Measurement of polymeric time scales from linear drop oscillations

[EN] The oscillating drop method allows material properties of liquids to be measured from damped drop oscillations. The literature discusses, e.g., the measurement of the liquid dynamic viscosity and the surface tension against the ambient medium, predominantly for Newtonian liquids. We use this method for measuring pairs of material properties of polymeric liquids. Pairs of properties may be measured, since the quantity measured is a complex frequency with a real and an imaginary part. For the measurements, individual drops are levitated in air by an ultrasonic levitator and imaged with a high-speed camera. Amplitude modulation of the ultrasound drives shape oscillations of the levitated drop. When the modulation is switched off, with the levitating force maintained, the drop performs free oscillations which are damped due to the liquid viscosity. The data acquired from the images recorded are the angular frequency and the damping rate which are used as an input into the characteristic equation of the oscillating drop. Our measurements intend to yield either two viscoelastic time scales with the zero-shear viscosity known, or one time scale and the zero-shear viscosity, with the other time scale known. The two time scales are the stress relaxation and the deformation retardation times. The latter is difficult to get for polymer solutions. The present contribution presents results from a large set of measurements of the deformation retardation time. Liquids studied are aqueous solutions of poly(acryl-amides) at varying concentration. The corresponding values of the zero-shear viscosity agree well with the values from shear rheometry. Values of the deformation retardation time differ substantially from the values commonly used in viscoelastic flow simulations. Furthermore, the measured values disagree with the predictions from the viscous-elastic stress splitting approach in linear viscoelasticity. With our study we will provide a consistent set of material properties for the Oldroyd-B model in linear viscoelasticity. This will be important for material modelling in viscoelastic spray simulations.Plohl, G.; Brenn, G. (2017). Measurement of polymeric time scales from linear drop oscillations. En Ilass Europe. 28th european conference on Liquid Atomization and Spray Systems. Editorial Universitat Politècnica de València. 968-975. https://doi.org/10.4995/ILASS2017.2017.4686OCS96897

Universality of stretching separation

We develop a parameter-free model for the fragmentation of drops colliding off-center. The prediction is excellent over a wide range of liquid properties. The so-called stretching separation is attributed to the extension of the merged drop above a critical aspect ratio of {3.25}. The evolution of this aspect ratio {is influenced by the liquid viscosity} and can be interpreted via an energy balance. This approach is then adapted to drop-jet collisions, which we model as consecutive drop-drop collisions. {The fragmentation criterion is similar the one observed at drop-drop collisions}, while the evolution of the stretched jet aspect ratio is modified to account for the different flow fields and geometry.Comment: 11 pages, 4 figures and supplementary materia

Effects of viscosity on liquid structures produced by in-air microfluidics

This paper experimentally investigates the effect of viscosity on the outcomes of collisions between a regular stream of droplets and a continuous liquid jet. A broad variation of liquid viscosity of both the drop and the jet liquid is considered, keeping other material properties unchanged. To do so, only two liquid types were used: aqueous glycerol solutions for the drop and different types of silicone oil for the jet liquid. Combining these liquids, the viscosity ratio {\lambda} = {\mu}drop/{\mu}jet was varied between 0.25 and 3.50. The collision outcomes were classified in the form of regime maps leading to four main regimes: drops in jet, fragmented drops in jet, encapsulated drops, and mixed fragmentation.We demonstrate that, depending on the drop and jet viscosity, not all four regimes can be observed in the domain probed by our experiments. The experiments reveal that the jet viscosity mainly affects the transition between drops in jet and encapsulated drops, which is shifted towards higher drop spacing for more viscous jets. The drop viscosity leaves the previous transition unchanged but modifies the threshold of the drop fragmentation within the continuous jet. We develop a model that quantifies how the drop viscosity affects its extension, which is at first order fixing its shape during recoil and is, therefore, determining its stability against pinch-off.Comment: 18 pages, 7 figure

Drop Stream – Immiscible Jet Collisions: Regimes and Fragmentation Mechanisms

[EN] We investigate the collision of a continuous liquid jet with a regular stream of immiscible droplets. The immiscible liquids, namely silicon oil for the continuous jet and an aqueous glycerol solution for the drop stream, are selected to enable the total wetting of the drops by the jet liquid. Four different regimes are experimentally identified: drops in jet, encapsulation without satellites, encapsulation with satellites from the jet liquid and mixed fragmentation. The drops in jet regime, potentially of great interest for new applications, corresponds to a regular stream of drops embedded in a continuous jet and is described and reported for the first time. Using well known aspects of drop collision and jet stability, we propose to model the transition between the drops in jet regime and the others. Two dimensionless parameters are derived from this analysis which are thus used to produce a simple regime map where the drops in jet regime can be well distinguished from the other outcomes.Planchette, C.; Hinterbichler, H.; Brenn, G. (2017). Drop Stream – Immiscible Jet Collisions: Regimes and Fragmentation Mechanisms. En Ilass Europe. 28th european conference on Liquid Atomization and Spray Systems. Editorial Universitat Politècnica de València. 723-729. https://doi.org/10.4995/ILASS2017.2017.4707OCS72372

