Apex jets from impacting drops

2008 ◽  
Vol 614 ◽  
pp. 293-302 ◽  
Author(s):  
J. O. MARSTON ◽  
S. T. THORODDSEN
Keyword(s):  
Surface Tension ◽  
Reynolds Number ◽  
Weber Number ◽  
Limited Range ◽  
Upper Bounds ◽  
Drop Surface ◽  
Viscous Drops ◽  
Lower Viscosity ◽  
Viscous Drop ◽  
Liquid Pools

We present experiments showing vertical jetting from the apex of a viscous drop which impacts onto a pool of lower viscosity liquid. This jet is produced by the ejecta sheet which emerges from the free surface of the pool, and moves up and wraps around the surface of the drop. When this sheet of liquid converges and collides at the top apex of the drop it produces a thin upward jet at velocities of more than 10 times the drop impact velocity. This jetting occurs for a limited range of impact conditions, where the ejecta speed is sufficient for the sheet to travel around the entire drop periphery, but not so fast that it separates from the drop surface. The lower bound for the jetting region is thereby set by a minimal Reynolds number, but the upper bounds are subject to a maximum-Weber-number criterion. The strongest observed jets appear for viscous drops impacting onto liquid pools with the lowest viscosity as well as lowest surface tension, such as acetone and methanol. Jetting has also been observed for drops which are immiscible with the pool liquid, under a different range of impact conditions. However, jetting is never observed for pools of water, as the surface tension is then significantly larger than that of the drop. We believe that Marangoni stresses act in this case to promote separation of the sheet to prevent the jetting. A movie is available with the online version of the paper.

scholarly journals Spreading or contraction of viscous drops between plates: single, multiple or annular drops

2021 ◽  
Vol 925 ◽  
Author(s):  
H.K. Moffatt ◽  
Howard Guest ◽  
Herbert E. Huppert
Keyword(s):  
Surface Tension ◽  
Outer Boundary ◽  
Complete Separation ◽  
Small Perturbations ◽  
Air Bubble ◽  
Trapped Air ◽  
Viscous Drops ◽  
Fingering Instability ◽  
Pressure Region ◽  
Viscous Drop

The behaviour of a viscous drop squeezed between two horizontal planes (a squeezed Hele-Shaw cell) is treated by both theory and experiment. When the squeezing force $F$ is constant and surface tension is neglected, the theory predicts ultimate growth of the radius $a\sim t^{1/8}$ with time $t$. This theory is first reviewed and found to be in excellent agreement with experiment. Surface tension at the drop boundary reduces the interior pressure, and this effect is included in the analysis, although it is negligibly small in the squeezing experiments. An initially elliptic drop tends to become circular as $t$ increases. More generally, the circular evolution is found to be stable under small perturbations. If, on the other hand, the force is reversed ($F<0$), so that the plates are drawn apart (the ‘contraction’, or ‘lifting plate’, problem), the boundary of the drop is subject to a fingering instability on a scale determined by surface tension. The effect of a trapped air bubble at the centre of the drop is then considered. The annular evolution of the drop under constant squeezing is still found to follow a ‘one-eighth’ power law, but this is unstable, the instability originating at the boundary of the air bubble, i.e. the inner boundary of the annulus. The air bubble is realised experimentally in two ways: first by simply starting with the drop in the form of an annulus, as nearly circular as possible; and second by forcing four initially separate drops to expand and merge, a process that involves the resolution of ‘contact singularities’ by surface tension. If the plates are drawn apart, the evolution is still subject to the fingering instability driven from the outer boundary of the annulus. This instability is realised experimentally by levering the plates apart at one corner: fingering develops at the outer boundary and spreads rapidly to the interior as the levering is slowly increased. At a later stage, before ultimate rupture of the film and complete separation of the plates, fingering spreads also from the boundary of any interior trapped air bubble, and small cavitation bubbles appear in the very low-pressure region, far from the point of leverage. This exotic behaviour is discussed in the light of the foregoing theoretical analysis.

