Fluid Mechanics: Open Access

Complex fluid–fluid interfaces determine for an outsized part the macroscopic material properties of foams and emulsions that appear in applications like food, materials processing and consumer care products. As a step towards predicting these properties, a 2D axisymmetric and a 3D finite element model are developed for simulating the dynamics of one Newtonian drop by a Newtonian matrix fluid with a rheologically complex sharp interface in between. Interfaces with constant interfacial surface tension and with viscous, elastic and viscoelastic extra interfacial stresses are considered. The model has been validated by means of the tactic of manufactured solutions and by comparison with results from other studies using different discretisation methods. Higher-order convergence in space and time is obtained, demonstrating correct implementation of our numerical methods. Benchmark solutions for a drop with a Kelvin–Voigt interface under simple shear flow are provided. Compared to a viscous interface, the drop deformation becomes smaller and therefore the drop becomes less oriented within the direction of flow if interfacial elasticity is added. Fluid–fluid interfaces play a key role within the processing and functioning of multicomponent materials. samples of such materials are emulsions, where fluid drops of 1 phase are dispersed into another fluid phase immiscibly. Dispersion are often useful for designing material structures to e.g. gain synergy of properties. Emulsions are partly for this reason utilized in a spread of applications like in food, paint, cosmetics, materials processing (e.g. polymer blends) and within the industry , but they also appear in nature and biology. The interfacial area to volume ratio in emulsions is comparatively large, since albeit the drops in e.g. polymer blends are small in size (about tens of); they're present in large quantities. Therefore, the interfacial properties determine for an outsized part the general macroscopic material behaviour. When applying flow to an emulsion, the structure is continuously developing through the consecutive and simultaneous deformation, break-up and coalescence of drops interacting with one another and therefore the surrounding fluid during a complex manner. Curvature changes of the interface are opposed or helped by interfacial surface tension between the phases. Surfactants that are often added as stabilisers to the mixture and adsorb at the interface, lower the interfacial surface tension to hamper or hinder coalescence Hence, surfactants are required to get stable emulsions, but they also further complicate the behaviour of the interface. Surfactant concentration gradients within the interface cause spatially varying Marangoni stresses. Surfactant transport within the interface or between the interface and therefore the bulk introduces non-trivial time scales. Besides, interactions within the interface thanks to a big microstructure cause extra and deviatoric interfacial stresses and possibly rheologically complex behaviour of the interface, These complex interfaces can behave intrinsically viscoelastic.

In this paper we propose a completely unique approach to unravel the inverse problem of three-dimensional die design for extrudate swell, employing a real-time active control scheme. To the present end, we envisioned a feedback connection between the corner-line finite element method, wont to predict the positions of the free surfaces of the extrudate, and therefore the controller. The corner-line method allows for local mesh refinement and transient flow to be taken under consideration (Spanjaards et al., 2019). We show the validity of this method by showing optimization results for 2D axisymmetric extrusion flows of a viscoelastic fluid for various Weissenberg numbers. In 3D we first provides a proof of concept by showing the results of a Newtonian fluid exiting dies with increasing complexity in shape. Finally, we show that this method is in a position to get the specified extrudate shape of extrudates of a viscoelastic fluid for various Weissenberg numbers and different amounts of shear-thinning. Extrusion may be a common production technique within the polymer processing industry to get products with a desired cross-section. during this process a polymer is molten and pushed through a die with a particular cross-sectional shape, to get a product (extrudate) with this same cross-sectional shape. A standard requirement on the extrudate is dimensional precision. However, the size of the extrudate are highly influenced by a phenomenon called extrudate swell, where the extrudate starts to expand thanks to internal stresses within the polymer once it leaves the die.

We study the dynamics of a neutrally buoyant rigid sphere carried by an elastoviscoplastic fluid during a pressure-driven channel flow numerically. The yielding to flow is marked by the yield stress which splits the flow into two main regions: the core unyielded region and two sheared yielded regions on the brink of the walls. The particles which are initially within the plug region are observed to translate with an equivalent velocity because the plug with none rotation/migration. Keeping the Reynolds number fixed, we study the effect of elasticity (Weissenberg number) and plasticity (Bingham number) of the fluid on the particle migration inside the sheared regions. within the viscoelastic limit, within the range of studied parameters (low elasticity), inertia is dominant and therefore the refore the particle finds its equilibrium position between the centreline and the wall. An equivalent happens within the viscoplastic limit, yet the yield surface plays the role of centreline. However, the mixture of elasticity and plasticity of the suspending fluid (elastoviscoplasticity) trigger particle-focusing: within the elastoviscoplastic flow, for a particular range of Weissenberg numbers isolated particles migrate all the thanks to the centreline by getting into the core plug region. This behaviour suggests a particle-focusing process for inertial regimes which wasn't previously found during a viscoelastic or viscoplastic carrying fluid.Transporting suspension of particles during a yield-stress fluid may be a crucial problem to be understood thanks to intrinsic complexities from the carrying fluid rheology to the particle dynamics. a brief list of applications may include, but isn't limited to, construction and oil & gas industries. Efforts of Segré & Silberber and other scholars uncovered the behaviour of particles suspended during a Newtonian fluid Poiseuille flow from theoretical frameworks that extensively revealed features of this problem at the low Reynolds number limit, to experimental validations/extensions, Further studies uncovered the features of the matter in non-cylindrical conduits and migration of deformable and non-spherical particles.

A 3D transient non-isothermal finite element code is developed to predict the extrudate shape of viscoelastic fluids emerging from an asymmetric keyhole shaped die. The corner-line method is employed to model the movement of the free surfaces. The code is tested using two benchmark problems. First the corner-line method is tested employing a trumpet shaped object during a 3D uniaxial extensional flow. Secondly, the implementation of the energy balance and therefore the viscoelastic material behaviour is tested employing a non-isothermal pipeflow. For both benchmark problems convergence was obtained, giving confidence that the 3D non-isothermal swell problem is correctly implemented. The influence of shear-thinning, elasticity and temperature on the form of the extrudate is systematically studied. Results are shown for isothermal flows also as for non-isothermal flows, with isothermal and non-isothermal die walls. Results for isothermal die walls show increasing extrudate swelling with increasing elasticity which the swelling opposes extrudate bending. Shear-thinning on the opposite hand, opposes swelling, which initially promotes bending, but also flattens the asymmetric velocity profile, resulting in less extrudate bending for top amounts of shear-thinning. Furthermore, extrudate bending was observed even for purely viscous, isothermal extrudates, suggesting that bending is caused by asymmetry within the viscous stresses. Extrudate swelling are often influenced by the wall temperature of the die and non-isothermal die walls can cause a change in bending direction.

Extrusion is widely utilized in the polymer processing industry. Common requirement on the extrudate is dimensional accuracy. However, the size of the extrudate are highly influenced by a phenomenon called extrudate swell. For Newtonian fluids, having a continuing viscosity, extruded from cylindrical dies, the swell ratio is about 13% when physical phenomenon, inertia and gravitational forces are often neglected. For viscoelastic fluids, the swelling is far larger and therefore the final diameter of the extrudate are often several times the diameter of the die. This effect is attributed to normal stresses within the material.