Numerical Methods for the Flow of Complex Fluids

Complex fluids are fluids with structure. Examples are polymeric fluids, fluids with rigid or flexible solid particles and fluids consisting of multiple phases. Under flow the structure can change significantly: polymers can develop high local stresses due to extensional flows, particles can migrate or align/cluster and droplets can merge or break-up. In order to study these complicated phenomena numerical methods need to be used and developed.

We focus on the following two subjects:

1) Simulation of the flow of viscoelastic fluids filled with rigid particles

Under flow, migration, aligning and/or clustering of the rigid particles can occur due to complicated stress fields developed in the viscoelastic matrix fluid. In Figure 1 the development of stress fields and the aligning of three particles in shear is shown. The rigid particles usually are of a spherical shape, but also other (anisotropic) shapes can be studied.

Examples of research topics are: the influence of rigid particles on the stability of fluid-fluid interfaces, active mixing in biosensors using super-paramagnetic particles and rheology of viscoelastic suspensions.

The finite element method is used for spatial discretization. Special numerical methods are used and developed for viscoelastic fluid flow, including the DEVSS and log-conformation techniques. For describing the moving sharp interface between the rigid particle and the fluid both ALE (Arbitrary Lagrangian Euler) and XFEM (extended finite element) techniques are being developed and employed.

2) Simulation of the flow of multi-phase complex fluids and flows with free surface

Here we study the flow of complex fluids consisting of multiple phases/components. Under the influence of flow and/or surface tension the micro-structure developed can be quite complicated. For example droplets can migrate (see Figure 2), merge or break-up into multiple droplets. All components can be fluids, but we also study problems where one of the phases is an elastic solid. We are particularly interested in the stresses near interfaces, which can be influenced by the transport of surfactants on and towards the interface. If one of the phases has a very low viscosity (such as air) the phase can be neglected and the problem reduces to the special case of a flow with a free surface. The same methods as for the multi-phase problems can be used.

Examples of research topics are: the flow generated by artificial cilia (flexible externally activated structures), the migration and deformation of (biological) cells in very confined microchannels, draw-resonance of fiber spinning of high-molecular weight polymers, stability of electrospinning thin polymer fibers, stability of the flow front in injection molding and structure formation in polymer blends.

In addition to the numerical methods used for rigid particles, special techniques are needed for tracking or capturing the fluid-fluid or solid-fluid interface and/or free surface. Both sharp-interface and diffuse-interface techniques are being used. If the phases consist of Newtonian fluids under slow flow conditions, the boundary integral method is preferred over the finite element method for spatial discretization.