Drop Size Ratio Research Articles

Effect of Vent Area on Dynamic Characteristics of Premixed Methane/Air Explosions in End-vented Channels with Different Length/Diameter Ratios

ABSTRACT Further elucidate the interaction mechanism of pressure-flame-wall in channels under the effects of length/diameter ratio (L/D) and vent area, which helps to propose more effective decompression means. Experiments of premixed methane-air explosions in end-vented channels with L/D of 10, 15 and 20 were conducted under initial conditions (301 ± 2 K and 1 atm). The results demonstrate that L/D and vent area are critical external factors causing tulip flames and distorted tulip flames. When the vent area is 60 mm × 60 mm~40 mm × 40 mm, the distorted tulip flame can be generated at L/D of 20. Notably, the critical intrinsic factor causing distorted tulip flame is the interaction of reflected pressure waves-flame. It is deduced that flames stagnate or decelerate during the initial stages of irregular flames because rarefaction waves attenuate the driving force of flames. The new overpressure peaks (Ptulip, Pdis-tulip, and Pirr-tulip) induced by tulip flames, distorted tulip flames and irregular tulip flames are identified. Moreover, the drop size and drop ratio of the maximum overpressure decrease with increasing L/D.

Dynamics of two unequal-sized drops coalescence at a liquid–liquid interface

The secondary droplets formed during the coalescence of two drops have an important role in many applications, including raindrop formation in clouds and emulsions coarsening. The process of secondary drop generation at the liquid–liquid interface is numerically investigated using a coupled level set and volume of fluid method during the coalescence of two drops of different parent drop size ratios. The coalescence dynamics has been found to depend on the five-dimensionless parameters, namely, the Ohnesorge numbers for liquid-1 and 2, the Bond number, the Atwood number, and the diameter ratio of the two drops. As a function of these non-dimensional parameters, different pinch-off regimes, namely, first-, second-, and no pinch-off, are studied. The result shows that the local neck curvatures at the onset of pinch-off play a key role in the appearance of various pinch-off regimes. The second-stage pinch-off occurs primarily within the Ohnesorge number range from 0.002 to 0.01, i.e., inertio-capillary regime range. Above this range, a direct transition from the first-stage pinch-off to no pinch-off occurs with the increasing Ohnesorge number. Within the inertio-capillary regime, the pinch-off mechanism in both the first and second-stage pinch-off regime is found to be almost independent of the Atwood number and the parent drop size ratio. Capillary waves produced at the contact region of two drops have also been observed to influence the pinch-off process. A large parent size ratio induces the higher curvature near the neck zone, resulting in stronger capillary waves. Strong viscous forces, however, dampen the propagation of capillary waves at a large Ohnesorge number. The critical Ohnesorge number is obtained for both the first and second-stage pinch-off regimes above which the strong viscous forces hinder a secondary drop pinch-off.

The Combined Effects of Gravitational and Thermocapillary Driving Forces on the Interactions of Slightly Deformable, Surfactant - Free Drops

By an asymptotic approach previously employed for gravitational or thermocapillary motion alone, collision efficiencies are calculated for slightly deformable drops in combined gravitational and thermocapillary motion with negligible inertia and thermal convection. The constant imposed temperature gradient may be aligned with gravity in either the same or opposite direction. In the dimensionless parameter space, deformation becomes important at a smaller drop size ratio when the temperature gradient and gravity are aligned in the same direction, because the driving force is larger and induces dimple formation earlier. For the same reason, in a physical system of ethyl salicylate (ES) drops in an unbounded matrix of diethylene glycol (DEG), deformation becomes important for smaller drops when the driving forces have a parallel, rather than anti-parallel, arrangement. In developing the population dynamics for slightly deformable drops, a new, simplified expression for the collision efficiency for spherical drops in the absence of van der Waals forces is presented, which successfully separates the contributions of the two driving forces. Two collision-forbidden regions can occur for opposed driving forces leading to a shark-fin shaped collision efficiency curve for two slightly deformable drops. As shown in population dynamics, if the drop distribution is broad enough, it is possible for drops to jump the first collision-forbidden region.

