Effects of surface properties on the impact process of a yield stress fluid drop

The impact of a yield stress fluid drop onto a solid surface with diversified interface properties has been experimentally investigated. Two smooth substrates with distinct surface energies and three similar substrates with different roughnesses have been used. The bulk shear rheological behaviour of Carbopol gels, concentrated suspensions of swollen micro-gels, has been measured. Wall friction has also been characterized on each substrate. Slip effects of gels proved to be greater on a more hydrophobic substrate. They decreased with an increase in roughness. The drop hydrodynamics during the impact was correlated with the wall friction of the gels on all substrates and with the ratio of surface roughness to size of the swollen micro-gels. At very low impact velocities, the gravitational subsidence amplitude depends greatly on surface properties. At higher impact velocities, no significant difference is observed during the spreading phase. The drop behaviour differs during the retraction depending on the substrate. Interface effects during the retraction stage proved to diminish when the yield stress value increases.     

The free-fall of viscoplastic drops

The free-fall of liquid drops under the action of gravity is studied experimentally by high-speed imaging, with focus on drops of viscoplastic fluids (i.e., those materials which exhibit a fluid behaviour only when the applied stress exceeds a certain threshold value, called the yield stress), and compared to the behaviour observed in Newtonian drops. The yield stress of the fluid is shown to alter significantly the drop shape during free-fall. The results can be interpreted in terms of a dimensionless number comparing the yield stress magnitude and the capillary pressure.     

Spreading and fingering in a yield-stress fluid during spin coating

We study the deformation, spreading, and fingering of small droplets of a yield-stress fluid subjected to a centrifugal force on a rotating substrate. At low rotation rates and for small enough droplets, the droplets deform elastically but retain their essentially circular contact line. For large enough droplet volumes and rotation speeds, however, one or more fingers eventually form and grow at the edge of the drop. This fingering is qualitatively different from the contact line instability observed in other fluids, and appears to be a localized phenomenon that occurs when the stress at some point on the perimeter of the drop exceeds the yield stress.     

Interaction of viscous drops in a yield stress material

The interaction of Newtonian drops of various volumes moving in yield stress material is investigated experimentally. Tetrachloroethylene drops move in a rectangular reservoir filled with neutralized 0.07% w/w Carbopol gel under the action of gravity. For initially vertically aligned drop pairs, we present time evolution of separation distance, velocities during the interaction and conditions for coalescence of the drops, which depend on the volumes of the drops and the initial separation between them. For the asymmetric interaction of the pairs, we present interaction patterns, which have been used for estimation of the size of the yielded region and its shape around the leading drop.     

Low-Reynolds-number motion of a deformable drop between two parallel plane walls

The motion of a three-dimensional deformable drop between two parallel plane walls in a low-Reynolds-number Poiseuille flow is examined using a boundary-integral algorithm that employs the Green’s function for the domain between two infinite plane walls, which incorporates the wall effects without discretization of the walls. We have developed an economical calculation scheme that allows long-time dynamical simulations, so that both transient and steady-state shapes and velocities are obtained. Results are presented for neutrally buoyant drops having various viscosity, size, deformability, and channel position. For nearly spherical drops, the decrease in translational velocity relative to the undisturbed fluid velocity at the drop center increases with drop size, proximity of the drop to one or both walls, and drop-to-medium viscosity ratio. When deformable drops are initially placed off the centerline of flow, lateral migration towards the channel center is observed, where the drops obtain steady shapes and translational velocities for subcritical capillary numbers. With increasing capillary number, the drops become more deformed and have larger steady velocities due to larger drop-to-wall clearances. Non-monotonic behavior for the lateral migration velocities with increasing viscosity ratio is observed. Simulation results for large drops with non-deformed spherical diameters exceeding the channel height are also presented.     

Impact of liquid drops on a rough surface comprising microgrooves

Impact of water drops on a stainless steel surface comprising rectangular shaped parallel grooves is studied experimentally. Geometric parameters of the surface groove structure such as groove depth, groove width and solid pillar width separating any two successive grooves were kept at 7.5, 136 and 66 μm, respectively. The study was confined to the impact of drops in inertia dominated flow regime with Weber number in the range 15–257. Experimental results of drop impact process obtained for the grooved surface were compared with those obtained for a smooth surface to elucidate the influence of surface grooves on the impact process. The grooves definitely influence both spreading and receding processes of impacting liquid drops. A more striking observation from this study is that the receding process of impacting liquid drops is dramatically changed by the groove structure for all droplet Weber number.     

