed computing [3,4]—have advanced significantly. These developments have greatly enhanced our understanding of the fundamental physics of multiphase flows and have been widely applied to engineering problems involving multiphase phenomena. They have deepened insights into the dynamics of bubbles and droplets, which are essential in both science and engineering. Building upon this fundamental knowledge, further technological and engineering innovations are anticipated.

This Special Issue features five distinctive experimental and/or numerical studies:

• The Emptying of a Perforated Bottle: Influence of Perforation Size on Emptying Time and the Physical Nature of the Process.
• Ultrasonic Atomization—From Onset of Protruding Free Surface to Emanating Beads Fountain—Leading to Mist Spreading.
• Liquid–Solid Interaction to Evaluate Thermal Aging Effects on Carbon Fiber-Reinforced Composites.
• Influence of Bubble Shape on Mass Transfer in Multiphase Media: CFD Analysis of Concentration Gradients.
• An Application of Upwind Difference Scheme with Preconditioned Numerical Fluxes to Gas–Liquid Two-Phase Flows.

The papers presented in this Special Issue contribute significantly to the field of multiphase flow, heat transfer, and mass transfer, addressing both fundamental scientific questions and practical engineering applications.

A novel set of observations on the emptying of perforated single-outlet vessels (i.e., bottles) has been reported [5]. An inverted bottle empties in a time $T_{\mathrm{e},0}$ through a process called “glugging”, whereby gas and liquid compete at the neck (of diameter $D_N$). In contrast, an open-top container empties in a much shorter time $T_{\mathrm{e}}$ through “jetting” due to the lack of gas–liquid competition. Experiments and theory demonstrate that, by introducing a perforation (diameter $d_{\mathrm{p}}$), a bottle empties through glugging, jetting, or a combination of the two. For a certain range of $d_{\mathrm{p}}/D_{\mathrm{N}}$, the perforation increases the emptying time, and a particular value of $d_{\mathrm{p}}/D_{\mathrm{N}}$ is associated with a maximum emptying time $T_{\mathrm{e},\mathrm{m}\mathrm{a}\mathrm{x}}$. The authors show that the transition from jetting to glugging is initiated by the jet velocity reaching a low threshold, thereby allowing a slug of air to enter the neck, which stops jetting and starts the glugging. Once initiated, the glugging proceeds as though there is no perforation. Experimental results covered a range of Eötvös numbers (Eo) from Eo ∼ 20–200 (equivalent to a range of $D_{\mathrm{N}}/L_{\mathrm{c}}$∼ 4–15, where $L_{\mathrm{c}}$ is the capillary length). The phenomenon of a bottle emptying with a perforation adds to the body of bottle literature, which has already considered the influence of shape, inclination, liquid properties, etc. What remains are further interesting and open questions regarding the behavior outside of the range of liquid properties, scales (e.g., bottle volume), and shapes (e.g., neck length and shape) tested here. In addition, probing the details of what happens at the neck that allows for the jetting-to-glugging transition, which can only be undertaken through a careful photographic study, is left for future work.

The process of ultrasonic atomization involves a series of dynamic/topological deformations of the free surface, though not always, of a bulk liquid (initially) below the air. The study in [6] focuses on such dynamic interfacial alterations realized by changing some acoustic-related operating conditions, including ultrasound excitation frequency, acoustic strength or input power density, and the presence/absence of a “stabilizing” nozzle. High-speed, high-resolution imaging made it possible to qualitatively identify four representative transitions/demarcations: (1) the onset of a protrusion on an otherwise flat free surface; (2) the appearance of an undulation along the growing protuberance; (3) the triggering of an emanating-beads fountain out of this foundation-like region; and (4) the induction of droplets bursting and/or mist spreading. Quantitatively examined were the two-parameter specifications—on the degrees as well as induction—of the periodicity in the protrusion–surface and beads–fountain oscillations, detected over wider ranges of driving/excitation frequency (0.43–3.0 MHz) and input power density (0.5–10 $\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$) applied to the ultrasound transducer of a flat surface, on which the nozzle was either mounted or not. The resulting time sequence of images processed for the extended operating ranges, regarding the fountain structure pertaining to recurring beads, confirms the wave-associated nature, i.e., their size “scalability” to the ultrasound wavelength, predictable from the traveling-wave relationship. The thresholds in acoustic conditions for each of the four transition states of the fountain structure have been identified—notably, the onset of plausible “bifurcation” in the chain-beads’ diameter below a critical excitation frequency.

