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All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Sensitivity of C-Band Polarimetric Radar-Based Drop Size Distribution Measurements to Maximum Diameter Assumptions

The estimation of rain drop size distribution (DSD) parameters from polarimetric radar observations is accomplished by first establishing a relationship between differential reflectivity (Z(sub dr)) and the central tendency of the rain DSD such as the median volume diameter (D0). Since Z(sub dr) does not provide a direct measurement of DSD central tendency, the relationship is typically derived empirically from rain drop and radar scattering models (e.g., D0 = F[Z (sub dr)] ). Past studies have explored the general sensitivity of these models to temperature, radar wavelength, the drop shape vs. size relation, and DSD variability. Much progress has been made in recent years in measuring the drop shape and DSD variability using surface-based disdrometers, such as the 2D Video disdrometer (2DVD), and documenting their impact on polarimetric radar techniques. In addition to measuring drop shape, another advantage of the 2DVD over earlier impact type disdrometers is its ability to resolve drop diameters in excess of 5 mm. Despite this improvement, the sampling limitations of a disdrometer, including the 2DVD, make it very difficult to adequately measure the maximum drop diameter (D(sub max)) present in a typical radar resolution volume. As a result, D(sub max) must still be assumed in the drop and radar models from which D0 = F[Z(sub dr)] is derived. Since scattering resonance at C-band wavelengths begins to occur in drop diameters larger than about 5 mm, modeled C-band radar parameters, particularly Z(sub dr), can be sensitive to D(sub max) assumptions. In past C-band radar studies, a variety of D(sub max) assumptions have been made, including the actual disdrometer estimate of D(sub max) during a typical sampling period (e.g., 1-3 minutes), D(sub max) = C (where C is constant at values from 5 to 8 mm), and D(sub max) = M*D0 (where the constant multiple, M, is fixed at values ranging from 2.5 to 3.5). The overall objective of this NASA Global Precipitation Measurement Mission (GPM/PMM Science Team)-funded study is to document the sensitivity of DSD measurements, including estimates of D0, from C-band Z(sub dr) and reflectivity to this range of D(sub max) assumptions. For this study, GPM Ground Validation 2DVD's were operated under the scanning domain of the UAHuntsville ARMOR C-band dual-polarimetric radar. Approximately 7500 minutes of DSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSD's were then used as input to a T-matrix model for computation of polarimetric radar moments at C-band. All necessary model parameterizations, such as temperature, drop shape, and drop fall mode, were fixed at typically accepted values while the D(sub max) assumption was allowed to vary in sensitivity tests. By hypothesizing a DSD model with D(sub max) (fit) from which the empirical fit to D0 = F[Z(sub dr)] was derived via non-linear least squares regression and a separate reference DSD model with D(sub max) (truth), bias and standard error in D0 retrievals were estimated in the presence of Z(sub dr) measurement error and hypothesized mismatch in D(sub max) assumptions. Although the normalized standard error for D0 = F[Z(sub dr)r] can increase slightly (as much as from 11% to 16% for all 7500 DSDs) when the D(sub max) (fit) does not match D(sub max) (truth), the primary impact of uncertainty in D(sub max) is a potential increase in normalized bias error in D0 (from 0% to as much as 10% over all 7500 DSDs, depending on the extent of the mismatch between D(sub max) (fit) and D(sub max) (truth)). For DSDs characterized by large Z(sub dr) (Z(sub dr) > 1.5 to 2.0 dB), the normalized bias error for D0 estimation at C-band is sometimes unacceptably large (> 10%), again depending on the extent of the hypothesized D(sub max) mismatch. Modeled errors in D0 retrievals from Z(sub dr) at C-band are demonstrated in detail and comparedo similar modeled retrieval errors at S-band and X-band where the sensitivity to D(sub max) is expected to be less. The impact of D(sub max) assumptions to the retrieval of other DSD parameters such as Nw, the liquid water content normalized intercept parameter, are also explored. Likely implications for DSD retrievals using C-band polarimetric radar for GPM are assessed by considering current community knowledge regarding D(sub max) and quantifying the statistical distribution of Z(sub dr) from ARMOR over a large variety of meteorological conditions. Based on these results and the prevalence of C-band polarimetric radars worldwide, a call for more emphasis on constraining our observational estimate of D(sub max) within a typical radar resolution volume is made

Carey, Lawrence D.↗
NASA NTRS1998

Internal Flows in Free Drops (IFFD)