The consequences of yield stress on deployment of a non-Newtonian anti-HIV microbicide gel

A recent study in South Africa has confirmed, for the first time, that a vaginal gel formulation of the antiretroviral drug Tenofovir, when applied topically, significantly inhibits sexual HIV transmission to women [10]. However the gel for this drug, and anti-HIV microbicide gels in general, have not been designed using full understanding of how gel spreading and retention in the vagina govern successful drug delivery. Elastohydrodynamic lubrication theory can be applied to model such spreading of microbicide gels, which are inherently non-Newtonian [13], [15]. A yield stress is emerging as one of the important properties of microbicide gel vehicle deployment, as this may improve retention within the vaginal canal. On the other hand, a yield stress may decrease the initial extent of the coating flow. Here, we first explain a certain yield stress paradox observed generally in many lubrication flows. Four conditions are determined, via scaling analysis, which mitigate the inconsistency in the use of lubrication theory to analyze the specific problem of elastic wall squeezing flow of yield stress fluid. Parameters characterizing these conditions are obtained experimentally for a test gel. Using them, it is shown that the lubrication approximation may be applied to the elastic wall-squeezing problem for this gel.     

Spreading of inkjet droplet of non-Newtonian fluid on solid surface with controlled contact angle at low Weber and Reynolds numbers

The dynamics of inkjet droplet of non-Newtonian fluid on glass substrates was investigated experimentally and compared with that of Newtonian fluid. The non-Newtonian fluids used here were 100 ppm solutions of polyethylene oxide (300k, 600k and 900k) dissolved in the 1:1 mixture of water and glycerin. Weber number (We) was 2–35 and Ohnesorge number was fixed at 0.057 ± 0.003. The wettability of solid substrate was also varied. The diameter of inkjet droplets in the present study was about 50 μm and was much smaller than the size of the previous studies on drop impact. Due to the development of a thin and long thread at the rear of the main drop the jetting window of polymer solution was much narrower than that of Newtonian fluid, and hence the experimental range of Weber number was restricted. The impact scenarios of non-Newtonian inkjet droplets were found to be qualitatively different from those of Newtonian droplets during the receding phase while they were almost the same as the Newtonian fluid case during the kinematic phase. The spreading diameter at the equilibrium was well correlated with the modified Weber number (We′ = We/(1 − cos θ_eq)) as in the case of Newtonian fluid, where θ_eq is the equilibrium contact angle. The similarity or disparity between the Newtonian and non-Newtonian cases was discussed considering the conformation of polymer chains during each stage of drop deformation.     

The vortex ring velocity resulting from an impacting water drop

Experimental observations are reported on the evolution of a vortex ring for the first 70 ms after it is created by the impact of a dyed water drop upon a pool of clear water. The 2.6 mm diameter drops were released from two heights. The drops impacted the pool with Weber numbers of 23.2 and 16.6 and Froude numbers of 25.2 and 18.0. The Reynolds number of the resulting relaminarized vortex rings based on their diameter was in the range of 320 to 390. Precisely controlled multiple exposure photographs were used to measure the position and shape of the vortex ring versus time, and calculate velocity. It is proposed here that the appropriate time scale is the time it takes for the impact crater to reach its maximum depth. Excellent agreement was found when using this scaling to compare both the present data sets and that previously published for a larger drop.This work was supported by the Natural Sciences and Engineering Research Council of Canada Grant No. OGP 00 41747. Mr. B. Faulkner is thanked for help with the strobe-timing     

Assessment of gas and liquid velocities induced by an impacting liquid drop

A two-phase flow model using the boundary element method was applied to investigate the physics of a liquid drop impacting onto a solid, dry plate. Xu et al. showed that air pressure plays an important role in splashing: as air pressure was reduced, splashing of an ethanol drop with a Weber number of 838 was suppressed. This remarkable observation provided the motivation for the current modeling effort. We numerically investigate how air pressure affects the behavior of an impacting drop. Surveying both inside and outside the impacting drop, velocities of both the liquid and gas are computed. Simulations show that gas speed, as it is displaced by the falling drop, is more than three times higher than the incoming drop speed. Air entrainment induced by the displaced gas seems to be an important contributor to corona formation, which always precedes any instability, fingering, or splashing of the liquid. To describe drop-impact phenomena, the maximum spreading diameter of the drop and the topology of the impacting fluid are reported as functions of Weber number and gas density.     

