Collision dynamics of high-speed droplets upon layers of variable thickness

The collision dynamics between a droplet and a film has been studied with high-impact energy that can be grouped in a dimensionless Weber number, We, as normalized by surface energy. To accomplish this, we have developed a technique based on cutting of a high-speed jet, which can generate a single droplet with speed up to 23 m/s and We on the order of thousands. It was found that the boundaries indicating the occurrence of a central jet and that of a secondary droplet disintegrated from the jet decreased monotonically with increased dimensionless film thickness, H, and remained constant when the film thickness was larger than the crater depth. However, the transition designating multiple droplets that are originated from a central jet shows a non-monotonic trend with the variation of H, with a minimum We being at H ≈ 3, which is about the maximum crater depth, owing to a tuning behavior. The critical We for splashing that occurs at an early phase immediately after the impact is relatively sensitive to the film thickness only when H is between 1 and 2, which increases with reduced H. At large We (≳2,570 for high H), the ejected crown is closed to form a bubble and the transition boundary reveals a similar dependence on H as that for creation of a central jet.     

Investigation of binary drop rebound and coalescence in liquids using dual-field PIV technique

Experiments on binary drop collisions within an index-matched liquid were conducted for Weber numbers (We) in the range of 1–50. Drop pairs of water/glycerin mixture were injected horizontally into silicone oil and, due to gravitational effects, travelled on downward trajectories before colliding. A dual-field high-speed PIV measurement system was employed to quantify drop trajectories and overall collision conditions while simultaneously examining detailed velocity fields at the collision interface. Sequences of velocity and vorticity fields were computed for both larger and smaller fields of view. In the We range examined, both rebounding and coalescing behavior occurred. Coalescence was found to result from a combination of vortical flow within drops and strong drop deformation characteristic of higher We. Flow through the centers of opposing ring vortices, strengthened by drop deformation, enhanced drainage of the thin film in the impact region, leading to film rupture and coalescence. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Droplet impact dynamics for two liquids impinging on anisotropic superhydrophobic surfaces

Droplet impingement experiments were performed on grooved hydrophobic surfaces with cavity fractions of 0, 80, and 93?% using droplets of water and a 50?%/50?% water/glycerol mixture. The influence of liquid viscosity, cavity fraction, and spreading direction, relative to the surface grooves, is explored qualitatively and quantitatively. The maximum droplet spread diameter, velocity of the rebounding jet, and the time delay between droplet impact and jet emission were characterized for Weber numbers, We, based on droplet impact speed and diameter, up to 500. The unequal shear stresses and contact angles influence the maximum spread diameters in the two primary spread directions. At We?>?100, the ratio of the spread diameter along the direction of the grooves to the spread diameter perpendicular to the grooves increases above unity with increasing We. The maximum droplet spread diameter is compared to recent predictive models, and the data reveal differing behavior for the two fluids considered. The results also reveal the existence of very high relative jet velocities in the range 5????We????15 for water droplets, while such jets were not observed for the more viscous mixture. Further, in the range 115????We????265, the water/glycerol jet formation dynamics are radically different from the water behavior. Most evident is the existence of two-pronged jets, which arise from the anisotropy of the surface and the unequal shear stresses and contact angles that prevail on the surfaces. It is these influences that give rise to differences in the maximum spread diameters in the two primary spread directions. Similar two-pronged jet emission was observed for water over the very narrow range of We from 91 to 96. The issuing jet velocities were also observed to increase with increasing cavity fraction for both fluids and over the entire range of We explored. Lastly, the elapsed time between droplet impact and jet emission decreased with increasing cavity fraction.     

Investigation of droplets impinging on a deep pool: transition from coalescence to jetting