Numerical Simulation of Droplet Generation in Series Co-Flow Capillaries

2009 ◽  
Author(s):  
Yanxi Song ◽  
Jinliang Xu
Keyword(s):  
Reynolds Number ◽  
Disperse Phase ◽  
Weber Number ◽  
Three Dimensional ◽  
Continuous Phase ◽  
Disperse Flow ◽  
Double Emulsions ◽  
Wide Range ◽  
In Series ◽  
Dispersed Phases

We study the production and motion of monodisperse double emulsions in microfluidics comprising series co-flow capillaries. Both two and three dimensional simulations are performed. Flow was determined by dimensionless parameters, i.e., Reynolds number and Weber number of continuous and dispersed phases. The co-flow generated droplets are sensitive to the Reynolds number and Weber number of the continuous phase, but insensitive to those of the disperse phase. Because the inner and outer drops are generate by separate co-flow processes, sizes of both inner and outer drops can be controlled by adjusting Re and We for the continuous phase. Meanwhile, the disperse phase has little effect on drop size, thus a desirable generation frequency of inner drop can be reached by merely adjusting flow rate of the inner fluid, leading to desirable number of inner drops encapsulated by the outer drop. Thus highly monodisperse double emulsions are obtained. It was found that only in dripping mode can droplet be of high mono-dispersity. Flow begins to transit from dripping regime to jetting regime when the Re number is decreased or Weber number is increased. To ensure that all the droplets are produced over a wide range of running parameters, tiny tapered tip outlet for the disperse flow should be applied. Smaller the tapered tip, wider range for Re and we can apply.

scholarly journals Cavity Detachment from a Wedge with Rounded Edges and the Surface Tension Effect

2021 ◽  
Vol 9 (11) ◽  
pp. 1253
Author(s):  
Yuriy N. Savchenko ◽  
Georgiy Y. Savchenko ◽  
Yuriy A. Semenov
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Solution Process ◽  
Cavity Flow ◽  
Surface Tension Effect ◽  
Force Coefficient ◽  
Hodograph Method ◽  
Wide Range ◽  
Critical Weber Number ◽  
Cavity Boundary

Cavity flow around a wedge with rounded edges was studied, taking into account the surface tension effect and the Brillouin–Villat criterion of cavity detachment. The liquid compressibility and viscosity were ignored. An analytical solution was obtained in parametric form by applying the integral hodograph method. This method gives the possibility of deriving analytical expressions for complex velocity and for potential, both defined in a parameter plane. An expression for the curvature of the cavity boundary was obtained analytically. By using the dynamic boundary condition on the cavity boundary, an integral equation in the velocity modulus was derived. The particular case of zero surface tension is a special case of the solution. The surface tension effect was computed over a wide range of the Weber number for various degrees of cavitation development. Numerical results are presented for the flow configuration, the drag force coefficient, and the position of cavity detachment. It was found that for each radius of the edges, there exists a critical Weber number, below which the iterative solution process fails to converge, so a steady flow solution cannot be computed. This critical Weber number increases as the radius of the edge decreases. As the edge radius tends to zero, the critical Weber number tends to infinity, or a steady cavity flow cannot be computed at any finite Weber number in the case of sharp wedge edges. This shows some limitations of the model based on the Brillouin–Villat criterion of cavity detachment.

scholarly journals An Experimental Study on Wetting of Coal Dust by Surfactant Solution

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yidan Jiang ◽  
Pengfei Wang ◽  
Ronghua Liu ◽  
Ye Pei ◽  
Gaogao Wu
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Reverse Osmosis ◽  
Sodium Sulfate ◽  
Moisture Absorption ◽  
Coal Dust ◽  
Pure Water ◽  
Surfactant Solution ◽  
Limited Range ◽  
Dust Reduction