Within the framework of an Earth-based research task investigating the internal flows within freely levitated drops, a low-gravity technology development experiment has been designed and carried out within the NASA Glovebox facility during the STS-83 and STS-94 Shuttle flights (MSL-1 mission). The goal was narrowly defined as the assessment of the capabilities of a resonant single-axis ultrasonic levitator to stably position free drops in the Shuttle environment with a precision required for the detailed measurement of internal flows. The results of this entirely crew-operated investigation indicate that the approach is fundamentally sound, but also that the ultimate stability of the positioning is highly dependent on the residual acceleration characteristic of the Spacecraft, and to a certain extent, on the initial drop deployment of the drop. The principal results are: the measured dependence of the residual drop rotation and equilibrium drop shape on the ultrasonic power level, the experimental evaluation of the typical drop translational stability in a realistic low-gravity environment, and the semi-quantitative evaluation of background internal flows within quasi-isothermal drops. Based on these results, we conclude that the successful design of a full-scale Microgravity experiment is possible, and would allow accurate the measurement of thermocapillary flows within transparent drops. The need has been demonstrated, however, for the capability for accurately deploying the drop, for a quiescent environment, and for precise mechanical adjustments of the levitator.

Trinh, E. H.↗
NASA NTRS1999

A New Approach to Measure Contact Angle and Evaporation Rate with Flow Visualization in a Sessile Drop

The contact angle and the spreading process of sessile droplet are very crucial in many technological processes, such as painting and coating, material processing, film-cooling applications, lubrication, and boiling. Additionally, as it is well known that the surface free energy of polymers cannot be directly, measured for their elastic and viscous restraints. The measurements of liquid contact angle on the polymer surfaces become extremely important to evaluate the surface free energy of polymers through indirect methods linked with the contact angle data. Due to the occurrence of liquid evaporation is inevitable, the effects of evaporation on the contact angle and the spreading become very important for more complete understanding of these processes. It is of interest to note that evaporation can induce Marangoni-Benard convection in sessile drops. However, the impacts of the inside convection on the wetting and spreading processes are not clear. The experimental methods used by previous investigators cannot simultaneously measure the spreading process and visualize the convection inside. Based on the laser shadowgraphic system used by the present author, a very simple optical procedure has been developed to measure the contact angle, the spreading speed, the evaporation rate, and to visualize inside convection of a sessile drop simultaneously. Two CCD cameras were used to synchronously record the real-time diameter of the sessile drop, which is essential for determination of both spreading speed and evaporation rate, and the shadowgraphic image magnified by the sessile drop acting as a thin plano-convex lens. From the shadowgraph, the inside convection of the drop can be observed if any and the image outer diameter, which linked to the drop profile, can be measured. Simple equations have been derived to calculate the drop profile, including the instantaneous contact angle, height, and volume of the sessile drop, as well as the evaporation rate. The influence of the inside convection on the wetting and spreading processes can be figured out through comparison of the drop profiles with and without inside convection when the sessile drop is placed at different evaporation conditions.

Zhang, Nengli↗
NASA NTRS2000

Rotating Molten Metallic Drops and Related Phenomena: A New Approach to the Surface Tension Measurement

Molten aluminum and tin drops were levitated in a high vacuum by controlled electric fields, and they were systematically rotated by applying by a rotating magnetic field. When the evolution of the drop shape was measured as a function of rotation frequency, it agreed quantitatively well with the Brown and Scriven's theoretical prediction. The normalized rotation frequencies at the bifurcation point agreed with the predicted value 0.559, within 2%. An anomalous phenomenon which totally deviated from the prediction was observed in rotating molten tin drops when they were kept in a high rotation rate for several hours. No anomaly was observed in aluminum drops when they underwent similar condition. It was speculated that under the strong centrifugal force in the drop the tin isotopes must be separating. Since Al-27 is essentially the only naturally abundant isotope in the aluminum drops, the same anomaly is not expected. Based on the shape deformation of a rotating drop, an alternate approach to the surface tension measurement was verified. This new surface tension measurement technique was applied to a glassforming alloy, Zr(41.2)Ti(13.8)Cu(12.5)Ni(10.0)Be(22.5) in its highly viscous states. Also demonstrated in the paper was a use of a molten aluminum drop to verify the Busse's prediction of the influence of the drop rotation on the drop oscillation frequency.