An experimental study on the drop/interface partial coalescence with surfactants

This paper presents investigations on the partial coalescence of an aqueous drop with an organic-aqueous interface with and without surfactants. The organic phase was different silicone oils and the aqueous phase was a glycerol-water solution at different concentrations. It is found that when the surfactant Span 80 is introduced into the organic phase, the partial coalescence region is reduced in the Oh–Bo coalescence map. The range of the inertio-capillary regime reduces when surfactants are present, while the drop size ratio decreases with increasing surfactant concentration. The velocity fields inside the aqueous drop were studied with high speed particle image velocimetry for the first time. In the surfactant-free system, it was found that the inward motion of the fluids at the upper part of the drop favours the generation of a liquid cylinder at the early stages of coalescence. The pressure gradient created by the downward stream at the bottom of the liquid cylinder drives the pinch-off of the secondary drop. When surfactants are present, the rupture of the film between the drop and the interface occurs at an off-axis location. The liquid cylinder formed in this case is not symmetric and does not lead to pinch-off. It is also found that the vortices inside the droplet have little impact on the partial coalescence.

Simulations of coalescence of two colliding liquid drops using lattice Boltzmann method

In this paper, two-dimensional numerical simulations of the head-on and off-center binary collision of liquid drops are carried out using lattice Boltzmann method. The coalescence process of drops colliding is freely captured, regardless of tracking equations and drops model. Special attention is paid to investigate the effect of the Weber number, impact velocity, drop size ratio on the coalescence process. The research results demonstrate that numerical results of lattice Boltzmann method are in agreement with qualitatively experimental data in the same Weber number. It is also noted that the first oscillation period is invariably shorter than the second period, regardless of the Weber number. It is further found that variation of the first period of oscillation in off-center collision of two equal-size drops as function of Weber number are higher than the variation of the first period of oscillation in head-on collision of two equal-size drops in the same Weber number.

Deposition of Colloidal Drops Containing Ellipsoidal Particles: Competition between Capillary and Hydrodynamic Forces.

Ellipsoidal particles have previously been shown to suppress the coffee-ring effect in millimeter-sized colloidal droplets. Compared to their spherical counterparts, ellipsoidal particles experience stronger adsorption energy to the drop surface where the anisotropy-induced deformation of the liquid-air interface leads to much greater capillary attractions between particles. Using inkjet-printed colloidal drops of varying drop size, particle concentration, and particle aspect ratio, the present work demonstrates how the suppression of the coffee ring is not only a function of particle anisotropy but rather a competition between the propensity for particles to assemble at the drop surface via capillary interactions and the evaporation-driven particle motion to the contact line. For ellipsoidal particles on the drop surface, the capillary force (Fγ) increases with the particle concentration and aspect ratio, and the hydrodynamic force (Fμ) increases with the particle aspect ratio but decreases with drop size. When Fγ/Fμ > 1, the surface ellipsoids form a coherent network inhibiting their migration to the drop contact line, and the coffee-ring effect is suppressed, whereas when Fγ/Fμ < 1, the ellipsoids move to the contact line, resulting in coffee-ring deposition.

Two touching spherical drops in a uniaxial compressional flow: The effect of interfacial slip

This study presents a semi-analytical solution for the problem of two touching drops with slipping interfaces pushed against each other in a uniaxial compressional flow at low capillary and Reynolds numbers. The jump in the tangential velocity at the liquid-liquid interface is modeled using the Navier slip condition. Analytical solutions of the contact force, the drop-scale stresses, and the drop-scale pressure are provided as functions of the slip coefficient α, the viscosity ratio κ, and the drop size ratio k. Since unequal drop sizes are considered, two problems are solved in the tangent sphere co-ordinate system to determine the steady state position: a pair of touching drops with its contact point at the origin of an axisymmetric straining flow, and two touching drops placed in a uniform flow parallel to the axis of symmetry of the drops. A general observation is that the effect of slip is manifested most strongly for drops whose viscosity is much greater than the suspending fluid κ≫1. For highly viscous drops, the flow and stress fields transition from those corresponding to solid particles for ακ ≪ 1, to those for inviscid drops in the limit ακ ≫ 1. The analytical expressions provided here for the contact force and the stress distributions will serve to provide the restrictions that complete the definition of the lubrication flow problem in the thin film between the two colliding drops. While the contact force that drains fluid out of the thin film is relatively unaffected by slip, the tangential stress and pressure in the near-contact region are mitigated significantly for ακ ≫ 1. The latter is expected to assist coalescence at high capillary numbers.

