Rayleigh Instability Research Articles

Electrical effects on droplet behaviour

The effect of charge on water droplets modulates various aspects of their behaviour. These include the droplet stability, evaporation, and lifetime. Microphysical models have been developed such that a reasonably good understanding of these processes has been achieved. However, the specific effects of charge deserve further scrutiny as they are an intrinsic component of the factors controlling droplet characteristics. Describing the effects of these requires an understanding of the electrostatic pressure present in the droplet and its surface tension. One way to test these effects and assess droplet response to charge is to take an experimental approach to make observations directly. In this study, individual droplets are levitated in an acoustic wave to allow isolated measurements to be taken. The droplets are monitored using a CCD camera with a microscope objective lens. In some cases, with sufficient charge present, effects on droplet stability can be observed as Rayleigh explosions, where a sudden drop in mass is seen superimposed on the evaporation profile. These events also allow the charge on the droplet to be calculated, which is then compared with the droplet evaporation. Another factor that plays a part in droplet behaviour is droplet composition. Different substances have different surface tension, and this is explored by performing some experiments on sulphuric acid droplets. Theory predicts that the more highly charged a droplet is, the more resistant to evaporation it becomes. Experimental data collected during this study agrees with this, with more highly charged droplets observed to have slower evaporation rates. However, highly charged drops were also observed to periodically become unstable during evaporation and undergo Rayleigh explosions. Each instability of a highly charged drop removes mass, reducing the overall droplet lifetime regardless of the slower evaporation rate. The sulphuric acid droplets were observed to be much more resistant to evaporation and no Rayleigh instabilities were observed.

Study on Marangoni explosion of binary mixtures in liquid layer

In this work, the process of forming micro-droplets due to instability and fragmentation after short chain alcohol solution spreads on the surface of oil layers is studied. Based on the free energy theory of the liquid-liquid interface, the relationship between the binary mixtures spreading on the surface of the liquid layer is derived, and the concentration range of short chain alcohol solution spreading as a thin film on the surface of the oil layer is calculated from the Hiskovsky formula. The Malangoni flow caused by the difference in evaporation rate between the center and edge of the droplet film perturbs the boundary of the liquid film, causing finger-shaped liquid columns to grow at the edge when the droplet spreads to its maximum. In this work, the expression for the critical wavelength and maximum wavelength of boundary instability are derived based on the perturbation model, and the reason for finger shaped liquid column fragmentation is explained based on the Plateau Rayleigh instability. A concentric cylindrical shell liquid column model is established to simplify the calculation and predict the location range of “droplet explosion” of droplets with different viscosity ratios on the liquid layer. Through theoretical calculations and experimental verification, it is found that the alcohol solution fragmented into small droplets within a length range of 4.51–5.98 times the width of the liquid column. This study provides theoretical guidance for existing application fields such as film forming technology and coating technology. The hypotheses, assumptions, and simplified models preliminarily verified experimentally provide solutions for some technical difficulties in the research fields of micro reactions and nanoparticle preparation in chemical industry.

Formation characteristics and acoustic regulation of liquid metal droplets in low-aspect-ratio channels

The uniformity in size of liquid metal droplets is crucial in determining the accuracy of flexible circuit printing as well as the stability in signal transmission. In this study, the numerical simulation and the experiment method are combined to analyze the droplet preparation process of liquid metal. Furthermore, the mechanism of the surface acoustic wave as an external force dominating the breakup of the liquid metal interface is investigated. The results show that the squeezing pressure and the capillary force are the dominant forces of the interface evolution in the low-aspect-ratio (height/width) channel. When the dispersed phase flow rate is low, the interface will retract upstream of the channel under the influence of large interfacial tension after breakup, resulting in fluctuations in flow rate, and therefore, the stability of droplet size is weak. When the dispersed phase flow rate is high, the interface randomly breaks up under the influence of the Rayleigh–Plateau instability, which also leads to uneven droplet size. As the acoustic intensity increases, the acoustic radiation pressure gradually becomes the dominant force responsible for the squeezing and breakup of the interface. It increases the radial contraction rate of the interface, shortens the droplet generation period, and ultimately reduces the droplet size. Additionally, the size deviation value is significantly reduced from 10.13% to 1.05%. This study is useful in elucidating the evolution mechanism of liquid metal interfaces in low-aspect-ratio channels, improving the fundamental theory of interface breakup caused by acoustic radiation pressure, and providing theoretical guidance for the controlled and stable production of liquid metal droplets.