Rhim, Won-Kyu↗
NASA NTRS1999

Thermocapillary Migration and Interactions of Bubbles and Drops

Experiments were performed aboard the LMS mission of the Space Shuttle in summer 1996 in the BDPU on isolated air bubbles and Fluorinert FC-75 drops as well as on interacting bubbles/drops migrating in a temperature gradient in a Dow-Corning DC-200 series silicone oil of nominal viscosity 10 centistokes. The data, recorded in the form of videotape images as well as cine images in selected runs, have been analyzed. The behavior of the isolated objects is consistent with earlier observations made aboard the IML-2 mission while the range of Reynolds and Marangoni numbers has been extended substantially over that in the IML-2 experiments. Large bubbles were found to be slightly deformed to an oblate shape while no deformation could be detected in the case of similarly large drops. Results on interacting drops and bubbles display interesting and unanticipated features. In some experiments, drops are found to follow a three-dimensional trajectory. In others, trailing drops and bubbles are found to move off the axis of the cell when migrating behind a leading drop or bubble which moves along the axis. In this type of run, if the trailing drop is sufficiently large, it is found to pass the leading drop. Finally, behavior similar to that observed in IML-2, namely that a small leading drop slows the movement of a larger trailing drop moving along the cell axis, was observed as well.

Subramaniam, R. Shankar↗
NASA NTRS2001

Dynamics and Morphology of Superfluid Helium Drops in a Microgravity Environment

We developed an apparatus that makes it possible to observe and study magnetically levitated drops of superfluid helium. The force on a diamagnetic substance in a magnetic field is proportional to the gradient of the square of the magnetic field B. For the magnetic force on helium to be equal to the gravitational force on Earth, it is necessary for the product of B with the field gradient dB/d z to be 21.5 T(exp 2)/cm. In addition, in order for the magnetic field to provide a stable trap, the value of B(exp 2) must increase in all directions in the horizontal plane that passes through the point where the field/field gradient product in the vertical direction has the critical value of 21.5 T(exp 2)/cm. A specially designed superconducting magnet that meets these specifications has been installed in a large helium dewar with optical access. Helium drops levitated by the magnet can be viewed along the axis of the solenoid. The sample chamber within the bore of the magnet is thermally isolated from the magnet and helium reservoir. Its temperature can be varied between 4 and 0.5 K, the lower part of the range being reached using a He-3 refrigerator. Liquid helium can be injected into the magnetic trap using a small capillary. Once a drop is contained in the trap it can be held there indefinitely. With this apparatus we have conducted a number of different types of experiments on helium drops so as to gain information necessary for performing experiments in space. With magnetically levitated drops we are limited to working with drops of 1 cm. or less in diameter. The shape of the drops larger than a few mm diameter can be distorted by the profile of the magnetic field. The study of phenomena such as the initial motion of the surfaces of two drops as they just make contact, requires the use large drops to resolve the behavior of interest. We have performed a detailed investigation of the shape oscillations of superfluid drops.

Seidel, George M.↗
NASA NTRS2002

A New Look Into the Treatment of Large Drops in Radiative Transfer

One of the weakest links in conventional cloud radiation models is the way a size distribution of cloud particles is mathematically handled: one averages measured drop concentrations over space, evaluates the extinction and scattering cross sections using the mean drop size distribution function and solves the radiative transfer equation with average characteristics. This technique assumes that all drop sizes are well represented in ary given interval along the direction of photon travel. But the concentration of large drops can be so law that this assumption is significantly violated. This is clearly seen if one examines of how the appearance of drops changes with the scale. In the poster we demonstrate the results of our analysis of FSSP data acquired during FIRE'87 and both FSSP and DC1 data from cloud IOP in Spring 2000. The analysis shows that, in general, the average number of drops observed in an interval along the direction of photon travel is proportional to the interval's length (or scale) powered to a drop scaling exponent. For small droplets the scaling exponent is equal to 1, as predicted by a conventional radiative transfer model. However, for large drops, the scaling exponent can fall distinctly below 1. Since the solution of radiative transfer equation depends on the drop scaling exponent, its deviation from unity can lead to a systematic bias in estimation of cloud radiative properties. We discuss the importance of the scaling exponent for the characteristics of the small-scale drop size variability for large and small droplets. Most of the existing cloud radiation models, however, are insensitive to this parameter.