Stable isotopic differences between summer and winter monsoon rains over southern India

Rain drop size and isotopic composition of rain, important parameters that shed light on rain formation processes, are highly sensitive to the ambient weather. We reported earlier a significant correlation between them in individual rain events (with limited sampling), but this is yet to be tested with better, longer term sampling. Here we attempt to do so over a tropical region (i.e. Tirupati, India). Rain samples were collected at short time intervals (<1 h) to capture even small variations in their stable oxygen (δ18O) and hydrogen (δD) isotopic compositions. Isotopic analyses were made using an isotope ratio mass spectrometer, and a disdrometer measured the drop size distribution. Summer rains show a progressive 18O & D depletion with time, while the winter rains fluctuate about a mean value. We find no definite correlation between the drop size and stable isotope ratios as was reported earlier, based on a smaller number of samples: the complexity of rain formation process and varying ambient weather conditions for individual rain events could be the reason. Further, there is no significant difference between the local meteoric water lines (δ18O- δD line) of summer and winter monsoon rains, though the intercepts in both the cases were significantly smaller than global meteoric waterline, suggesting significant strong influence of secondary evaporation. However, the winter rains are more depleted in D & 18O. Paleoclimate proxies such as δ18O of cave calcite or teak cellulose form this region need to be interpreted in terms of the relative seasonality of the rainfall rather than the total annual rain.

Systematic Analysis of Single Droplet Coalescence

Coalescence behavior in liquid-liquid dispersions is controlled by various parameters. Thus, data from different research groups can differ significantly. Dynamic coalescence processes were analyzed systematically with the EFCE standard test system toluene/water in two different research laboratories. After comparability was proven with standardized batch settling tests and drop rise velocity measurements, the influence of drop size ratio and varying NaCl and NaOH concentrations on coalescence probability was investigated. Since the ions led to a coalescence inhibition, no clear impact of drop size ratio could be observed. The analysis of drop contact showed longer contact times for increasing equivalent drop diameter. This promotes coalescence and corresponds to film drainage model.

Coalescence of viscous drops translating through a capillary tube

An experimental study of the interaction and coalescence of viscous drops moving through a cylindrical capillary tube under low Reynolds number conditions is presented. The combined pressure- and buoyancy-driven motion of drops in a Newtonian continuous phase is examined. The interaction between two drops is quantified using image analysis, and measurements of the coalescence time are reported for various drop size ratios, Bond numbers, and viscosity ratios. The time scale for coalescence in the non-axisymmetric configuration is found to be substantially larger than that for coalescence in the axisymmetric configuration. Measurements of the radius of the liquid film formed between the two drops at the instant of apparent contact are used in conjunction with a planar film drainage model to predict the dependence of the coalescence time on drop size ratio for coalescence of low viscosity-ratio drops in the axisymmetric configuration.

Analysis of droplet expulsion in stagnant single water-in-oil-in-water double emulsion globules

Double emulsions created by phase inversion can be used for fast liquid–liquid separation; therefore, the coalescence behaviors of these types of multiple emulsions need to be predictable for different physical properties and drop size ratios. The aim of this study is to determine the influence of the effective overall drop diameter and the internal droplet size on the coalescence time and the coalescence behavior. Experimental investigations on the physical stability of single stagnant water-in-oil-in-water (W 1/O/W 2) double emulsion globules are performed. For this investigation, a formation device to inject one water droplet into an oil drop inside a water bulk phase is developed. The coalescence process of the sole internal water droplet floating on the O/W 2 interface with the water bulk phase, often termed droplet expulsion or external coalescence, is recorded with a high speed camera. Based on image analysis, the diameters of the effective overall drop D, containing the oil and entrapped water volume, and the internal water droplet d are determined. Additionally, the coalescence time τ, including the time from the first contact of the internal droplet and the drop-bulk interface to the film rupture is measured. A large increase in coalescence time with increasing water droplet diameters is found. For the investigated paraffin oil–water system and initial drop sizes, partial coalescence occurs. In this case, the diameter ratio of daughter-to-mother droplet ψ is determined.