Plateau-Rayleigh instability of a soft layer coated on a rigid cylinder.

We study the Plateau-Rayleigh instability of a soft viscoelastic solid layer coated on a rigid cylinder i.e., a soft fibre with a rigid core. The onset of instability is examined using a linear stability analysis. We find that increasing the rigid cylinder radius or the stiffness of the layer reduces the growth rate of the fastest growing mode. For each rigid cylinder radius, a critical elastocapillary number is found below which all wavelengths of disturbances are stable. The critical value for a soft fibre with a thick rigid cylindrical core can be several orders of magnitudes larger than that for a totally soft fibre (no rigid core). This highlights the strong stabilizing effect of the rigid core on the system. Increasing the relaxation timescale of the viscoelastic material also slows down the growth of disturbances, but has no effect on the critical elastocapillary number. Interestingly, the wavelength of the fastest growing mode is independent of the rigid cylinder radius for the purely elastic case.

Local volume-conservation-improved diffuse interface model for simulation of Rayleigh–Plateau fluid instability

The Rayleigh–Plateau instability is a typical multi-phase fluid interface problem which is driven by the surface tension. After the break-up of a liquid thread, the satellites droplets will appear. To prevent the disappearance of small droplets due to interfacial length minimization, we present a new Cahn–Hilliard-type diffuse interface model to improve the conservation of local volume. By coupling with the incompressible Navier–Stokes equations, the fluid flow-coupled binary system and its axisymmetric form are derived. The pressure projection method and the semi-implicit time-marching method are used to discretize the fluid equations and the diffuse interface equations in time. In the axisymmetric domain, the finite difference method is used to perform the spatial discretization. The fully discrete solution algorithm is introduced in detail. The numerical experiments show that the proposed model has better local volume conservation than the classical Cahn–Hilliard model. The qualitative comparison with a real experiment indicates that the proposed model has a good potential to simulate the coating problem of a cylindrical fibre with a liquid film.

Contact Time of Droplet Impact on Superhydrophobic Cylindrical Surfaces with a Ridge.

This study investigates whether adding ridges to a superhydrophobic cylindrical surface can reduce contact times compared to those of ridged flat or cylindrical surfaces, inspired by the shortened contact time achieved by adding ridges to flat surfaces. The study focuses on studying azimuthal ridges on the cylinder through experimentation, emphasizing the impact dynamics and contact time characteristics under varying We (Weber number) and D* (dimensionless droplet diameter). Within the ultralow Weber number range (ULWR), low Weber number range (LWR), and medium Weber number range (MWR), the contact time is longer than on ridged flat surfaces. In the high Weber number range (HWR), the opposite is observed: increased inertial forces lead to the rupture of the liquid film above the ridges due to Rayleigh-Plateau instability. As a result, the primary droplet splits into two sections with curvature effects promoting its recoiling and rebounding. This study introduces a criterion, defined as C = We/D*, and finds that when C exceeds 2.42, not only is the contact time shorter than on ridged flat or cylindrical surfaces, but it also further decreases with an increase in We or a decrease in D*. The contact time characteristics observed in the HWR offer potential applications in areas such as anti-icing.

Convection instability in phase-change Rayleigh–Bénard convection systems at a finite Stefan number

In this paper, we revisit the convection instability in phase-change Rayleigh–Bénard convection systems at a finite Stefan number, where a pure solid substance confined between two horizontal walls is isothermally heated from below in order to induce melting, assuming no heat conduction in the solid phase. By establishing a connection between the heat transfer behaviors in the conduction and convection melting regimes through the jump events in the temporal evolution of the heat flux and the melted liquid fraction, two criteria (the critical average fluid temperature θ¯fc and the critical melted liquid fraction flc) are derived to characterize the convection onset. In contrast to the conventional instability analysis, the derivation in the present work is much more convenient and removes the limitation of a vanishing Stefan number (Ste→0). The two obtained criteria are successfully validated by the data available in the literature, together with the numerical simulations conducted in this paper. The validations revealed that the proposed θ¯fc and flc work well at a finite Ste and that flc is slightly less accurate than θ¯fc, due to the error inherited from the employed scaling law describing the convective heat flux. With the relation between the effective and global parameters, flc is further converted into the commonly used critical effective Rayleigh number by Raec=Raflc3, which is found depending on Ste only, being the same as the criterion of θ¯fc, while its precision is less satisfying due to amplified error from the cubic power operation of flc3.

