Drop Rupture Research Articles

Morphology of Anisotropic Banded Structures in an Emulsion under Simple Shear

The formation of flow-induced, oriented structures in two-phase systems, as in this study, is a phenomenon of considerable interest to the scientific and industrial sectors. The main difficulty in understanding the formation of bands of droplets is the simultaneous interplay of physicochemical, hydrodynamic, and mechanical effects. Additionally, banded structure materials frequently show multiple length scales covering several decades as a result of complex time-dependent stress fields. Here, to facilitate understanding a subset of these structures, we studied water in oil emulsions and focused on the effects of three variables specifically: the confinement factor (Co=2R/H), the viscosity ratio (p), and the applied shear rate (γ˙). The confinement (Co) is the ratio between the drop’s diameter (2R) and the separation of (the gap between) the circular rotating disks (H) containing the emulsion. We carried out (a) observations of the induced structure under different simple shear rates, as well as (b) statistical and morphological analysis of these bands. At low shear rates, the system self-assembles into bands along the direction of the flow and stacked normal to the velocity gradient direction. At higher shear rates is possible to observe bands normal to the vorticity direction. Here, we show that a detailed analysis of the dynamics of the band structures is amenable, as well as measurements of flow field anomalies simultaneously observed. The local emulsion viscosity varies in time, increasing in regions of higher droplet concentration and subsequently inducing velocity components perpendicular to the main flow direction. Thus, the emulsion morphology evolves and changes macroscopically. A relatively plausible explanation is attributed to the competitive effects of coalescence and the rupture of drops, where p values less than one predominate coalescence.

Oil drop stretch and rupture behavior at throat and pore junction during imbibition with active nanofluid: A microfluidic approach

Imbibition is an effective method to recover oil from small pore and throat. Here we report the formation of oil drop at pore and throat junction during spontaneous imbibition with active nanofluid. A T-channel microfluidic model combined with high-speed camera was used to observe the stretch and rupture process of oil discharged from throat to pore. When oil drop was discharged from throat gradually, its width/length was kept deceasing before rupturing. With more active content in the aqueous phase, the interfacial tension decreased from 33.8 to 8.7 mN/m, and the oil recovery increased by 12.4% by spontaneous imbibition. The oil drop rupture frequency increased by 3.0 times, but the length and width of the oil drop decreased by 32.2% and 28.0%, respectively. The reduced size of the oil drop would benefit the oil transportation in porous media. Higher flow rate in pores and throat would all intensify rupturing of the oil drop. Moreover, small throat could further reinforce the rupturing process. From combination of fluid flow rate, interfacial tension, and viscosity, higher capillary number reduced the maximum dimensionless width and length of the oil drop by 44.3% and 42.7%, respectively. The reduced size of oil drops ruptured at pore and throat junction contributes to the transportation of oil in porous media. Overall, this study provides a basic theory for active nanofluid to enhance imbibition oil recovery in tight reservoirs.

Numerical study on coalescence behavior of suspended drop pair in viscous liquid under uniform electric field

Coalescence of drops under externally applied electric field is a significant physical process, which has been applied in many applications such as emulsion breakup, electric dehydration and raindrop formation. The morphological characteristics of two identical adjacent drops under uniform electrical strength were numerically investigated in present study. From the simulated morphologies, the behavior of the meniscus, the major axis, the minor axis, and the cone angle of coalesced drop were analyzed in details. The results indicated that drop coalescence was dependent on the electric field strength, and only below a critical threshold, coalesce occurred. Though variation might occur in lengths of the meniscus, major\minor axis, and size in cone angles, a steady state can always be reached under which electro-coalescence complete. On the other hand, drops failed to coalesce if they could not reach a steady state, and even the coalesced drop rupture due to oversized electric filed strength. Analysis of coalescence behavior of suspended drop pair in viscous liquid under uniform electric field could further promote our understanding on the physical phenomenon of electro-coalescence and provide insight for the design of the electro-coalescers in practical applications.

