Fully implicit interface tracking for a viscous drop under simple shear

In this article we present a novel 3D implicit interface tracking method for sharp interfaces with interfacial tension in the creeping flow regime, employing the finite element method. The interface nodes are allowed to move only in the normal direction and thus remeshing can be avoided, most of the times. The implicit method allows us to overcome certain time step limitations imposed by the mesh capillary time. To validate our method, we use a fairly simple and very well understood problem of a single viscous drop suspended in a viscous matrix that deforms under an applied shear rate. This problem was first studied by Taylor [1] and has been extensively reviewed by Rallison [2] and Stone [3]. The second moment of inertia tensor was used to compute the deformation parameter D and the inclination angle θ and the results are compared to the theory for small deformations of Taylor [1]

Head-on collision of Newtonian drops in a viscoelastic medium

Depending on the application, one needs to either stabilize or destabilize the interfacial properties of an emulsion. An aspect of the dynamics that governs the stability of emulsions in general is the drainage time of the film that is formed when two drops collide. In this work, we study the effect that viscoelasticity of the matrix fluid has on this drainage time of two Newtonian drops that perform a head-on collision under an applied macroscopic extensional rate. For the modeling of the viscoelastic matrix material, the Giesekus model is chosen. A cylindrical coordinate system is applied with imposed axisymmetry and the resulting equations are solved using fully resolved numerical simulations employing a finite element discretization. Our results show that viscoelasticity reduces the drainage time, which is a combined effect of three different stages.ISSN:1613-4982ISSN:1613-499

Shear-Induced Migration of Rigid Particles near an Interface between a Newtonian and a Viscoelastic Fluid

Simulations of rigid particles suspended in two-phase shear flow are presented, where one of the suspending fluids is viscoelastic, whereas the other is Newtonian. The Cahn–Hilliard diffuse-interface model is employed for the fluid–fluid interface, which can naturally describe the interactions between the particle and the interface (e.g., particle adsorption). It is shown that particles can migrate across streamlines of the base flow, which is due to the surface tension of the fluid–fluid interface and a difference in normal stresses between the two fluids. The particle is initially located in the viscoelastic fluid, and its migration is investigated in terms of the Weissenberg number <i>Wi</i> (shear rate times relaxation time) and capillary number <i>Ca</i> (viscous stress over capillary stress). Four regimes of particle migration are observed, which can roughly be described by migration away from the interface for <i>Wi</i> = 0, halted migration toward the interface for low <i>Wi</i> and low <i>Ca</i>, particle adsorption at the interface for high <i>Wi</i> and low <i>Ca</i>, and penetration into the Newtonian fluid for high <i>Wi</i> and high <i>Ca</i>. It is found that the angular velocity of the particle plays a large role in determining the final location of the particle, especially for high <i>Wi</i>. From morphology plots, it is deduced that the different dynamics can be described well by considering a balance in the first-normal stress difference and Laplace pressure. However, it is shown that other parameters, such as the equilibrium contact angle and diffusion of the fluid, are also important in determining the final location of the particle

Liquid bridge length scale based nondimensional groups for mapping transitions between regimes in capillary break-up experiments

Criteria to identify transitions between dynamic self-similar linear thinning regimes of liquid bridges are of utmost importance in order to accurately interpret results in capillary break-up rheometry. Currently available criteria encompass many experimental difficulties or rely on numerical approaches. Here, we introduce a different set of nondimensional groups, OhL=ηin/γρL and a=R/L, based on the experimentally relevant axial length scale of a liquid bridge L, for viscous-dominated fluids undergoing capillary break-up in air. This framework is further extended to encompass the effect of outer viscous fluids. As a result, we present a two-dimensional operating map in which the boundaries are set by fluid properties and a single geometrical parameter, related to the experimental configuration. This approach establishes guidelines to correctly interpret experimental data and identify transitions in capillary break-up experiments of liquid bridges surrounded by fluids of different viscosities