Addressable and stable physically unclonable functions based on cross-linked poly(2-vinylpyridine)

Counterfeiting poses a significant threat to global trade and public health. Effectively combating counterfeiting involves benefiting from stochastic physical processes to build physically unclonable functions (PUFs). Polymers, as low-cost materials with a wide range of functionalities, hold huge potential for PUF applications. In this context, while there are ongoing applications and studies related to PUF systems today, the development of PUF systems that provide high stochastic characteristics and robustness through simple and low-cost production methods remains critically important. In this regard, we propose stable and addressable polymer PUFs, utilizing a cross-linkable poly(2-vinylpyridine) (P2VP). The Rayleigh instability phenomenon occurring in electrohydrodynamic processes is used to fabricate randomized polymeric features. A brief thermal annealing process enhances adhesion with the substrate, while UV-ozone treatment cross-links P2VP. When applied through stencil masks, UV-ozone treatment results in localized cross-linking, yielding addressable randomized features. Structural and chemical analysis is employed to examine the cross-linked polymer features. Adjusting the conditions of electrospraying and cross-linking leads to PUFs with outstanding stability against solvents, oxygen plasma, and thermal heating. The randomized response of polymer features is evaluated through various statistical criteria. Feature matching algorithms enable direct authentication of images captured under different rotations and lighting conditions. This study demonstrates a versatile strategy for creating polymer-based PUFs with remarkable stability and addressability, enabled by a cross-linkable polymer system.

A single-phase GPU-accelerated surface tension model using SPH

This paper presents an accelerated single-phase surface tension smoothed particle hydrodynamics (SPH) solver developed to run entirely on a graphics processing unit (GPU) capable of simulating millions of particles in three dimensions on a single GPU. The single-phase surface tension model is augmented with a contact line force to improve the prediction of the physics at the liquid-solid contact point. The surface tension model uses the modified dynamic boundary condition (mDBC) to impose no-slip conditions at the wall boundary. To enable simulations with millions of particles, the single-phase surface tension model has been implemented in the open-source SPH code DualSPHysics to exploit the GPU acceleration, paying special attention to the size of the kernel support and integration of the neighbour lists. The new scheme is validated using 2-D and 3-D test cases including drop deformation, drop oscillation, Rayleigh-Plateau instability and surface contact angles. The results show a good agreement with the analytical solutions with a standard spatial convergence behaviour. Profiling the new surface tension solver shows an additional computational complexity. The performance analysis shows that the new code has a speed up of up two orders of magnitude (x70-80) compared to the CPU-only code. Profiling the new CUDA kernels shows they have the near identical performance metrics with the main CUDA kernels in the original DualSPHysics solver.

Preparation of pH-sensitive alginate-based hydrogel by microfluidic technology for intestinal targeting drug delivery

Hydrogel microspheres stand out in drug delivery due to their small particle size, biocompatibility and good internal stability. In this paper, pH-sensitive hydrogels are prepared by microfluidic technology for targeted drug delivery in the small intestine. A coaxial dual-channel microfluidic chip is constructed. By analyzing the effects of flow rates and three fracture stages (Rayleigh-Plateau instability crushing stage, pressure difference crushing stage and shear force crushing stage) on the size of hydrogel microspheres, the optimal control stage of the microsphere size is determined (shear force crushing stage). Based on this, the accurate control model of the hydrogel microsphere size is proposed. In addition, based on the coaxial dual channel microfluidic chip, a monolayer hydrogel microcapsule loaded with Indometacin is prepared. The core-shell hydrogel microcapsules loaded with Indometacin are prepared by an improved coaxial three channel microfluidic chip. The swelling rates of both microcapsules in simulated intestinal fluid are significantly higher than those in simulated gastric fluid. The results of in vitro simulated release experiments show that the two hydrogel microcapsules basically do not release in simulated gastric juice. In simulated intestinal fluid, single-layer hydrogel microcapsules show rapid release, while core-shell hydrogel microcapsules showed slow release. In conclusion, the alginate-based hydrogel microcapsules have good stability and pH sensitivity, and are suitable for targeted drug delivery in the small intestine.