Hydrodynamics of a submerging drop: Lined structures on the crown surface

Macrophotography and high-speed videofilming are used to investigate the material transfer in a falling drop upon collision with the surface of a fluid at rest. In the experiments the drops of colored water, milk, mineral oil, and seed oil fell in pure or colored water. Emphasis was placed on recording the pattern of the drop material spreading over the surface of the receiving fluid. On the continuous surface of the primary cavity and the crown the drop material is concentrated in the form of thin fibers which form a regular streaky or netlike pattern in which triangular, quadrangular, and pentagonal cells are expressed. The cell rows are ordered in the form of layers on the lateral walls and the bottom of the cavity. The fiber dimensions and the degree of their expressiveness vary in the process of flow evolution. The upper row of structures on the crown surface is formed by vertical fibers.     

Secondary atomisation produced by single drop vertical impacts onto heated surfaces

The paper reports an experimental analysis of the secondary atomisation produced by the impact of a single drop on a solid heated surface. Different wall temperatures were used to study different boiling regimes. The size of secondary drops produced by the impact was measured by two techniques, namely the phase Doppler anemometry (PDA) and the image analysis technique (IAT); this allowed to extend the measurable size range from 5.5 μm up to few mm. Two impacting walls with different surface roughness were used to show the effect of this parameter on different atomisation regimes. The liquid viscosity was also varied in a limited range by using water–glycerol mixtures. Image analysis allowed also to define the details of the morphology of drop spreading and break-up.     

Inertia dominated flow and heat transfer in liquid drop spreading on a hot substrate

The present work deals with computational modeling of the fluid flow and heat transfer taking place in the process of impact of a cold liquid drop (T_d = 20-25 °C) onto a dry heated substrate characterized by different thermophysical properties. The computational model, based on the volume-of-fluid method for the free-surface capturing, is validated by simulating the configurations accounting for the conjugate heat transfer. The simulations were performed in a range of impact Reynolds numbers (Re = 2000-4500), Weber numbers (We = 27-110) and substrate temperatures (T_s = 100-120 °C). The considered temperature range of the drop-surface, i.e. liquid-solid system does not account for the phase change, that is boiling and evaporation. The model performances are assessed by contrasting the results to the reference database originating from the experimental and complementary numerical investigations by Pasandideh-Fard et al. [Pasandideh-Fard, M., Aziz, S., Chandra, S., Mostaghimi, J., 2001. Cooling effectiveness of a water drop impinging on a hot surface. International Journal of Heat and Fluid Flow, 22, 201-210] and Healy et al. [Healy, W., Hartley, J., Abdel-Khalik, S., 2001. On the validity of the adiabatic spreading assumption in droplet impact cooling. International Journal of Heat and Mass Transfer, 44, 3869-3881]. In addition, the thermal field obtained is analyzed along with the corresponding asymptotic analytical solution proposed by Roisman [Roisman, I.V., 2010. Fast forced liquid film spreading on a substrate: flow, heat transfer and phase transition. Journal of Fluid Mechanics, 656, 189-204]. Contrary to some previous numerical studies, the present computational model accounts for the air flow surrounding the liquid drop. This model feature enables a small air bubble to be resolved in the region of the impact point. The reported results agree reasonably well with experimental and theoretical findings with respect to the drop spreading pattern and associated heat flux and temperature distribution.     

Calculation of the force of interaction of two drops in a plastic medium

In calculating the force of interaction of two spherical drops, the stress tensor component normal to the drop surface is taken from the solution of the corresponding problem of the elasticity theory, while the shear component is determined by the plastic properties of the medium. The results of the calculations performed are demonstrated to be in good agreement with experimental data on the character of drop motion and on the yield point of the medium surrounding the drops.     

