1. The Soft Matter Engineering Lab Laboratory of Modeling and Simulation of Soft Matter G. D’Avino, T. Tuccillo, S. Nazir, P.L. Maffettone COMPUTING IN SOFT MATTER ENGINEERING: EFFECT OF THE CONFINEMENT ON PARTICLE DYNAMICS IN SHEARED VISCOELASTIC LIQUIDS GRISU’ Open Day su Scienza ed Ingegneria dei Materiali e Grid 03 Aprile 2009, Napoli F. Greco Dipartimento di Ingegneria Chimica, Università “Federico II” di Napoli, ITALY Istituto di Ricerche sulla Combustione, IRC, CNR, Napoli, ITALY

2. The Soft Matter Engineering Lab Laboratory of Modeling and Simulation of Soft Matter The motion of particles in confined geometries occurs in several practical and industrial applications Introduction In hematology: cells, vescicles, leukocytes flow in blood vessels Microfluidic devices: particles have dimensions comparable with channel size  microfiltration  separation  fluid-flow fractionation  electrophoreses  …

3. The Soft Matter Engineering Lab Laboratory of Modeling and Simulation of Soft Matter In such systems, several theoretical and experimental studies reported the existence of the migration phenomenon 1,2, i.e. the motion of the particle across the streamlines of the externally imposed flow A lot of work has been carried out for Newtonian suspensions and the migration has always been explained as an inertial effect 1,2 However, in microfluidic devices, the Reynolds number is very small so that inertial effects are irrelevant Nevertheless, as soon as the suspending fluid exhibits a viscoelastic behavior, the migration phenomenon still occurs 3,4 Background 1 Acrivos, J. Rheol., (1995) 2 Yang, Wang, Joseph, Hu, Pan & Glowinski, J. Fluid Mech., (2005) 3 Gauthier, Goldsmith & Mason, Rheol. Acta, (1971) 4 Lormand & Phillips, J. Rheol., (2004)

4. The Soft Matter Engineering Lab Laboratory of Modeling and Simulation of Soft Matter Background Recently, the motion of a particle in a sheared viscoelastic fluid in a Couette cylindric geometry is experimentally studied 1 1 Lormand & Phillips, J. Rheol., (2004) The migration is influenced by many factors such as:  fluid rheology  particle dimension  external flow parameters Isolated particles in a flowing viscoelastic fluid migrate towards the channel walls

5. The Soft Matter Engineering Lab Laboratory of Modeling and Simulation of Soft Matter Motivation Theoretical studies on particle migration are mainly reported only for Newtonian suspending fluids Few works take into account the viscoelasticity of the suspending medium and all of them are limited to 2D systems No information about the migration velocity is reported  Objective of this work is to study the migration of a single sphere in a viscoelastic liquid subjected to shear flow  The analysis is carried out through 3D Direct Numerical Simulations (DNS)

6. The Soft Matter Engineering Lab Laboratory of Modeling and Simulation of Soft Matter Mathematical model Particle motion Governing equations Hydrodynamics Assumptions:  rigid, spherical, non- Brownian particle  inertialess fluid and solid  no-slip conditions on par- ticle boundary  periodic conditions along x-direction  VpVp UpUp x y z Boundary conditions

7. The Soft Matter Engineering Lab Laboratory of Modeling and Simulation of Soft Matter Numerical method The balance equations are solved through the finite element method Proper numerical techniques are used to improve the numerical stability and convergence of the method Computational domain symmetry Discretized domain x y z

8. The Soft Matter Engineering Lab Laboratory of Modeling and Simulation of Soft Matter Results The simulations are performed by setting: D p /H = 0.2, De = 1.0,  = 0.2,  s /  p = 0.1 Particle trajectories Impenetrable region Regardless the starting position y p0, the particle migrates towards the closest wall (for symmetry only one-half channel is reported) A qualitative agreement with experiments is found

9. The Soft Matter Engineering Lab Laboratory of Modeling and Simulation of Soft Matter Results All the trajectories overlap onto a single trend by simply translating them in time different particle starting positions 1 Lormand & Phillips, J. Rheol., (2004)

10. The Soft Matter Engineering Lab Laboratory of Modeling and Simulation of Soft Matter Some computational detail about the simulations just shown:  N° CPU: 1  CPU time: about 24 hr  CPU RAM: about 2 Gb  Solver: Iterative, GMRES + ILUt Why the GRID? a mesh fixed in time and space is considered the accuracy of the solution depends on the n° of elements in the finer region x y z Instead of considering a hole in the mesh, the particle is described by moving its surface only FICTITIOUS DOMAIN METHOD  x y z Let’s consider a bit more complicated case:

11. The Soft Matter Engineering Lab Laboratory of Modeling and Simulation of Soft Matter The following results refer to the angular velocity for an ellipsoid in an unbounded sheared Newtonian fluid Why the GRID? Coarsest mesh: Direct solver: 12 hr Iterative solver: 2.5 hr Analytical solution Intermediate mesh: Direct solver: not possible Iterative solver: 4.5 hr Finest mesh: Direct solver: not possible Iterative solver: 8 hr

12. The Soft Matter Engineering Lab Laboratory of Modeling and Simulation of Soft Matter The test problem is quite simple (single particle in a Newtonian fluid) If a viscoelastic fluid is considered, the matrix size increases by a factor 2 The preliminary results show that a 3D multi-particle system cannot be managed by a sequential code Why the GRID? A collaboration with the group of Prof. Murli is actually in progress The parallelized version of the code will be run on the Grid SCOPE For these reasons, a parallelization of the code is required So far, our simulations are limited to 2D systems

13. The Soft Matter Engineering Lab Laboratory of Modeling and Simulation of Soft Matter Thank you for your attention…