The interaction of a droplet with an immiscible deep liquid pool for density ratio greater than unity

Droplet interaction with liquid pools has been widely studied. The focus of these studies has primarily been on like-fluids, the droplet being miscible with the pool. Such miscible droplet–pool interactions have been extensively studied for their regimes of Rayleigh jet formation, crater formation, splashing, and coalescence. However, the case of immiscible droplet fluid has received considerably less attention from researchers. The immiscible case is relatively complex to understand owing to the involvement of three interfacial tensions. In the current study, we investigate the regimes of droplet–pool interaction for the case of immiscible droplet fluid having higher density and surface tension than pool fluid. Droplet properties are characterized through Weber number while Ohnesorge number is used to characterize pool fluid. Weber number is controlled through velocity of droplet and viscosity of pool is used to predict Ohnesorge number. Validating the numerical methods with experimental data, extensive numerical simulations are performed to gain insight into droplet–pool interaction. Current investigation reveals that for the case of immiscible fluids, regime formation is observed due to Rayleigh–Plateau instability as well as droplet fluid interacting with the pool fluid. This enables the pool fluid jet separation at high Ohnesorge numbers too, in contrast to miscible fluids case. The regimes of droplet–pool interaction for current case are described in detail and classified over wide range of Weber and Ohnesorge numbers.

Microwave enhancement of extractions and reactions in Liquid-Liquid biphasic systems

Microwaves (MWs) are a powerful technology for electrifying chemical processing and can enable selective heating, which is impossible in conventional systems. This effect was recently ascribed to enhancing liquid–liquid reactive extractions in biomass derivative chemistry. Expanding upon prior research that showcased MW-induced temperature gradients and their optimization, this study delves into the impact of these gradients on extraction using a combination of experiments and simulations. The findings illustrate that the colder organic phase enforced by the MW heating leads to alterations in solute partitioning and phase behavior. Partitioning can be further tuned by adding salts or by carefully selecting solvents, as demonstrated via COSMO-RS calculations. The colder organic phase also leads to Rayleigh instabilities and active buoyancy-driven mixing. These effects, measured experimentally and simulated in COMSOL, can greatly enhance mass transfer rates in liquid–liquid systems. Under conditions reported in the literature, the MW enhancement to reactive extractions is minimal. Conditions that may lead to more impressive extractions and reactive extractions are suggested. Additionally, it's observed that temperature gradients retard byproduct formation.

Optimal boundary control of a model thin-film fiber coating model

This paper considers the control of fluid on a solid vertical fiber, where the fiber radius is larger than the film thickness. The fluid dynamics is governed by a fourth-order partial differential equation (PDE) that models this flow regime. Fiber coating is affected by the Rayleigh–Plateau instability that leads to breakup into moving droplets. In this work, we show that control of the film profile can be achieved by dynamically altering the input flux to the fluid system that appears as a boundary condition of the PDE. We use the optimal control methodology to compute the control function. This method entails solving a minimization of a given cost function over a time horizon. We formally derive the optimal control conditions, and numerically verify that subject to the domain length constraint, the thin film equation can be controlled to generate a desired film profile with a single point of actuation. Specifically, we show that the system can be driven to both constant film profiles and traveling waves of certain speeds.

Study on atomization mechanisms and spray fragmentation characteristics of water and emulsion butachlor.