Evolution of the Size Distribution of an Emulsion under a Simple Shear Flow

Understanding the rheology of immiscible liquids mixtures, as well as the role played by its micro-structures are important criteria for the production of new materials and processes in industry. Here, we study changes over time of the droplet size distributions of emulsions induced by slow shearing flows. We observe that the initial heterogeneous microstructure may evolve toward more complex structures (such as bimodal distribution) as a result of coalescence and rupture of droplets. These dynamic structures were produced using a flow cell made up of two parallel disks, separated by a gap of 100 µm. The steady rotation of the lower disk generates a simple shear flow of γ˙=0.75 s−1, during ~400 s. After a brief rest time, this procedure was repeated by applying a step ramp until the maximum shear rate of 4.5 s−1 was reached, using step increments of 0.75 s−1. During the last portion of the flow and during the rest time in between flows, structures of emulsions were characterized. Initially, a broad single-peak distribution of drops was observed, which evolved toward a rather narrower bimodal distribution, at first due to the coalescence of the smaller droplets and subsequently of the larger drops. The rupture of drops at higher shear rates was also observed. The observed evolutions also presented global structures such as “pearl necklaces” or “bands of particles”, the latter characterized by alternating bands of a high density of particles and regions of the continuous phase with only a few droplets. These changes may indicate complex, time-dependent rheological properties of these mixtures.

Studying the field induced breakup of acoustically levitated drops.

Coulomb fission of charged droplets (The terms drop and droplet are often used synonymous. Throughout this manuscript, to avoid confusion, the terms drop and droplet will be used for liquid spheres with radii in the millimeter range and the micrometer range, respectively. In our experiments, the first correspond to the parent drop while the latter describes the ejected progeny droplets.) is a well-studied natural phenomenon. Controlled droplet fission is already successfully employed in several technological applications. Still, since the occurring surface rupture relies on the exact understanding and description of the liquid gas boundary, some details are still under debate. Most empirical systematic studies observe falling micrometer droplets passing through the electric field inside a plate capacitor. This approach, although easily applicable and reliable, limits the experimental degrees of freedom regarding the observable time and the maximum size of the drops and can only be performed in consecutive individual observations of different subsequent drops. Here we present a novel setup to study the field induced breakup of acoustically levitated drops. The design does not bear any restrictions towards the temporal window of observation, and allows handling of drops of a tunable radius ranging from 10 μm to several millimeters and a real-time monitoring of one single drop. Our comprehensive study includes a time resolved visual inspection, laser shadowgraphy, laser induced fluorescence imaging, and ambient mass spectrometric interrogation of the nascent Taylor cone. The results shown for a millimeter sized drop, previously inaccessible for Coulomb fission experiments, are mostly comparable with previous results for smaller drops. The major difference is the time scale and the threshold potential of the drop rupture. Both values, however, resemble theoretically extrapolations to the larger radius. The technique allows for a systematic study of breakup behavior of drops of different charge, material, and size.

Two‐stage stabilizer addition protocol as a means to reduce the size and improve the uniformity of polymer beads in suspension polymerization

ABSTRACTA two‐stage stabilizer addition protocol is suggested for reducing the size and improving the uniformity of polymer beads resulting from conventional suspension polymerization. The stabilizer load was divided into an initial charge and a secondary addition. The use of a low concentration of stabilizer in the initial charge served to assist drop rupture while avoiding significant reduction in drop size and production of too many satellite droplets. The secondary addition time of stabilizer occurred just before the onset of the growth stage when drops were vulnerable to coalescence but robust against break up due to their high viscosity. The secondary addition of stabilizer served to provide stability to monomer drops during the growth stage and as a result the drops underwent limited coalescence. This resulted in the formation of smaller and more uniform polymer beads in comparison to beads obtained by conventional suspension polymerization at the same overall concentration of stabilizer. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018, 135, 45671.

Suspension polymerisation in the presence of an inhibitor; prolonged transition stage and suppressed emulsion particle formation

A typical suspension polymerisation accommodates a simultaneous emulsion polymerisation that produces emulsion particles. A consecutive emulsion and suspension polymerisation was carried out, which clearly indicates that these emulsion particles destabilise the suspension by adsorbing the stabiliser and thus enlarge the size of final beads. These emulsion particles can coagulate and reach a size that is similar to those of satellite particles formed by drop rupture mechanisms in the stirred reactors. Methyl methacrylate was considered as a model monomer. Inclusion of a water-soluble inhibitor in the formulation recipe was found to decrease the average bead particle size and sharpen their size distribution. An inhibition effect contributes to drop stability in two ways. First, it does not allow polymerisation to occur in the drops during induction time and thus prolongs the transition period during which the size of drops is reduced. Second, it hinders particle nucleation in the water phase so that the stabiliser remains available for protecting the bead particles against coalescence. The main conclusion is that the inhibitor should not always be removed from monomers prior to suspension polymerisation.