Weakly nonlinear instability of a viscous liquid jet

[EN] A weakly nonlinear stability analysis of an axisymmetric viscous liquid jet is performed. The calculation is based on a small-amplitude perturbation method and restricted to second order. Contrary to the inviscid jet and the planar viscous sheet cases studied by Yuen in 1968 [1] and Yang et al. in 2013 [2], respectively, a part of the solution results from a polynomial approximation of Bessel functions. Results on interface shapes for a small wave number and initial perturbation amplitude, four different Ohnesorge numbers, taking into account the approximate part or not, are used to predict the influence of liquid viscosity on satellite drop formation and evaluate the influence of the approximation. It is observed that the liquid viscosity has a retarding effect on satellite drop formation, in agreement with previous experimental and numerical work. In addition, it is found that the approximate terms can be reasonably ignored, providing a simpler viscous weakly nonlinear model for the description of the first nonlinearity growth in liquid jets. The present work replaces the ILASS 2016 paper [3] by the authors on the same subject.G.B. is indebted to I.M. and his team at the LOMC of the CNRS in Le Havre, and to Christophe Dumouchel at CORIA in Rouen, for their hospitality during three sabbatical stays in September 2014, September 2015, and December 2016 and acknowledges the inspiring atmospheres at the two laboratories. MC.R. was supported by the LABEX EMC3 under the project TUVECO.Renoult, M.; Brenn, G.; Mutabazi, I. (2017). Weakly nonlinear instability of a viscous liquid jet. En Ilass Europe. 28th european conference on Liquid Atomization and Spray Systems. Editorial Universitat Politècnica de València. 613-620. https://doi.org/10.4995/ILASS2017.2017.4711OCS61362

An Extended Volume of Fluid Method and its Application to Single Bubbles Rising in a Viscoelastic Liquid

An extended volume of fluid method is developed for two-phase direct numerical simulations of systems with one viscoelastic and one Newtonian phase. A complete set of governing equations is derived by conditional volume-averaging of the local instantaneous bulk equations and interface jump conditions. The homogeneous mixture model is applied for the closure of the volume-averaged equations. An additional interfacial stress term arises in this volume-averaged formulation which requires special treatment in the finite-volume discretization on a general unstructured mesh. A novel numerical scheme is proposed for the second-order accurate finite-volume discretization of the interface stress term. We demonstrate that this scheme allows for a consistent treatment of the interface stress and the surface tension force in the pressure equation of the segregated solution approach. Because of the high Weissenberg number problem, an appropriate stabilization approach is applied to the constitutive equation of the viscoelastic phase to increase the robustness of the method at higher fluid elasticity. Direct numerical simulations of the transient motion of a bubble rising in a quiescent viscoelastic fluid are performed for the purpose of experimental code validation. The well-known jump discontinuity in the terminal bubble rise velocity when the bubble volume exceeds a critical value is captured by the method. The formulation of the interfacial stress together with the novel scheme for its discretization is found crucial for the quantitatively correct prediction of the jump discontinuity in the terminal bubble rise velocity

Experimental and Computational Investigation of binary drop collisions under elevated pressure

[EN] Spray systems often operate under extreme ambient conditions like high pressure, which can have a significant influence on important spray phenomena. One of these phenomena is binary drop collisions. Such collisions, depending on the relative velocity and the impact parameter (eccentricity of the collision), can lead to drop bouncing, coalescence or breakup. This experimental and computational study is focused on the description of the phenomenon of drop bouncing, which is caused by a thin gas layer preventing the drops coalescence. To identify the main influencing parameters of this phenomenon, experiments on binary drop collisions are performed in a pressure chamber. This experimental system allows us to investigate the effect of an ambient pressure (namely the density and viscosity of the surrounding gas) on the bouncing/coalescence threshold.This research was supported by the the German Scientific Foundation (Deutsche Forschungsgemeinschaft) in the framework of the SFB TRR 75 Collaborative Research Center, subprojects C04 and A07. The author Louis Reitter has contributed to the present manuscript in the framework of the course "Sprays and Atomization".Reitter, L.; Liu, M.; Breitenbach, J.; Huang, K.; Bothe, D.; Brenn, G.; Pan, K.... (2017). Experimental and Computational Investigation of binary drop collisions under elevated pressure. En Ilass Europe. 28th european conference on Liquid Atomization and Spray Systems. Editorial Universitat Politècnica de València. 815-821. https://doi.org/10.4995/ILASS2017.2017.4758OCS81582

Analytical solutions for transport processes: fluid mechanics, heat and mass transfer

This book provides analytical solutions to a number of classical problems in transport processes, i.e. in fluid mechanics, heat and mass transfer. Expanding computing power and more efficient numerical methods have increased the importance of computational tools. However, the interpretation of these results is often difficult and the computational results need to be tested against the analytical results, making analytical solutions a valuable commodity. Furthermore, analytical solutions for transport processes provide a much deeper understanding of the physical phenomena involved in a given process than do corresponding numerical solutions. Though this book primarily addresses the needs of researchers and practitioners, it may also be beneficial for graduate students just entering the field.