Agricultural chemicals are commonly used to control pests and weeds, but cause pesticide waste problems. Oil-based emulsions are often used as pesticide formulations to improve pesticide utilization. In this study, the spray visualization experiment of the water and oil-based emulsion butachlor is carried out using an ST flat fan nozzle at 0.1-0.5 MPa pressure. The dimensionless method is used to analyze the difference in liquid sheet fragmentation morphology and disintegration process and the influence of different fragmentation methods on droplet size. It is found that the hydrophobic components in pesticide have a significant effect on the morphology and process of atomization fragmentation. When spray liquid is water, the liquid sheet breaks up into liquid ligaments due to the Rayleigh instability, then the ligaments break up into droplets. The side view of a liquid sheet is a large-amplitude wave disturbance. When the spray liquid is the emulsion butachlor, holes are generated on the liquid sheet, then the holes break up into droplets. The fragmentation method of emulsion spray is the perforation mechanism. Compared with water spray, the presence of the pesticide butachlor increases the droplet size and spray angle and improves the uniformity of droplet size distribution but reduces the breakup length. The spray angle shows a power law dependence of the Weber number with a power of 0.17 for all conditions tested here. At 0.3 MPa, DV50 increases 25%, and span decreases from 1.187 to 1.172. This study could provide reference for the addition of agricultural additives, the improvement of spray operation efficiency, and the establishment of spray fragmentation mechanism.

Surfactant amplifies yield-stress effects in the capillary instability of a film coating a tube.

To assess how the presence of surfactant in lung airways alters the flow of mucus that leads to plug formation and airway closure, we investigate the effect of insoluble surfactant on the instability of a viscoplastic liquid coating the interior of a cylindrical tube. Evolution equations for the layer thickness using thin-film and long-wave approximations are derived that incorporate yield-stress effects and capillary and Marangoni forces. Using numerical simulations and asymptotic analysis of the thin-film system, we quantify how the presence of surfactant slows growth of the Rayleigh-Plateau instability, increases the size of initial perturbation required to trigger instability and decreases the final peak height of the layer. When the surfactant strength is large, the thin-film dynamics coincide with the dynamics of a surfactant-free layer but with time slowed by a factor of four and the capillary Bingham number, a parameter proportional to the yield stress, exactly doubled. By solving the long-wave equations numerically, we quantify how increasing surfactant strength can increase the critical layer thickness for plug formation to occur and delay plugging. The previously established effect of the yield stress in suppressing plug formation [Shemilt et al., J. Fluid Mech., 2022, vol. 944, A22] is shown to be amplified by introducing surfactant. We discuss the implications of these results for understanding the impact of surfactant deficiency and increased mucus yield stress in obstructive lung diseases.

Evaporation of alcohol droplets on surfaces in moist air

Droplets of alcohol-based formulations are common in applications from sanitizing sprays to printing inks. However, our understanding of the drying dynamics of these droplets on surfaces and the influence of ambient humidity is still very limited. Here, we report the drying dynamics of picoliter droplets of isopropyl alcohol deposited on a surface under controlled humidity. Condensation of water vapor in the ambient environment onto alcohol droplets leads to unexpectedly complex drying behavior. As relative humidity (RH) increases, we observed a variety of phenomena including enhanced spreading, nonmonotonic changes in the drying time, the formation of pancake-like shapes that suppress the coffee-ring effect, and the formation of water-rich films around an alcohol-rich drop. We developed a lubrication model that accounts for the coupling between the flow field within the drop, the shape of the drop, and the vapor concentration field. The model reproduces many of the experimentally observed morphological and dynamic features, revealing the presence of unusually large spatial compositional gradients within the evaporating droplet and surface-tension-gradient-driven flows arising from water condensation/evaporation at the surface of the droplet. One unexpected feature from the simulation is that water can evaporate and condense concurrently in different parts of the drop, providing fundamental insights that simpler models based on average fluxes lack. We further observed rim instabilities at higher RH that are well-described by a model based on the Rayleigh-Plateau instability. Our findings have implications for the testing and use of alcohol-based disinfectant sprays and printing inks.