An experimental investigation of droplets impinging vertically on a deep liquid pool of the same fluid was conducted. Coalescence and jetting as two of the main regimes were identified and studied. Five fluids, distilled water, technical ethanol, n-pentane, methanol and 1-propanol were used for providing different liquid-phase physical properties with density from 600 to 1,000 kg/m³, viscosity from 0.20 to 2.00 mPa s, and surface tension from 13.7 to 72.0 mN/m. Except for the experimental run of n-pentane, which was carried out in n-pentane saturated vapor, the ambient gas for the other experiments was air. The impact processes of micro-level (diameter below 1 mm) droplets were captured using a high-speed camera with a backlight. The observations, velocity and diameter ranges of the experimental runs were described, and based on them, the effects of the liquid-phase properties were studied. It was found that both low viscosity and low surface tension can increase the instability during impact processes. By curve-fitting, the transition from coalescence to jetting was characterized by using two models, one employing the Weber number (We) and the Ohnesorge number (Oh), and one employing the Froude number (Fr) and the Capillary number (Ca). Both models characterize the coalescence-jetting threshold well. The We-Oh model was based on a commonly used model from Cossali et al. (in Exp Fluids 22:463–472, 1997) for characterizing coalescence-splashing. For the small droplet diameters (below 1 mm) considered in this study, it was required to modify the We-Oh model with a diameter-dependent term to fit the sharp change in thresholds for fluids with relatively high viscosity. The Fr-Ca model has not previously been presented in the literature. A comparison of the two models with literature data (Rodriguez and Mesler, J Colloid Interface Sci 106(2):347–352, 1985) indicates that they are also valid for impacts of droplets with diameters above 1mm. Calculation methods to generalize the two models were proposed.     

An experimental study of a water droplet impinging on a liquid surface

An experimental study is presented for water droplet impingement on a liquid surface. The impaction process was recorded using a high-speed digital camera at 1,000 frames/s. The initial droplet diameter was fixed at 3.1 mm ± 0.1 mm, and all experiments were performed in atmospheric air. The impact velocity was varied from 0.36 m/s to 2.2 m/s thus varying the impact Weber number from 5.5 to 206. The impacted liquid surface consisted of two fluids, namely water and methoxy-nonafluorobutane, C₄F₉OCH₃ (HFE7100). The depth of the water and HFE7100 pool was varied from 2 mm to 25 mm. The collision dynamics of water in the HFE7100 pool was observed to be drastically different from that observed for the water droplet impingement on a water pool. The critical impact Weber number for jet breakup was found to be independent of liquid depth. Water–HFE7100 impact resulted in no jet breakup over the range of velocities studied. Therefore, no critical impact Weber number can be defined for water–HFE7100 impact. Received: 27 June 2001/Accepted: 29 November 2001     

Large strain requirements for shear-induced crystallization of isotactic polypropylene

We studied strain effects on the crystallization of a series of isotactic polypropylenes (iPP) of various molecular weights using rheology, rheo-optical measurements, differential scanning calorimetry (DSC), and wide-angle X-ray diffraction (WAXD). The samples were pre-sheared and then crystallized both at the same temperature. Transmitted light intensity measurements demonstrate that the effect of pre-shear on crystallization rate keeps increasing with strain up to surprisingly large strain levels, much beyond strains that are required to reach steady shear flow (at given We). Crystal orientation sets in at a total strain of about or higher. WAXD and DSC measurements corroborated the light transmission results. Total shear strains to 1000 were applied to the iPP samples at the beginning of a crystallization experiment, after the samples had reached the crystallization temperature of 145°C (under-cooled state). A constant Weissenberg number We=1 (We is defined as the product of shear rate and a relaxation time) was maintained for all pre-shearing of this study. We=1 corresponds to the onset of shear thinning in steady shear. Deborah number values were low, De<<1, indicating that steady shear flow had been reached in all pre-shearing runs (De is defined as the ratio of relaxation time to pre-shearing time). Further studies are needed at high We as there are indications that strain requirements are much reduced at high We. A fundamental understanding is still missing.     

Binary droplet collisions in a vacuum environment: an experimental investigation of the role of viscosity

An experimental investigation of viscous binary droplet collisions in a vacuum environment is conducted. The fundamental ramifications of conducting such experiments in a vacuum environment are twofold. The first, which is the motivating factor of this work, assures that the collision products are unimpeded by aerodynamic effects which tend to disrupt the collision process at a much earlier stage in the processes than if they were absent, and second, the phenomenon of encapsulation of the host medium between the colliding droplets is not present in this study; a fact that limits the scope of direct application of this study to a number of (but not all) applications. Droplets are generated from capillary stream breakup with the imposition of an amplitude-modulated disturbance which results in the generation of highly uniform pre-collision drops at separations far extending those which are possible from a standard (monochromatic) sinusoidal disturbance. Hence, the collision products are able to deform unimpeded by interactions with neighboring collision products. Measurements over a broad range of Weber number, We, indicate that the value of the critical Weber number, We_c, is more than 100 times greater for the 30-cSt fluid than the corresponding value for similarly sized water drops in a standard ambient environment. Measurements of the oblate and prolate half-cycle oscillation periods resulting from the binary collision reveal a distinct behavior that is observed and documented here for the first time. Additionally, measurements of the radial extent of the deformed mass at the instant of maximum deformation have been conducted and allow quantification of the energy dissipation. These measurements show that the energy dissipation increases with increasing fluid viscosity, which contradicts the results published by others.     

