Kristof Verhulst

Drop shape dynamics of a Newtonian drop in a non-Newtonian matrix during transient and steady shear flow

Transient and steady deformation of a single Newtonian drop immersed in a non-Newtonian matrix subjected to a homogeneous shear flow is investigated microscopically. Two model Boger fluids have been used as non-Newtonian matrices. The three-dimensional drop shape is completely determined as observations from both the velocity-vorticity and velocity-velocity gradient plane are available. Start-up and relaxation are investigated varying both the capillary number and the elasticity of the matrix fluid, while the viscosity ratio is kept constant. The extensive data set demonstrates that matrix elasticity reduces the steady drop deformation and promotes droplet orientation, can induce a drop deformation overshoot in the start-up experiments and slows down the relaxation phenomena. The experimental results have been compared with predictions of a phenomenological model [M. Minale, J. Non-Newtonian Fluid Mech. 123, 151–160 (2004)], that is slightly modified in the present work. It shows good agreement with the experimental data up to moderate capillary numbers (Ca≈0.2). For higher Ca, the observed trends are still correctly predicted, although quantitative agreement is less satisfying. A systematic deviation is observed at the end of the relaxation process. This result, together with a systematic, quantitative discrepancy in the experimental data between the two Boger fluids, suggests that the underlying rheological model is probably too simplistic to allow a quantitative prediction of all effects caused by matrix elasticity.Transient and steady deformation of a single Newtonian drop immersed in a non-Newtonian matrix subjected to a homogeneous shear flow is investigated microscopically. Two model Boger fluids have been used as non-Newtonian matrices. The three-dimensional drop shape is completely determined as observations from both the velocity-vorticity and velocity-velocity gradient plane are available. Start-up and relaxation are investigated varying both the capillary number and the elasticity of the matrix fluid, while the viscosity ratio is kept constant. The extensive data set demonstrates that matrix elasticity reduces the steady drop deformation and promotes droplet orientation, can induce a drop deformation overshoot in the start-up experiments and slows down the relaxation phenomena. The experimental results have been compared with predictions of a phenomenological model [M. Minale, J. Non-Newtonian Fluid Mech. 123, 151–160 (2004)], that is slightly modified in the present work. It shows good agreement with the e...

Influence of confinement on the steady state behavior of single droplets in shear flow for immiscible blends with one viscoelastic component

By using a counter rotating plate-plate device, single droplets in shear flow have been microscopically studied at confinement ratios ranging from 0.1 to 0.75. The droplet-to-matrix viscosity ratio was fixed at 0.45 and 1.5. Results are presented for systems with a viscoelastic Boger fluid matrix or a viscoelastic Boger fluid droplet, at a Deborah number of 1. Although the separate effects of confinement and component viscoelasticity on droplet dynamics in shear flow are widely studied, we present the first systematic experimental results on confined droplet deformation and orientation in systems with viscoelastic components. Above a confinement ratio of 0.3, wall effects cause an increase in droplet deformation and orientation, similar to fully Newtonian systems. To describe the experimental data, the Shapira–Haber theory [Shapira, M., and S. Haber, Int. J. Multiph. Flow 16, 305–321 (1990)] for confined slightly deformed droplets in Newtonian-Newtonian systems is combined with phenomenological bulk model...

Transient Droplet Behavior and Droplet Breakup during Bulk and Confined Shear Flow in Blends with One Viscoelastic Component: Experiments, Modelling and Simulations

The transient droplet deformation and droplet orientation after inception of shear, the shape relaxation after cessation of shear and droplet breakup during shear, are microscopically studied, both under bulk and confined conditions. The studied blends contain one viscoelastic Boger fluid phase. A counter rotating setup, based on a Paar Physica MCR300, is used for the droplet visualisation. For bulk shear flow, it is shown that the droplet deformation during startup of shear flow and the shape relaxation after cessation of shear flow are hardly influenced by droplet viscoelasticity, even at moderate to high capillary and Deborah numbers. The effects of droplet viscoelasticity only become visible close to the critical conditions and a novel break-up mechanism is observed. Matrix viscoelasticity has a more pronounced effect, causing overshoots in the deformation and significantly inhibiting relaxation. However, different applied capillary numbers prior to cessation of shear flow, with the Deborah number fixed, still result in a single master curve for shape retraction, as in fully Newtonian systems. The long tail in the droplet relaxation can be qualitatively described with a phenomenological model for droplet deformation, when using a 5-mode Giesekus model for the fluid rheology. It is found that the shear flow history significantly affects the droplet shape evolution and the breakup process in blends with one viscoelastic component. Confining a droplet between two plates accelerates the droplet deformation kinetics, similar to fully Newtonian systems. However, the increased droplet deformation, due to wall effects, causes the steady state to be reached at a later instant in time. Droplet relaxation is less sensitive to confinement, leading to slower relaxation kinetics only for highly confined droplets. For the blend with a viscoelastic droplet, a non-monotonous trend is found for the critical capillary number as a function of the confinement ratio. Finally, experimental data are compared with 3D simulations, performed with a volume-of-fluid algorithm.

Steady state droplet deformation and orientation during bulk and confined shear flow in blends with one viscoelastic component: Experiments, modeling and simulations

The steady deformation and orientation of droplets in shear flow, both under bulk and confined conditions, is microscopically studied for blends with one viscoelastic phase and a viscosity ratio of 1.5. The experiments are performed with a Linkam shearing cell and a counter rotating setup, based on a Paar Physica MCR300. For bulk shear flow, it is shown that matrix viscoelasticity suppresses droplet deformation and promotes droplet orientation towards the flow direction. Interestingly, these effects saturate at Deborah numbers above 2. For ellipsoidal droplets, viscoelasticity of the droplet fluid hardly affects the droplet deformation and droplet orientation, even up to Deborah numbers as high as 16. When the droplet is confined between two plates, the droplet deformation and the orientation towards the flow direction increase with confinement ratio, as in fully Newtonian systems. At a Deborah number of 1, the effect of component viscoelasticity under confined conditions remains qualitatively the same as...

Numerical Investigation of the Influence of Viscoelasticity on Drop Deformation in Shear

Numerical simulations and experimental data are compared for the investigation of the influence of viscoelasticity on drop deformation in shear. A viscoelastic drop suspended in a Newtonian liquid, or a Newtonian drop suspended in a viscoelastic liquid, is sheared and investigated for transients, relaxation after cessation of shear flow, and step‐up in shear rate. The numerical simulations are conducted at parameters chosen to model the experiments. We use the volume of fluid (VOF) continuum surface force (CSF) algorithm for situations dominated by shear. For drop relaxation experiments, we use the paraboloid representation of the interface in the surface tension force (PROST) algorithm. The Oldroyd‐B and Giesekus constitutive models are implemented. An interesting result is that by stepping up in the capillary number gradually, a stationary states is achieved at higher capillary numbers than without the graduated steps. The experimental work is described in Verhulst, Moldenaers and Cardinaels [l]. We pre...