Surfactants can improve the wetting performance of the dust-reduction spraying water, thus improving the dust-reduction effect by spray. In this study, the performance of surfactant solution in wetting coal dust was investigated through experiments. In addition, the effects of surfactant type, mass fraction, metamorphic degree of coal, particle size, and additives were investigated. According to the results of surface tension experiments, the surface tension of the solution decreased with the increase of the concentration of surfactant. However, after reaching CMC, the surface tension did not have significantly decrease. SDBS and OP-10 had higher efficiency in decreasing the surface tension than the other two types of surfactants. The addition of sodium sulfate additives can further reduce the surface tension of the surfactant solution by a limited range. The coal dust wetting experiment showed that with the increase in the concentration of the surfactant, the contact angle of the droplets on the coal dust tablet was continuously reduced, and the wettability of the solution was continuously improved. The wettability of the OP-10 solution was optimal. At the same concentration, the minimum contact angle can be obtained in the OP-10 solution. As the contact angle of the coal dust increased, the growth rate in the coal dust reverse osmosis moisture absorption of the surfactant solution relative to the pure water increased. After the addition of sodium sulfate, the reverse osmosis moisture absorption of coal dust increased to varying degrees. In addition, as the concentration of additives increased, the moisture absorption of coal dust increased.

scholarly journals Assessment of inner–outer interactions in the urban boundary layer using a predictive model

2019 ◽  
Vol 875 ◽  
pp. 44-70 ◽  
Author(s):  
Karin Blackman ◽  
Laurent Perret ◽  
Romain Mathis
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Predictive Model ◽  
Boundary Layers ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Limited Range ◽  
Rough Wall ◽  
Wall Boundary ◽  
Layer Flow

Urban-type rough-wall boundary layers developing over staggered cube arrays with plan area packing density, $\unicode[STIX]{x1D706}_{p}$, of 6.25 %, 25 % or 44.4 % have been studied at two Reynolds numbers within a wind tunnel using hot-wire anemometry (HWA). A fixed HWA probe is used to capture the outer-layer flow while a second moving probe is used to capture the inner-layer flow at 13 wall-normal positions between $1.25h$ and $4h$ where $h$ is the height of the roughness elements. The synchronized two-point HWA measurements are used to extract the near-canopy large-scale signal using spectral linear stochastic estimation and a predictive model is calibrated in each of the six measurement configurations. Analysis of the predictive model coefficients demonstrates that the canopy geometry has a significant influence on both the superposition and amplitude modulation. The universal signal, the signal that exists in the absence of any large-scale influence, is also modified as a result of local canopy geometry suggesting that although the nonlinear interactions within urban-type rough-wall boundary layers can be modelled using the predictive model as proposed by Mathis et al. (J. Fluid Mech., vol. 681, 2011, pp. 537–566), the model must be however calibrated for each type of canopy flow regime. The Reynolds number does not significantly affect any of the model coefficients, at least over the limited range of Reynolds numbers studied here. Finally, the predictive model is validated using a prediction of the near-canopy signal at a higher Reynolds number and a prediction using reference signals measured in different canopy geometries to run the model. Statistics up to the fourth order and spectra are accurately reproduced demonstrating the capability of the predictive model in an urban-type rough-wall boundary layer.

Laminar to Turbulent Buoyant Vortex Ring Regime in Terms of Reynolds Number, Bond Number, and Weber Number

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Xueying Yan ◽  
Rupp Carriveau ◽  
David S. K. Ting
Keyword(s):  
Reynolds Number ◽  
Vortex Ring ◽  
Weber Number ◽  
High Speed ◽  
Reynolds Numbers ◽  
Bond Number ◽  
Vortex Rings ◽  
Transition Regime ◽  
Turbulent Vortex ◽  
Buoyant Vortex Rings

When buoyant vortex rings form, azimuthal disturbances occur on their surface. When the magnitude of the disturbance is sufficiently high, the ring will become turbulent. This paper establishes conditions for categorization of a buoyant vortex ring as laminar, transitional, or turbulent. The transition regime of enclosed-air buoyant vortex rings rising in still water was examined experimentally via two high-speed cameras. Sequences of the recorded pictures were analyzed using matlab. Key observations were summarized as follows: for Reynolds number lower than 14,000, Bond number below 30, and Weber number below 50, the vortex ring could not be produced. A transition regime was observed for Reynolds numbers between 40,000 and 70,000, Bond numbers between 120 and 280, and Weber number between 400 and 800. Below this range, only laminar vortex rings were observed, and above, only turbulent vortex rings.