Marshak, Alexander↗
NASA NTRS2004

Model of Mixing Layer With Multicomponent Evaporating Drops

A mathematical model of a three-dimensional mixing layer laden with evaporating fuel drops composed of many chemical species has been derived. The study is motivated by the fact that typical real petroleum fuels contain hundreds of chemical species. Previously, for the sake of computational efficiency, spray studies were performed using either models based on a single representative species or models based on surrogate fuels of at most 15 species. The present multicomponent model makes it possible to perform more realistic simulations by accounting for hundreds of chemical species in a computationally efficient manner. The model is used to perform Direct Numerical Simulations in continuing studies directed toward understanding the behavior of liquid petroleum fuel sprays. The model includes governing equations formulated in an Eulerian and a Lagrangian reference frame for the gas and the drops, respectively. This representation is consistent with the expected volumetrically small loading of the drops in gas (of the order of 10 3), although the mass loading can be substantial because of the high ratio (of the order of 103) between the densities of liquid and gas. The drops are treated as point sources of mass, momentum, and energy; this representation is consistent with the drop size being smaller than the Kolmogorov scale. Unsteady drag, added-mass effects, Basset history forces, and collisions between the drops are neglected, and the gas is assumed calorically perfect. The model incorporates the concept of continuous thermodynamics, according to which the chemical composition of a fuel is described probabilistically, by use of a distribution function. Distribution functions generally depend on many parameters. However, for mixtures of homologous species, the distribution can be approximated with acceptable accuracy as a sole function of the molecular weight. The mixing layer is initially laden with drops in its lower stream, and the drops are colder than the gas. Drop evaporation leads to a change in the gas-phase composition, which, like the composition of the drops, is described in a probabilistic manner

Bellan, Josette↗
NASA NTRS2011

Drop Shapes Versus Fall Velocities in Rain: 2 Contrasting Examples

Rainfall retrievals from polarimetric radar measurements require the knowledge of four fundamental rain microstructure parameters, namely, drop size distribution, drop shape distribution, canting angles and drop fall velocities. Some recent measurements of all four parameters in natural rain are summarized in [1]. In this paper, we perform an in-depth analysis of two events, using two co-located 2D video disdrometers (2DVD; see [2]) both with high calibration accuracy, and a C-band polarimetric radar [3], located 15 km away. The two events, which occurred 7 days apart (on the 18th and the 25th of Dec 2009), had moderate-to-intense rainfall rates, but the second event had an embedded convection line within the storm. The line had passed over the 2DVD site, thus enabling the shapes and fall velocities to be determined as the line crossed the site. The first event was also captured in a similar manner by both the 2DVDs as well as the C-band radar. Drop fall velocity measurements for, say, the 3 mm drops show noticeable differences between the two events. Whereas for the first event, the velocity distribution showed a narrow and symmetric distribution, with a mode at the expected value (7.95 m/s, as given by the formula in [4]), the second event produced a wider distribution with a significant skewness towards lower velocities (although its mode too was close to the expected value). Moreover, the slower 3 mm drops in the second event occurred when the convection line was directly over the 2DVD site (03:35-03:45 utc), and not before nor after. A similar trend was observed in terms of the horizontal dimensions of the 3 mm drops, i.e. large fluctuations during the same time period, but not outside the period. Vertical dimensions of the drops also fluctuated but not to the same extent. Interestingly, the horizontal dimensions tended towards larger values during the 10-minute period, implying an increase in drop oblateness, which in turn indicates the possibility of the horizontal mode oscillation, one of the three fundamental modes of drop oscillations [5], albeit the most difficult one to excite.

Thurai, M.↗
NASA NTRS2022

The Dark Annulus of a Drop in a Hele-Shaw Cell Is Caused by the Refraction of Light through Its Meniscus

Knowing the meniscus shape of confined drops is important for understanding how they make first contact and then coalesce. When imaged from the top view by brightfield microscopy, a liquid drop (e.g., corn syrup) confined in a Hele-Shaw cell, surrounded by immiscible liquid (e.g., mineral oil), had a dark annulus, and the width of the annulus decreased with increasing concentration of corn syrup. Since the difference in the annulus width was presumed to be related to the meniscus shape of the drops, three-dimensional images of the drops with different concentrations were obtained using confocal fluorescence microscopy, and their cross-sectional meniscus profile was determined by image processing. The meniscus of the drops remained circular despite varying concentration. Since the refractive index of corn syrup increased with concentration, while the surface tension coefficient between corn syrup and mineral oil remained unchanged, the observed change in the annulus width was then attributed to the refraction of light passing through the drop’s meniscus. As such, a ray optics model was developed, which predicted that the annulus width of the drop would decrease as the refractive index of the drop approached that of the surrounding liquid. Therefore, the dark annulus of the drops in the Hele-Shaw cell was caused by the refraction of light passing through the circular meniscus of the drop.

