Scientific report

Scope and challenges Mixing of scalars (e.g. chemical species or heat) by laminar and deterministic flows is key to many industrial and natural fluid systems of size extending from microns to hundreds of kilometers. Examples are diverse and include mixing of viscous fluids, compact processing equipment and a rapidly expanding range of micro-fluidic applications as well as magma transport in the Earth’s mantle, gas exchange in lung alveoli and distribution of blood-borne pathogens.

Profound fundamental insight into mixing has great relevance and is imperative for further technological development of, especially, micro-fluidics applications and process engineering. Key challenges are: 3D realistic fluid systems; experimental mixing studies; (further) mathematical and conceptual development of 3D transport formalisms; their translation and integration into analysis and design strategies; (further) development of numerical and experimental methods for transport studies.

Aim and format The workshop sought to address the above challenges by providing a platform for physicists, mathematicians and engineers for exchanging their ideas and views on mixing and promote cross-disciplinary collaboration. To this end a programme of keynote lectures by leading experts and (invited) contributed talks by senior and junior scientists was compiled around the following themes:

Theme 1: Mathematical concepts for mixing and chaotic advection

Theme 2: Mixing and chaotic advection in viscous flows and microfluidics

Theme 3: Mixing and chaotic advection in environmental and natural systems

The workshop and beyond The participants represented a good cross-section of the mixing community, ranging from leading experts to junior scientists. The workshop was well received and considered a timely event. Attendance at presentations was high and interaction and active contribution was strong. Moreover, participants were highly appreciative of the excellent facilities and organisation of the Lorentz Center. In conclusion, we feel that the workshop was successful and achieved its aims.

The status of mixing research and future directions were wrapped up in a closing lecture. Moreover, methods and concepts in mixing studies will be reviewed in a special issue in Advances in Applied Mechanics (aimed at non-experts and students) and a state-of-the-art article in Reviews of Modern Physics (aimed at experts). This is currently in progress and includes contributions primarily by workshop participants. Finally, first plans for a follow-up meeting in 2-3 years from now were made.

Acknowledgment The organisers wish to express their sincere gratitude to the Lorentz Center for facilitating and co-organising the workshop. They furthermore acknowledge additional financial support by FOM, the JM Burgers Centre and TU/e.

Michel Speetjens (Eindhoven, The Netherlands)

Herman Clercx (Eindhoven, The Netherlands)

Julyan Cartwright (Granada, Spain)

Gert-Jan van Heijst (Eindhoven, The Netherlands)