An experimental evaluation of the behaviour of mono and polydisperse polystyrenes in Cross-Slot flow

The behaviour of a number of mono and polydisperse polystyrenes are probed experimentally in complex extensional flow within a Cross-Slot geometry using flow-induced birefringence. Polystyrenes with similar molecular weight (M _w) and increasing polydispersity (PD) illustrated the effect of PD on the principal stress difference (PSD) pattern in extensional flow. Monodisperse materials exhibited only slight asymmetry at moderate flowrates, although increased asymmetry and cusping was observed at high flowrates. The response of monodisperse materials of different M _w at various flowrates is presented and characterised by Weissenberg numbers for both chain stretch and orientation using a theory for linear entangled polymers. The comparison of stress profiles against Weissenberg number for each process is used to determine whether the PSD pattern observed is independent of M _w and elucidate which relaxation mechanism is dominant in the flow regimes probed. For monodisperse materials, at equivalent chain orientation Weissenberg number (We _τd), different molecular weight materials were seen to exhibit similar steady state PSD patterns independent of We _τR (chain stretch We). Whilst no obvious critical Weissenberg number (We) was found for the onset of increased asymmetry and cusping, it was found to occur in the “orientating flow without chain stretch” regime.     

Asymptotic analysis of the finite cone-and-plate flow of a non-newtonian fluid

Consider the shearing flow of a viscoelastic fluid trapped by surface tension between a cone and a plate. An asymptotic analysis of this problem in the limit of small gap angle has been done. This limit is realized in many practical situations. It is assumed that the Deborah number De, the Reynolds number Re, and the retardation parameter β are all order unity and that the shape of the free surface is very nearly spherical. Closed form analytic expressions are obtained for the leading terms of the primary and weak secondary motion of the fluid as well as the meniscus shape. It is found that the velocity field is bounded and continuous if and only if . There is a family of curves in the De-β plane on which the velocity field has a removable singularity at the origin. The secondary flow is made up of either one or two toroidal vortices. The meniscus has a bulge near the rotating cone and a trough near the stationary plate.     

Simultaneous droplet impingement dynamics and heat transfer on nano-structured surfaces

This study examines the hydrodynamics and temperature characteristics of distilled deionized water droplets impinging on smooth and nano-structured surfaces using high speed (HS) and infrared (IR) imaging at We = 23.6 and Re = 1593, both based on initial drop impingement parameters. Results for a smooth and nano-structured surface for a range of surface temperatures are compared. Droplet impact velocity, transient spreading diameter and dynamic contact angle are measured. The near surface average droplet fluid temperatures are evaluated for conditions of evaporative cooling and boiling. Also included are surface temperature results using a gold layered IR opaque surface on silicon. Four stages of the impingement process are identified: impact, boiling, near constant surface diameter evaporation, and final dry-out. For the boiling conditions there is initial nucleation followed by severe boiling, then near constant diameter evaporation resulting in shrinking of the droplet height. When a critical contact angle is reached during evaporation the droplet rapidly retracts to a smaller diameter reducing the contact area with the surface. This continues as a sequence of retractions until final dry out. The basic trends are the same for all surfaces, but the nano-structured surface has a lower dissipated energy during impact and enhances the heat transfer for evaporative cooling with a 20% shorter time to achieve final dry out.     