Sangjin Ryu↗
NASA NTRS2019

Nasa Glenn Icing Research Tunnel: 2018 Change in Drop-Sizing Equations Due to Change in Cloud Droplet Probe Sample Area

Although there has been no physical change to the cloud drop diameters in the NASA Glenn Icing Research Tunnel (IRT), the IRT cloud calibration team now has an improved understanding of the facility’s drop-sizing instrumentation, which has resulted in a recent change to the drop-sizing equations. Only the calculated values given in the previous calibration report have changed. In 2017, IRT staff found reason to believe that since at least 2014, the sample area for its Cloud Droplet Probe (CDP) (Droplet Measurement Technologies, Inc.) has been closer to 0.289 mm2, rather than the user manual’s suggested value of 0.24 mm2. In September 2017, the probe’s sample area was measured both before and after the probe was realigned, and the end sample area was measured to be 0.248 mm2. Following the probe’s realignment, drop size measurements were made in the IRT using the CDP as well as optical array probes OAP–230X and OAP–230Y (Particle Measurement Systems, Inc.). These measurements suggested that 0.289 mm2 was the more accurate value for historical measurements. When the CDP sample area used for calculations was changed from 0.24 to 0.289 mm2, distributions previously reported to have a median volumetric diameter (MVD) between 30 and 100 μm were instead calculated to have MVD values 10 to 18 percent higher. The analyses that led to these conclusions are reported in this paper, as well as the new drop-sizing equations that have been developed for the corrected measurement values. This report contains updates to drop-sizing data for the IRT’s “normal” operating conditions (MVD < 50 μm) and discusses the effects on the IRT’s “large-drop” conditions (Mod1 nozzles, Pair < 10 psig), but it does not include updates to the drop-sizing equations for those large-drop conditions.

Particle sizing↗
NASA NTRSDate not supplied

Drop Towers for Fun and Research

Microgravity is the apparent weightlessness that occurs during freefall – it affects objects orbiting the Earth, which is why astronauts on the International Space Station (ISS) float. Due to this, experiments and technologies that are sent to the ISS needs to function properly in the microgravity environment. There are only a few ways for scientists and engineers to test in such an environment on Earth and one way is with drop tower facilities. On top of being used for research, drop towers can also be used as a tool for educational outreach. The Drop Towers for Fun and Research website was created as a natural extension of that outreach. It can be used as a tool for teaching the public about drop towers including what drop towers are, what they are used for, and why they are important for microgravity research. Additionally, there will be videos that help answer these questions and that show actual experiments from past drop tower experiments. There will also be a section that highlight Drop Tower used in amusement parks for fun. It is our hope this site will be able to educate the public on drop towers and show them drop tower that they can be used for both fun and research.

drop towers↗
NASA NTRS1982

Large amplitude drop shape oscillations

An experimental study of large amplitude drop shape oscillation was conducted in immiscible liquids systems and with levitated free liquid drops in air. In liquid-liquid systems the results indicate the existence of familiar characteristics of nonlinear phenomena. The resonance frequency of the fundamental quadrupole mode of stationary, low viscosity Silicone oil drops acoustically levitated in water falls to noticeably low values as the amplitude of oscillation is increased. A typical, experimentally determined relative frequency decrease of a 0.5 cubic centimeters drop would be about 10% when the maximum deformed shape is characterized by a major to minor axial ratio of 1.9. On the other hand, no change in the fundamental mode frequency could be detected for 1 mm drops levitated in air. The experimental data for the decay constant of the quadrupole mode of drops immersed in a liquid host indicate a slight increase for larger oscillation amplitudes. A qualitative investigation of the internal fluid flows for such drops revealed the existence of steady internal circulation within drops oscillating in the fundamental and higher modes. The flow field configuration in the outer host liquid is also significantly altered when the drop oscillation amplitude becomes large.