Droplet break-up by in-line Silverson rotor–stator mixer

Silverson high shear in-line rotor–stator mixers are widely applied in industry for the manufacture of emulsion-based products but the current understanding of droplet breakage and coalescence in these devices is limited. The aim of this paper is to increase the understanding of droplet break-up mechanisms and to identify appropriate literature correlations for in-line rotor–stator mixers. Silicone oils with viscosities ranging from 9.4 to 969 mPa s were emulsified with surfactant in an in-line Silverson at rotor speeds up to 11,000 rpm and flow rates up to 5 tonnes/h. The effect of rotor speed, flow rate, dispersed phase fraction up to 50 wt%, inlet drop size and viscosity ratio on droplet size was investigated. It was found that rotor speed and dispersed phase viscosity have a significant effect on the droplet size, while flow rate, inlet droplet size, viscosity ratio and dispersed phase volume have a lesser effect. The results indicate that low viscosity droplets are broken by turbulent inertial stresses, while droplets smaller than the Kolmogorov length scale are broken by a combination of inertial and viscous stresses. It also appears that the weak dependence of drop size on flow rate enables the energy efficiency of an in-line high shear Silverson to be significantly improved by operating at as high a flow rate as possible.

Simulation of Mixing within Drops due to Surface Tension Variations

We present the results of a numerical investigation of the mixing within drops caused by surface tension variations. With microfluidic applications in mind, we simulate drops surrounded by a fluid of equal density and viscosity. We investigate both stationary coalescing drops and steadily flowing drops, and study the influence of drop size ratio, viscous effects, and surface tension variations. We measure the mixing efficiency using the variance of the concentration distribution and find that surface tension variations may result in faster mixing than geometric effects.

Partial coalescence between a drop and a liquid-liquid interface

This Letter reports experimental results for partial coalescence when a drop merges with an interface. We find an intermediate range of drop sizes in which the merger is not complete but a daughter drop is left behind. This phenomenon is governed primarily by inertia and interfacial tension, and three regimes can be further delineated depending on the roles of viscosity and gravity. Scaling relationships are developed for the drop size ratio and the coalescence time. For drops that are too large or too small, partial coalescence is arrested by gravity or viscosity, respectively.

Interaction and Coalescence of Drops and Bubbles Rising through a Tube

An experimental study of the interaction and coalescence of two drops (of the same fluid) or bubbles translating under the action of buoyancy in a cylindrical tube is performed. The close approach of two Newtonian drops or bubbles of different size in a Newtonian continuous phase is examined using image analysis, and measurements of the coalescence time are reported for various drop size ratios, Bond numbers, and drop to suspending fluid viscosity ratios. The time scale for coalescence in the non-axisymmetric configuration is found to be substantially larger than that for coalescence in the axisymmetric configuration. Experimental measurements of the radius of the liquid film between the two drops are used in conjunction with a simple film-drainage model to predict the dependence of the coalescence time on the drop size ratio. The agreement between the model predictions and the experimental measurements is satisfactory for axisymmetric coalescence in the low viscosity ratio systems. For the systems with O(1) viscosity ratio, on the other hand, model predictions are qualitatively different from experimental observations.