Experimental investigation on splashing and nonlinear fingerlike instability of large water drops

The fluid physics of the splashing and spreading of a large-scale water drop is experimentally observed and investigated. New phenomena of drop impact that differ from the conventional Rayleigh–Taylor instability theory are reported. Our experimental data shows good agreement with previous work at low Weber number but the number of fingers or instabilities begins to deviate from the R–T equation of Allen at high Weber numbers. Also observed were multiple waves (or rings) on the spreading liquid surface induced from pressure bouncing (or pulsation) within the impacting liquid. The first ring is transformed into a radially ejecting spray whose initial speed is accelerated to a velocity of 4–5 times that of the impacting drop. This first ring is said to be “splashing,” and its structure is somewhat chaotic and turbulent, similar to a columnar liquid jet surrounded by neighboring gas jets at relatively high impact speed. At lower impact speeds, splashing occurs as a crown-shaped cylindrical sheet. A second spreading ring is observed that transforms into fingers in the circumferential direction during spreading. At higher Weber number, the spreading of a third ring follows that of the second. This third ring, induced by the pressure pulsation, overruns and has fewer fingers than the second, which is still in a transitional spreading stage. Several important relationships between the drop impact speed, the spray ejection speed of the first ring, and the number of fingers of the second and third rings are presented, based on data acquired during a set of drop impact experiments. Issues related to the traditional use of the R–T instability are also addressed.     

Fluorescence imaging of multi-component wetting

Fluorescence imaging methods are explored as tools to study multi-component wetting of liquids. A novel approach was employed using polymer labeled with contrasting fluorescent dyes, which allow optical recognition and also caused differences in surface tension between blend components. Total internal reflection-fluorescence microscopy probes a thin surface layer to the order of 100 nm to investigate the structure of the spreading drop next to the substrate. Dye segregation out of solution and phase separation of polymer blends were observed. Confocal microscopy can visualize the larger three-dimensional structure of sessile drops. Component segregation was observed and quantified using relative fluorescence intensities.     

A boundary integral method for two-dimensional (non)-Newtonian drops in slow viscous flow

A boundary integral method for the simulation of the time-dependent deformation of Newtonian or non-Newtonian drops suspended in a Newtonian fluid is developed. The boundary integral formulation for Stokes flow is used and the non-Newtonian stress is treated as a source term which yields an extra integral over the domain of the drop. The implementation of the boundary conditions is facilitated by rewriting the domain integral by means of the Gauss divergence theorem. To apply the divergence theorem smoothness assumptions are made concerning the non-Newtonian stress tensor. The correctness of these assumptions in actual simulations is checked with a numerical validation procedure. The method appears mathematically correct and the numerical algorithm is second order accurate. Besides this validation we present simulation results for a Newtonian drop and a drop consisting of an Oldroyd-B fluid. The results for Newtonian and non-Newtonian drops in two dimensions indicate that the steady state deformation is quite independent of the drop-fluid. The deformation process, however, appears to be strongly dependent on the drop-fluid. For the non-Newtonian drop a mechanical model is developed to describe the time-dependent deformation of the cylinder for small capillary numbers.     

双液滴热毛细迁移的实验研究

在地面实验中,研究在竖直向上温度梯度流场中,双液滴的热毛细迁移运动和它们间的相互 作用. 豆油和硅油分别作为实验系统的母液和液滴. 液滴迁移轨迹被记录和分析. 实验结果 表明,大小液滴的实验迁移速度均小于理论迁移速度;两个液滴之间的相互作用对小液滴的 影响更为明显,使之出现倾斜``8'字的迁移轨迹;两个液滴的运动速度都出现了振荡现象, 小液滴可能出现短时反向迁移. 实验结果与数值模拟结果较为相似,但尚有差异,需要进一 步进行研究.     

Coalescence and break-up of drops in two-phase flows

The systematic experimental study of physical phenomena taking place at collisions of drops of water, water-glycerine solutions and transformer oil moving with moderate and high relative velocities has been carried out. The cases of drops interaction of one fluid and various fluids are considered. The regularities of drops collisions both in the quiescent and the moving gaseous medium have been studied. It has been stated that interaction is almost always accompanied by breaking a large drop with forming a certain amount of polydisperse fragments. The generalizing formulae are obtained for the parameter of coalescence and break-up Φ_ji, as well as for the function of fragments distribution by their size and initial velocity.