Bubble nucleation and jetting inside a millimetric droplet

In this work we present experiments and simulations on the nucleation and successive dynamics of laser-induced bubbles inside liquid droplets in free-fall motion, i.e. a case where the bubbles are subjected to the influence of a free boundary in all directions. Within this spherical millimetric droplet, we have investigated the nucleation of secondary bubbles induced by the rarefaction wave that is produced when the shock wave emitted by the laser-induced plasma reflects at the drop surface. Interestingly, three-dimensional clusters of cavitation bubbles are observed. Their shape is compared with the negative pressure distribution computed with a computational fluid dynamics model and allows us to estimate a cavitation threshold value. In particular, we observed that the focusing of the waves in the vicinity of the free surface can give rise to explosive cavitation events that end up in fast liquid ejections. High-speed recordings of the drop/bubble dynamics are complemented by the velocity and pressure fields simulated for the same initial conditions. The effect of the proximity of a curved free surface on the jetting dynamics of the bubbles was qualitatively assessed by classifying the cavitation events using a non-dimensional stand-off parameter ${\Upsilon\hskip -1,05em -\,}$ that depends on the drop size, the bubble maximum radius and the relative position of the bubble inside the drop. Additionally, we studied the role of the drop's curvature by implementing a structural similarity algorithm to compare cases with bubbles produced near a flat surface to the bubbles inside the drop. Interestingly, this quantitative comparison method indicated the existence of equivalent stand-off distances at which bubbles influenced by different boundaries behave in a very similar way. The oscillation of the laser-induced bubbles promotes the onset of Rayleigh–Taylor and Rayleigh–Plateau instabilities, observed on the drop's surface. This phenomenon was studied by varying the ratio of the maximum radii of the bubble and the drop. The specific mechanisms leading to the destabilisation of the droplet surface were identified.

The formation mechanism of metal-ceramic interlayer interface during laser powder bed fusion

ABSTRACT Experiments on Laser powder bed fusion (LPBF) of powdered Ti on Al2O3 substrate were conducted and the interface formation was studied using a multi-material fluid dynamics model. Results show that the melt pool is relatively shallow, with relatively flat interlayer interface under LPBF’s conduction mode. In this condition, a thin sheath of molten Al2O3 forms and acts as a lubricating film for the molten Ti, leading to Rayleigh instability due to high flow inertia. Keyhole formation penetrates the Al2O3 substrate, resulting in a wavy interlayer interface. The recoil pressure from the keyhole and overall melt inertia are suppressed by the highly viscous molten Al2O3, thereby improving single-track melt pool stability. However, the thermal expansion coefficient difference between Ti and Al2O3 led to the formation of transverse cracks. Achieving a defect-free metal-on-ceramic single track remains a challenge, despite this study serving as a guide for melt track and interface control.

High-frequency instabilities in supersonic compression-ramp flow

We consider high Reynolds number supersonic flow over a compression ramp in the triple-deck formulation. Previous studies of compression-ramp stability have shown rapid growth of high-frequency disturbances in initial-value computations; however, no physical or numerical origin has yet been identified robustly. By considering linear perturbations to steady compression-ramp solutions, we show that instabilities observed in previous studies do not have a growth rate that is described by the integral eigenrelation of Tutty & Cowley (J. Fluid Mech., vol. 168, 1986, pp. 431–456) for a (long-wave) Rayleigh instability. We solve both the temporal and spatial instability problems in the limit of asymptotically large wavenumber $K$ (or equivalently frequency) and show that the growth rate of the instability remains $o(K)$ , being dominated by higher-order terms in the expansion at moderate ramp angles.

Formation of various cell-aggregated structures in the core of hydrogel filament using a microfluidic device and its application as an in vitro neuromuscular junction model

Microfluidic systems have been widely used in various in vitro tissue engineering models. In this paper, we present a new microfluidic system for manufacturing cell filaments laden with cell aggregates of various shapes (beads, rosaries, and filaments) in the core region. The structures were obtained using the Rayleigh-Plateau instability of the two-phase flow of the injected bioinks (continuous phase of collagen/poly[ethylene glycol] diacrylate [PEGDA] and a dispersed phase of methacrylated gelatin (GelMA)). To demonstrate the potential of the system at the neuromuscular junction in vitro model, we injected a C2C12-laden collagen/PEGDA bioink into the sheath region and GelMA mixed with motor neuron cells (NSC-34) into the core region of the fabricated cell aggregates. The rosary-shaped NSC-34 aggregate in the core exhibited higher cell viability and more developed neurogenic gene expression than the cell aggregates of beads and filaments in the core region, owing to much greater mechanotransduction. Furthermore, when comparing the cell-laden struts (C2C12 in the sheath region and NSC34 in the rosary core region) with normally bioprinted struts with the same cell density, the expressions of myogenesis-, neuromuscular junction (NMJ)-, and neurogenesis-related genes in struts laden with rosary-shaped cell aggregates were significantly upregulated. The results of these experiments demonstrate the potential for the fabrication of new cell-laden core-sheath structures, which could be used for designing various in vitro models.