Investigation of droplet collisions for solutions with different solids content

The collision behaviour of droplets and the collision outcome are investigated for high viscous polymer solutions. For that purpose, two droplet chains produced by piezoelectric droplet generators are directed towards each other at a certain angle so that individual droplet pairs collide. For recording the collision event, one double-image and one high-speed CCD camera were used. One camera is positioned perpendicular to the collision plane recording the outcome of the collision, and the second camera is aligned parallel to the collision plane to assure that the droplet chains are exactly in one plane. A new approach for tracking droplets in combination with an extended particle tracking velocimetry algorithm has been developed. Time-resolved series of pictures were used to analyse the dynamics of droplet collisions. The three different water soluble substances were saccharose and 1-Ethenyl-2-pyrrolidone (PVP) with different molecular weights (K17, K30). The solvent was demineralised water. The solids contents ranged from 20 to 60 %, 5 to 25 % and 5 to 35 %, yielding dynamic viscosities in the range of 2–60 mPa s. Results were collected for different pairs of impact angles and Weber numbers in order to establish common collision maps for characterising the outcomes. Here, relative velocities between 0.5 and 4 m/s and impact parameters in the interval from 0 to 1 for equal-sized droplets (Δ = 1) have been investigated. Additionally, satellite formation will be discussed exemplarily for K30. A comparison with common models of different authors (Ashgriz and Poo in J Fluid Mech 221:183–204, 1990; Estrade et al. in Int J Heat Fluid Flow 20:486–491, 1999) mainly derived for low viscous droplets revealed that the upper limit of their validity is given by an Ohnesorge number of Oh = 0.115 and a capillary number of Ca = 0.577. For higher values of these non-dimensional parameters and hence higher dynamic viscosities, these models are unable to predict correctly the boundaries between collision scenarios. The model proposed by Jiang et al. (J Fluid Mech 234:171–190, 1992), which includes viscous dissipation, is able to predict the boundary between coalescence and stretching separation for higher viscosities (i.e. Oh > 0.115 and Ca > 0.577). However, the model constants are not identical for different solution properties. As a conclusion, an alteration of the collision appearance takes place because of the relative importance between surface tension and viscosity.     

Spectral and instantaneous flow field characteristics of the laminar to turbulent transition in a cone and plate apparatus

Fluid-surface interaction, is very much influenced by the flow distribution and the flow spectra. For biological surfaces, cell functions such as mytosis and cell turnover, can be triggered by the instantaneous flow fluctuations which induce augmented shear stress levels inside the wall surface boundary layer. The objective of this work is to study the flow field along a cellular surface and to understand the interaction process. For that purpose, a cone and plate apparatus was built in which the transitional and turbulent instantaneous flow field characteristics, especially near the plate surface, were investigated using spatial hot wire anemometry, concentrating on time domain and spectral analysis. The frequency spectrum of velocity fluctuations near the plate is influenced by the plate roughness. We found that there is a linear relation between wall roughness and the preferred frequencies of the spectra. In addition a universal law exists for mean velocities, similar to the logarithmic law of the wall, when normalized by R˜ ^1/2, the apparatus Reynolds number. Received: 31 March 1998/Accepted: 11 January 1999     

Acoustically excited air-assisted liquid sheets

The effect of acoustic excitation on the disintegration characteristics of air-assisted liquid sheets, which utilize water at ambient temperature, and for velocities up to 1.8 m/s, is investigated. The study using high-speed imaging techniques revealed that optimum frequency modulation of the perturbation generator has a pronounced influence on the associated surface waves and the subsequent breakup of the liquid sheet. The analysis includes characterization of critical wave amplitude, breakup length, and breakup frequency, for Weber numbers in the range 0.30<We_abs<0.44, which are compared with flow features in the absence of acoustic excitation. The results show that acoustic perturbation can effectively suppress the dominance of gravitational and surface tension effects. As a consequence, for low Weber number flows, the interfacial waves exhibit regularity, and thus a better control of primary breakup processes of liquid sheet may be accomplished.     