Distorted gas bubbles at large Reynolds number

1974 ◽  
Vol 62 (1) ◽  
pp. 163-183 ◽  
Author(s):  
M. El Sawi
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Liquid Metals ◽  
Gas Bubbles ◽  
Joint Effect ◽  
Large Reynolds Number ◽  
Recent Experimental Data ◽  
Approximate Theory ◽  
Axis Ratio ◽  
Comparison Of The Results

The distortion of a gas bubble rising steadily in an inviscid incompressible liquid of infinite extent under the action of surface tension forces is investigated theoretically using an appropriate extension of the tensor virial theorem. A convenient parameter for distinguishing the bubble shape is the Weber numberW. The virial method leads to an expression relatingWand the axis ratio χ, of the transverse and longitudinal axes of the bubble. To first order inW, this relation agrees with the linear theory established by Moore (1959). Also, comparison of the results with his (1965) approximate theory reveals similar features and excellent agreement up to χ = 2. In particular, it confirms his prediction of the existence of a maximum Weber number. Although the present work does not consider the stability of these bubbles, it is interesting to note that the maximum value of 3.271 attained byWdiffers only by about 2.8% from the critical Weber number obtained by Hartunian & Sears (1957) for the onset of instability.An approximate method for the study of slightly distorted spheroidal gas bubbles is also formulated and the resulting boundary-value problem solved numerically. The theory is then extended to include gravity. The joint effect of surface tension as well as gravitational forces has not been included in earlier theories. The shapes of the bubbles are traced and compared with the unperturbed spheroids. Comparisons for the velocity of bubble rise are made between the present predictions and some experimental results. In particular the results are compared with recent experimental data for the motion of gas bubbles in liquid metals.

scholarly journals Antibubbles and fine cylindrical sheets of air

2015 ◽  
Vol 779 ◽  
pp. 87-115 ◽  
Author(s):  
D. Beilharz ◽  
A. Guyon ◽  
E. Q. Li ◽  
M.-J. Thoraval ◽  
S. T. Thoroddsen
Keyword(s):  
Layer Thickness ◽  
Stability Theory ◽  
Extended Period ◽  
Viscous Drops ◽  
Pool Surface ◽  
Lower Viscosity ◽  
Air Layers ◽  
The Stability ◽  
Air Film ◽  
The Way

Drops impacting at low velocities onto a pool surface can stretch out thin hemispherical sheets of air between the drop and the pool. These air sheets can remain intact until they reach submicron thicknesses, at which point they rupture to form a myriad of microbubbles. By impacting a higher-viscosity drop onto a lower-viscosity pool, we have explored new geometries of such air films. In this way we are able to maintain stable air layers which can wrap around the entire drop to form repeatable antibubbles, i.e. spherical air layers bounded by inner and outer liquid masses. Furthermore, for the most viscous drops they enter the pool trailing a viscous thread reaching all the way to the pinch-off nozzle. The air sheet can also wrap around this thread and remain stable over an extended period of time to form a cylindrical air sheet. We study the parameter regime where these structures appear and their subsequent breakup. The stability of these thin cylindrical air sheets is inconsistent with inviscid stability theory, suggesting stabilization by lubrication forces within the submicron air layer. We use interferometry to measure the air-layer thickness versus depth along the cylindrical air sheet and around the drop. The air film is thickest above the equator of the drop, but thinner below the drop and up along the air cylinder. Based on microbubble volumes, the thickness of the cylindrical air layer becomes less than 100 nm before it ruptures.

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