Trinh, E. H.↗
NASA NTRS1993

Head-on collision of drops: A numerical investigation

The head-on collision of equal sized drops is studied by full numerical simulations. The Navier-Stokes equations are solved for fluid motion both inside and outside the drops using a front tracking/finite difference technique. The drops are accelerated toward each other by a body force that is turned off before the drops collide. When the drops collide, the fluid between them is pushed outward leaving a thin later bounded by the drop surface. This layer gets progressively thinner as the drops continue to deform and in several of the calculations this double layer is artificially removed once it is thin enough, thus modeling rupture. If no rupture takes place, the drops always rebound, but if the film is ruptured the drops may coalesce permanently or coalesce temporarily and then split again.

Nobari, M. R.↗
NASA NTRS1994

Numerical Simulations of Drop Collisions

Three-dimensional simulations of the off-axis collisions of two drops are presented. The full Navier-Stokes equations are solved by a Front-Tracking/Finite-Difference method that allows a fully deformable fluid interface and the inclusion of surface tension. The drops are accelerated towards each other by a body force that is turned off before the drops collide. Depending on whether the interface between the drops is ruptured or not, the drops either bounce or coalesce. For drops that coalesce, the impact parameter, which measures how far the drops are off the symmetry line, determines the eventual outcome of the collision. For low impact parameters, the drops coalesce permanently, but for higher impact parameters, a grazing collision, where the drops coalesce and then stretch apart again is observed. The results are in agreement with experimental observations.

Nobari, M. R. H.↗
NASA NTRS1994

The Flow Induced by the Coalescence of Two Initially Stationary Drops

The coalescence of two initially stationary drops of different size is investigated by solving the unsteady, axisymmetric Navier-Stokes equations numerically, using a Front-Tracking/Finite Difference method. Initially, the drops are put next to each other and the film between them ruptured. Due to surface tension forces, the drops coalesce rapidly and the fluid from the small drop is injected into the larger one. For low nondimensional viscosity, or Ohnesorge number, little mixing takes place and the small drop fluid forms a blob near the point where the drops touched initially. For low Ohnesorge number, on the other hand, the small drop forms a jet that penetrates far into the large drop. The penetration depth also depends on the size of the drops and shows that for a given fluid of sufficiently low viscosity, there is a maximum penetration depth for intermediate size ratios.

Nobari, M. R.↗
NASA NTRS1997

Formation and Combustion of Unconfined Drop Clusters in Microgravity

Single-drop and droplet array studies have become common methods to isolate and investigate the effects of any of the complexities that enter into the drop combustion process. Microgravity environments are required to allow larger drops to be studied while minimizing or eliminating the confounding effects of buoyancy. Based on the results from current isolated drop, drop array, and spray studies funded through the Microgravity Science and Applications Division, it has become clear that even with the effects of buoyancy removed, the extrapolation of results from droplet array studies to spray flames is difficult. The problem occurs because even the simplest spray systems introduce complexities of multi-disperse drop sizes and drop-drop interactions, coupled with more complicated fluid dynamics. Not only do these features make the interpretation of experimental data difficult, they also make the problem very difficult to analyze computationally. Group combustion models, in which the interaction between droplets is treated on a statistical manner, have become a popular method to investigate the behavior of large numbers of interacting droplets, particularly through the work of Ryan et al. and Bellan and co-workers. While these models idealize the actual spray systems to a point where they can be treated computationally, the experimental analogy to these models is difficult to achieve because it requires the formation and Combustion of drop clusters without the effects of buoyancy. Therefore, even though these models have provided useful and insightful information, the verification of the results by direct comparison with experimental data is still lacking.

Liu, S.↗
NASA NTRS2004

The Stability of Two Connected Pendant Drops

The stability of an equilibrium system of two drops suspended from circular holes is examined. The drop surfaces are disconnected surfaces of a connected liquid body. For holes of equal radii and identical pendant drops axisymmetric perturbations are always the most dangerous. The stability region for two identical drops differs considerably from that for a single drop. Loss of stability leads to a transition from a critical system of identical drops to a stable system of axisymmetric non-identical. This system of non-identical drops reaches its own stability limit (to isochoric or non-isochoric paturbations). For non-identical drops, loss of stability results in dripping or streaming from the holes. Critical volumes for non-identical drops have been calculated as functions of the Bond number, B. For unequal hole radii, stability regions have been constructed for a set of hole radius, K. The dependence of critical volumes on K and B is analyzed.

Slobozhanin, Lev A.↗