Model for drop coalescence in a locally isotropic turbulent flow field

The proposed model views drop coalescence in a turbulent flow field as a two-step process consisting of formation of a doublet due to drop collisions followed by coalescence of the individual droplets in a doublet due to the drainage of the intervening film of continuous phase under the action of colloidal (van der Waals and electrostatic) and random turbulent forces. The turbulent flow field was assumed to be locally isotropic. A first-passage-time analysis was employed for the random process of intervening continuous-phase film thickness between the two drops of a doublet in order to evaluate the first two moments of coalescence-time distribution of the doublet. The average drop coalescence time of the doublet was dependent on the barrier for coalescence due to the net repulsive force (net effect of colloidal repulsive and turbulent attractive forces). The predicted average drop coalescence time was found to be smaller for larger turbulent energy dissipation rates, smaller surface potentials, larger drop sizes, larger ionic strengths, and larger drop size ratios of unequal-sized drop pairs. The predicted average drop coalescence time was found to decrease whenever the ratio of average turbulent force to repulsive force barrier became larger. The calculated coalescence-time distribution was broader, with a higher standard deviation, at lower energy dissipation rates, higher surface potentials, smaller drop sizes, and smaller size ratios of unequal drop pairs. The model predictions of average coalescence-rate constants for tetradecane-in-water emulsions stabilized by sodium dodecyl sulfate (SDS) in a high-pressure homogenizer agreed fairly well with the inferred experimental values as reported by Narsimhan and Goel (J. Colloid Interface Sci. 238 (2001) 420–432) at different homogenizer pressures and SDS concentrations.

Comparison Of Actual Delivered Density And Fire Suppression Effectiveness Of Standard And Conventional Sprinklers In Rack-storage Fires

The Actual Delivered Density (ADD) of a standard sprinkler and a conventional sprinkler for rack-storage fires has been studied experimentally using an ADD apparatus equipped with a fire plume simulator. The variables examined included sprinkler discharge rates (76-212 L/min), heat release rates of the fire (0, 500, 1000, 1500 and 2000 kW), ceiling clearances (3.05, 4.57 and 6.10 m), and ignition locations (centered below one sprinkler and below four sprinklers). The sprinkler spacing was maintained at 3.05 m for all the tests. The results of the measurements indicate that the ADD decreased as the ceiling clearance is increased from 3.05 m to 6.10 m. The ADD data have been correlated satisfactorily using two parameters. One parameter corresponds to a drop size ratio and the other is the ratio of the spray momentum to the momentum of the fire plume. It is demonstrated that the ADD can be used to interpret the performance of the standard and conventional sprinklers in the large-scale rack storage fire tests conducted.

Coalescence collision of liquid drops

The coalescence collision of two liquid drops is studied using a Galerkin finite element method in conjunction with the spine-flux method for the free surface tracking. The effects of Reynolds number, impact velocity, drop size ratio, and internal circulation on the coalescence process is investigated. The long time oscillations of the coalesced drop are also studied and curves for the variations of the period and decay factor are provided as a function of the number of oscillations. In the study of non-equal-size drop collision, traces of different fluid particles are calculated to illustrate the liquid mixing during the collision.

A Three-Dimensional Boundary-Integral Algorithm for Thermocapillary Motion of Deformable Drops

A three-dimensional boundary-integral algorithm has been developed to handle the tangential Marangoni stresses in thermocapillary motion of drops. Depending on whether the integration and observation points are on the same or different drops, singularity or near-singularity subtraction is used in the inhomogeneous term of the boundary-integral formulation. Integration is then performed analytically over flat triangles in the subtracted region. Relative trajectories for two deformable drops are calculated for different values of the drop size ratio, drop-to-medium thermal conductivity ratio, and viscosity ratio and compared to those for spherical and slightly deformable drops. Results indicate that deformation increases the minimum separation and inhibits coalescence but is not important enough for appropriate physical parameters to induce the capture or breakup behaviors observed in buoyancy. Interaction times calculated by artificially continuing spherical drop trajectories yield results accurate to within about 10%.

Determination of viscosity from drop deformation

A novel technique for measuring viscosities of droplets is described. This technique uses the transient and steady state deformation of a droplet suspended in an immiscible fluid. Drop viscosities are derived from small deformation theory as ηd=(−5γ̇/2Dsα−1.5)ηs for hyperbolic flow, and ηd=(−5γ̇/4Dsα−1.5)ηs for shear flow. Here γ̇ is the flow rate, Ds is the steady state deformation, α is the exponent obtained from deformation growth or relaxation, and ηs is the suspending fluid viscosity. Drop viscosities measured using this technique, implemented on a four-roll mill apparatus, are compared with bulk viscosities measured using a conventional rheometer. The measurement scope of the new technique, with respect to capillary number, drop size, and viscosity ratio, is defined.