Modeling of multicomponent multiphase mixture flows on the basis of the density-functional method

Examples of numerical calculations of isothermal flows of two-phase two-component mixtures based on the density-functional method are presented. Using this method, the following problems are calculated in the two-dimensional formulation: drop impact on a liquid layer, drop rupture in a Couette flowfield, wetting-angle formation for a drop on a solid surface, development of Rayleigh-Taylor and Kelvin-Helmholtz instability on a gas-liquid interface.

Coalescence during emulsification. 3. Effect of gelatin on rupture and coalescence.

An oil-soluble fluorescent probe, undecyl pyrene (UDP), is used to measure the amount of coalescence that occurs during the emulsification of tri-2-ethylhexyl phosphate using a high-pressure homogenizer. From these measurements, the roles of anionic surfactant (SDS) and gelatin in stabilizing drops against coalescence and promoting drop rupture during emulsification are deduced. It is found that gelatin aids in reducing coalescence, whereas SDS aids in rupture of drops. The effect of variables such as gelatin MW, surfactant type, and pH on coalescence and final drop size is investigated.

Coalescence during Emulsification: 3. Effect of Gelatin on Rupture and Coalescence

An oil-soluble fluorescent probe, undecyl pyrene (UDP), is used to measure the amount of coalescence that occurs during the emulsification of tri-2-ethylhexyl phosphate using a high-pressure homogenizer. From these measurements, the roles of anionic surfactant (SDS) and gelatin in stabilizing drops against coalescence and promoting drop rupture during emulsification are deduced. It is found that gelatin aids in reducing coalescence, whereas SDS aids in rupture of drops. The effect of variables such as gelatin MW, surfactant type, and pH on coalescence and final drop size is investigated.

Induced burst of fluid drops in a two-component lattice Bhatnager-Gross-Krook fluid.

We describe a two-dimensional simulation of burst in neutrally buoyant drops subject to shear using a two-component, two-speed lattice Bhatnager-Gross-Krook (BGK) fluid. Measuring the dependence of critical shear rate for drop rupture on flow parameters, our results validate the method over a range of simulation variables. The model's interfacial tension parameter sigma, undeformed drop radius, and BGK relaxation parameter omega are all found to have the correct influence upon the process of burst required by simple hydrodynamic theory. Within the model, the macroscopic surface tension and fluid. viscosity are coupled; however, this does not limit the application of the technique.

The origin of fine drops in batch gas-agitated liquid—liquid systems

Fine drops pose a separation problem in batch gas-agitated liquid—liquid systems, such as pyrometallurgical and liquid—liquid extraction processes because a small amount of the more dense liquid phase remains dispersed in the less dense liquid phase in the form of fine drops long after agitation has ceased and the bulk liquid phases have separated. In this work the origin of drops with diameters between 10 μm and 100 μm was investigated. Three sources were identified: the disintegration of liquid columns entrained by gas bubbles as they cross the liquid—liquid interface, drop erosion resulting from collisions with large gas bubbles, multiphase drop rupture at the upper liquid—gas interface. Liquid entrainment was found to be the principal source of fine drops for systems with low liquid—liquid viscosity ratios, whereas drop erosion inside the upper liquid phase and to a lesser extent multiphase drop rupture were found to be the principal sources of fine drops at high liquid—liquid viscosity ratios. Criteria for minimizing fine drop formation in these systems are proposed.