Particle removal from a surface by a bounded vortex flow

A bounded vortex flow consists of an axisymmetric vortex that is confined top and bottom between two plates (the “confinement plate” and “impingement plate”, respectively) and surrounded laterally by a swirling annular slot jet. The bottom of the vortex terminates on the boundary layer along the impingement plate and the top of the vortex is drawn into a suction port positioned at the center of the confinement plate. The circumferential flow within the annular jet is important for supplying circulation to the central wall-normal vortex. This flow field is proposed as a method for mitigation of dust build-up on a surface, where the vortex–jet combination supplements the more traditional vacuum port by enhancing the surface shear stress and related particle transport rate. The paper reports on a computational study of the velocity field and particle transport by a bounded vortex flow. Fluid flow computations are performed using a finite-volume approach for an incompressible fluid and particle transport is simulated using a discrete-element method. Computations are performed for different values of two dimensionless parameters – the ratio of the plate separation distance and the average radial location of the jet inlet (the dimensionless confinement height) and the ratio of flow rate withdrawn at the suction outlet and that injected by the jet (the flow rate ratio). For small values of the flow rate ratio, the impinging jet streamlines pass down to the boundary layer along the bottom surface and then travel up the vortex core. By contrast, for large values of flow rate ratio, the annular jet is quickly entrained into the suction outlet and no wall-normal vortex is formed. Particles are observed to roll along the impingement surface in a direction determined by the fluid shear stress lines. Particles roll outward when they lie beyond a separatrix curve of the surface shear stress lines, where particles within this separatrix curve roll inward, piling up at the center of the flow field. A toroidal vortex ring forms for the small confinement height case with flow rate ratio equal to unity, which yields double separatrix curves in the shear stress lines. The inward rolling particles intermittently lift up due to collision forces and burst away from the impingement surface, eventually to become entrained into the flow out the suction port or resettling back onto the impingement surface.     

Droplet deformation of a strongly shear thinning dense suspension of polymeric micelles

We investigated the deformation of a strong shear thinning droplet undergoing simple shear flow in a Newtonian liquid. The droplet was an aqueous solution of poly(ethylene oxide) end capped with an alkyl group that forms spherical micelles in aqueous solution. At high concentrations and below a critical temperature, the jammed micelles showed strong shear thinning behaviour, and neither a yield stress nor a Newtonian viscosity was observed. At small shear rates, the droplet rotated and aligned in the flow, but did not deform or only very weakly. At high shear rates, the droplet deformation increased with increasing shear rate. The deformed droplet did not relax after the shear was stopped except for a modest rounding of the edges. For each shear rate, an apparent viscosity, η _ad, of the equivalent Newtonian droplet was calculated assuming affine deformation. η _ad showed a power law dependence on the capillary number Ca with an exponent of − 1.8 and was larger than the shear viscosity of the micelle suspension at the same shear rates. The results were explained by the existence of a strong gradient of the viscosity inside the droplet leading to a very low viscosity fluid layer near the droplet/matrix interface.     

Flow field analysis of a turbulent boundary layer over a riblet surface

The near-wall flow structures of a turbulent boundary layer over a riblet surface with semi-circular grooves were investigated experimentally for the cases of drag decreasing (s ⁺=25.2) and drag increasing (s ⁺=40.6). One thousand instantaneous velocity fields over riblets were measured using the velocity field measurement technique and compared with those above a smooth flat plate. The field of view was 6.75 × 6.75 mm² in physical dimension, containing two grooves. Those instantaneous velocity fields were ensemble averaged to get turbulent statistics including turbulent intensities and turbulent kinetic energy. To see the global flow structure qualitatively, flow visualization was also carried out using the synchronized smoke-wire technique under the same experimental conditions. For the case of drag decreasing (s ⁺=25.2), most of the streamwise vortices stay above the riblets, interacting with the riblet tips frequently. The riblet tips impede the spanwise movement of the streamwise vortices and induce secondary vortices. The normalized rms velocity fluctuations and turbulent kinetic energy are small near the riblet surface, compared with those over a smooth flat plate. Inside the riblet valleys, these are sufficiently small that the increased wetted surface area of the riblets can be compensated. In addition, in the outer region (y ⁺ > 30), these values are almost equal to or slightly smaller than those for the smooth plate. For the case of drag increasing (s ⁺=40.6), however, most of the streamwise vortices stay inside the riblet valleys and contact directly with the riblet surface. The high-speed down-wash flow penetrating into the riblet valley interacts actively with the wetted riblet surface and increases the skin friction. The rms velocity fluctuations and turbulent kinetic energy have larger values compared with those over a smooth flat plate. Received: 24 March 1999/Accepted: 10 March 2000     