The study in [7] investigated the effects of thermally induced aging on a carbon fiber-reinforced composite (CFRP) comprising benzoxazine (BZ) and cycloaliphatic epoxy resin (CER), using a wettability analysis besides the traditional techniques to assess the aging behavior of CFRP samples with differing CER and BZ ratios, including weight change quantification and qualitative analysis of surface morphology, revealing that a higher CER content correlates with increased aging. The wettability analysis demonstrates that both BZ and BZ-CER composites exhibit heightened hydrophilicity with thermal aging, potentially exacerbating concerns such as icing and surface erosion. Notably, the BZ-CER composite displays greater hydrophilicity compared to the BZ composite, consistent with weight change trends. These findings underscore the utility of the surface wettability analysis as a valuable tool for monitoring thermo-oxidative aging in polymers and their surface behavior in response to fluid interactions, particularly within high glass transition temperatures in BZ-CER systems, which are utilized in structural composite applications.

A computational study of dissolved-gas concentration gradients and mass transfer around bubbles of various shapes using a novel combination of analytical shape specifications and CFD (Computational Fluid Dynamics) simulation is reported [8]. Non-spherical bubbles (e.g., oblate or flattened shapes) exhibit highly non-uniform dissolved gas concentration fields, with enhanced mass transfer at the front and diminished transfer in the rear wake, while overall mass transfer rates for deformed bubbles can differ substantially from those of spherical bubbles under the same flow conditions, underscoring the importance of accounting for bubble shape in design and scale-up calculations. The use of the Superformula to prescribe bubble geometry proved to be an effective and flexible approach. It allowed us to easily generate a family of bubble shapes corresponding to different Eötvös numbers and to investigate their behavior without complex interface tracking. The proposed method preserves the essential physics of how shape influences flow and mass transfer while greatly simplifying the computational setup. Incorporating bubble shape effects through analytical modeling and efficient CFD is a promising avenue for advancing multiphase flow science. It enables a deeper physical understanding of gas–liquid mass transfer and provides practical modeling tools for engineers.

To analyze unsteady gas–liquid multiphase flows, a time-consistent upwind difference scheme was presented and applied to 2D flow problems through a backward-facing step channel. In the study reported by [9], the governing equations were derived in general curvilinear coordinates to apply to a variety of flow fields. To maintain the time consistency for unsteady problems and enhance the numerical stability in calculations of gas–liquid flows with incompressible and compressible flow properties, the fundamental equations were preconditioned only in the numerical dissipative terms without modifying the time-derivative terms. Therefore, the proposed scheme provides a time-consistent solution compared with conventional preconditioning methods. Furthermore, the fundamental equations with the primitive unknown variables were time-integrated without introducing any pseudo-time steps, so that the present scheme can reduce its computing time, compared with the dual time-step method, and improve simulations of the behavior of gas–liquid multiphase flows with the incompressible flow characteristics. The governing equations were solved using a third-order explicit Runge–Kutta method and the flux difference splitting finite-difference scheme combined with a third-order MUSCL TVD scheme. Through numerical experiments for various 2D single-phase and gas–liquid two-phase flows with different flow conditions, including cavitation numbers, the acceptability and capability of the present scheme were demonstrated. In particular, the present scheme was successfully applied to flows with very low Mach numbers of 0.001 and two-phase flows with different cavitation numbers. It was also confirmed that the preconditioned stability term significantly improves the convergence rate and numerical stability of steady and unsteady flow computations. Furthermore, the effectiveness and applicability of the present scheme in calculating unsteady gas–liquid multiphase flows were observed through numerical simulations of unsteady cavitating flows at high Reynolds numbers.