Rupture characteristics of the 1982 Tonga and 1986 Kermadec earthquakes

Source time functions are obtained for the December 19, 1982, Tonga and October 20, 1986, Kermadec earthquakes from deconvolution of P waves, using a model including a significant dip of the ocean bottom. In such a geometry, the amplitudes of subsequent water multiples are large and irregular. As a result, we can model these two events as consisting of a single pulse of short duration (23 s in the case of the 1982 event, and 19 s for the 1986 one), despite complex teleseismic waveshapes. This is in contrast to inversions using flat‐layered models, which required very complex source time functions, which were mutually inconsistent at different stations. The anomalously large tsunami generated by the 1982 event is modeled as the result of propagation of the rupture into the sedimentary wedge at the trench, rather than due to a long‐lived complex source time function, the latter being also incompatible with the total lack of excitation of the Earth's normal modes in the low‐frequency limit. For the 1986 event, we derive a source duration (19 s) very short in relation to its moment (8×1027 dyn‐cm). This earthquake, a high stress drop rupture featuring a unique combination of strike‐slip and thrust motion on a plane dipping oceanwards of the trench, is interpreted as expressing internal deformation of the subducting Pacific slab at a depth of 40 km, under the compressional stresses resulting from the collision.

Maximum electric charge of a hydrometeor in the electric field of a thundercloud

Computations have been made for the maximum electric charge that a hydrometeor can retain in the ambient field of a thundercloud. Two processes contribute to this limitation: water drop instability and corona discharge initiation. Solid hydrometeors are only affected by corona emission. Therefore, the numerical method presented here consists of computing the local electric field everywhere at the surface of the hydrometeor as a function of the ambient field and its net charge. When this surface field exceeds the corona onset at some point, as defined by Peek's law, the maximum charge is reached. For water drops the electric charge can be limited either by corona emission or by mechanical instability. The present model takes into account the influence of both drop rupture due to electrostatic pressure and corona emission. Dawson's experimental onset values are considered in this case. Since corona onset values are pressure dependent, so are the maximum charges of both kinds of hydrometeors. The computation results show that, at higher pressure, the maximum net charge of a solid, smooth hydrometeor is higher than that of a water drop of the same size located within the same ambient electric field. At lower pressures, this difference decreases. This preliminary work, in need of experimental confirmation, does not take into account temperature and purity of the particles but aims to reveal the relative parts played by the basic mechanisms in limiting net charge of the hydrometeors.

Interactions between drops and particles in simple shear

An experimental study has been made of the collisions and coalescence of solid spheres and liquid drops in a simple shear field. Asymmetric particle trajectories were ascribed to drop deformation due to the shear field and the collision. Analysis was made of the possible rest configurations of coalesced sphere—drop pairs in terms of the wetting characteristics of the particular system and their rotational behavior and break-up mode was studied in simple shear flow. Sphere—drop pairs consisting of liquid drops containing solid spheres at their center were found to exhibit a new mode of drop rupture involving impulsively started shear fields. Study was also made of the behavior in shear of liquid bridged doublets consisting of two identical solid spheres joined by a bridging liquid. In limiting cases their behavior may be compared with that of rigid dumbbells or pure drops.

Liquid dispersion in static in‐line mixers

AbstractLiquid/liquid dispersion in static mixers has been investigated using Lightnin “In‐liner” mixing elements. The average drop size was found to decrease with increasing residence time, gradually approaching an equilibrium size whose magnitude agrees reasonably well with Kolmogoroff's theory for drop rupture in turbulent flows.The efficiency at which mechanical energy is utilized in the generation of new interfacial area was evaluated as a function of design and operating conditions and was found to be highest when the final drop size is much larger than the achievable equilibrium value.

The stability of an inclined pendent drop

A pendent drop remains attached to the tip of an inclined circular tube only when the drop volume is below a critical value. At this critical volume the drop may either lose stability to a perturbation of the wetting line that lets the liquid climb along the outside of the tube or lose equilibrium because drop shapes that satisfy the balance of capillary and gravitational forces are no longer possible. These two models for the loss of the static shape are distinguished by finite-element analysis of drop shape and stability that calculates the limits of shape equilibria in terms of drop volume, inclination angle, and gravitational Bond number B ≡ gR 2Δρ σ . Numerical results are verified by comparison with previous calculations for vertical pendent drops and with experiments for inclined drops. The capillary mode for the loss of equilibrium controls drop stability as long as the local contact angle around the tube does not violate Gibbs' criterion for the advance of a wetting line over a sharp edge. Calculations determine the role of the shape of the contact curve in determining the onset of drop rupture.