Existence of supersonic zones in three-dimensional separation flows

Up till now the region of three-dimensional separation flows which occur with supersonic flow past obstacles has received insufficient study. Supersonic flow with a Mach number of 2.5 past a cylinder mounted on a plate was studied in [1]. A local zone with supersonic velocities was found in the reverse subsonic flow region ahead of the cylinder. Its presence is explained by the three-dimensional nature of the flow. Similar supersonic zones are not observed in the case of supersonic flow over plane and axisymmetric steps.The present paper presents the results of experimental studies whose objective was refinement of the flow pattern ahead of a cylinder on a plate and the study of the local supersonic zones.The experiments were performed in a supersonic wind tunnel with a freestream Mach number M₁=3.11. The 24-mm-diameter cylinder with pressure taps along the generating line was mounted perpendicular to the surface of a sharpened plate. The distance from the plate leading edge to the cylinder axis wasl ₀=140 mm. The plate was pressure tapped along the flow symmetry axis. The Reynolds number was Rl ₀=u₀ l ₀/v ₁, Rl ₀=1.87.10⁷, where u₁ andv ₁ are the freestream velocity and the kinematic viscosity, respectively. The pressures were measured using a Pilot probe with internal and external diameters of 0.15 and 0.9 mm, respectively.The probe was displaced in the flow symmetry plane at a distance of 1.6 mm from the plate surface and at a distance of 1.1 mm along the leading generator of the cylinder. The flow on the surface of the plate and cylinder was studied with the aid of a visualization composition and the flow past the model was photographed with a schlieren instrument. Typical patterns of the visualization composition distribution and the pressure distribution curves over the plate surface, and also photographs of the flow past the model, are shown in [1].     

The influence of gas phase velocity fluctuations on primary atomization and droplet deformation

The effects of grid-generated velocity fluctuations on the primary atomization and subsequent droplet deformation of a range of laminar liquid jets are examined using microscopic high-speed backlit imaging of the break-up zone and laser Doppler anemometry of the gas phase separately. This is done for fixed gas mean flow conditions in a miniature wind tunnel experiment utilizing a selection of fuels, turbulence-generating grids and two syringe sizes. The constant mean flow allows for an isolated study of velocity fluctuation effects on primary atomization in a close approximation to homogeneous decaying turbulence. The qualitative morphology of the primary break-up region is examined over a range of turbulence intensities, and spectral analysis is performed in order to ascertain the break-up frequency which, for a case of no grid, compares well with the existing literature. The addition of velocity fluctuations tends to randomize the break-up process. Slightly downstream of the break-up region, image processing is conducted in order to extract a number of metrics, which do not depend on droplet sphericity, and these include droplet aspect ratio and orientation, the latter quantity being somewhat unconventional in spray characterization. A turbulent Weber number $We^{\prime}$ which takes into account gas phase fluctuations is utilized to characterize the resulting droplet shapes, in addition to a mean Weber number <We _d>. Above a $We^{\prime}>0.05$ a clear positive relationship exists between the mean aspect ratio of droplets and the turbulent Weber number where $We^{\prime}$ is varied by altering all relevant variables including the velocity root mean square, the initial droplet diameter, the surface tension and the density.     

Thermal Capacity Effect on Transient Free Convection Adjacent to a Vertical Surface in a Porous Medium

In this paper we analyse how the presence of the thermal capacity of a vertical flat plate of finite thickness, which is embedded in a porous medium affects the transient free convection boundary-layer flow. At the time t = 0, the plate is suddenly loaded internally with a constant heat flux rate q, so that a transient boundary-layer flow is initiated adjacent to the plate. Initially, the transient effects due to the imposition of the uniform heat flux rate at the plate are confined to a thin fluid region near to the surface and are described by a small time solution. These effects continue to penetrate outwards and eventually evolve into a new steady state flow. Analytical solutions have been derived for these transient (small time) and steady state (large time) flow regimes, which are then matched by a numerical solution of the full boundary-layer equations. It has been found that the non-dimensional fluid temperature (or fluid velocity) profiles are reduced when the thermal capacity effects, described by a parameter Q ^*, are reduced. For small values of Q ^*, the approach of these profiles to their steady state values is monotonic. However, for large values of Q ^*, the temperature profiles are observed to locally exceed (pass through a maximum value) the final steady state values at certain distances from the plate. In general, the maxima in the temperature profiles increase in size as Q ^* increases and the time taken to approach the steady state solutions increases significantly.