Chaotic mixing

In chaos theory and fluid dynamics, chaotic mixing is a process by which flow tracers develop into complex fractals under the action of a fluid flow. The flow is characterized by an exponential growth of fluid filaments. Even very simple flows, such as the blinking vortex, or finitely resolved wind fields can generate exceptionally complex patterns from initially simple tracer fields. The phenomenon is still not well understood and is the subject of much current research. Context of chaotic advection Fluid flows Two basic mechanisms are responsible for fluid mixing: diffusion and advection. In liquids, molecular diffusion alone is hardly efficient for mixing. Advection, that is the transport of matter by a flow, is required for better mixing. The fluid flow obeys fundamental equations of fluid dynamics (such as the conservation of mass and the conservation of momentum) called Navier–Stokes equations. These equations are written for the Eulerian velocity field r

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Massively parallel flow computation with application to fluid mixing

EPFL1997

Chaotic mixing using source-sink microfluidic flows in a PDMS chip

Ata Tuna Ciftlik, Martinus Gijs, Abdeljalil Sayah, Venkataragavalu Sivagnanam, Hüseyin Cumhur Tekin, Caroline Vandevyver

We present an active fixed-volume mixer based on the creation of multiple source–sink microfluidic flows in a polydimethylsiloxane (PDMS) chip without the need of external or internal pumps. To do so, four different pressure-controlled actuation chambers are arranged on top of the 5 μl volume of the mixing chamber. After the mixing volume is sealed/fixed by microfluidic valves made using ‘microplumbing technology’, a virtual source–sink pair is created by pressurizing one of the membranes and, at the same time, releasing the pressure of a neighboring one. The pressurized air deforms the thin membrane between the mixing and control chambers and creates microfluidic flows from the squeezed region (source) to the released region (sink) where the PDMS membrane is turned into the initial state. Several schemes of operation of virtual source–sink pairs are studied. In the optimized protocol, mixing is realized in just a sub-second time interval, thanks to the implementation of chaotic advection.

Springer-Verlag2011

Understanding the mixing process in 3D microfluidic nozzle/diffuser systems: simulations and experiments

Martinus Gijs, Abdeljalil Sayah

We characterise computationally and experimentally a three-dimensional (3D) microfluidic passive mixer for various Reynolds numbers ranging from 1 to 100, corresponding to primary flow rates of 10-870 mu l min(-1). The 3D mixing channel is composed of multiple curved segments: circular arcs situated in the substrate plane and curved nozzle/diffuser elements normal to the substrate plane. Numerical simulation provides a detailed understanding of the mixing mechanism resulting from the geometrical topology of the mixer. These Comsol software-based simulations reveal the development of two secondary flows perpendicular to the primary flow: a swirling flow resulting from tangential injection of the flow into the nozzle holes and Dean vortices present in the circular arcs. These phenomena are particularly important at a Reynolds number larger than 30, where mixing occurs by chaotic advection. Experimentally, the 3D mixer is fabricated in a monolithic glass substrate by powder blasting machining, exploiting eroding powder beams at various angles of impact with respect to the substrate plane. Experimental mixing was characterised using two coloured dyes, showing nearly perfect mixing for a microfluidic footprint of the order of a few mm(2), in good agreement with the simulations.

Iop Publishing Ltd2016

Chaos theory

Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initi

ME-371: Discretization methods in fluids

Ce cours présente une introduction aux méthodes d'approximation utilisées pour la simulation numérique en mécanique des fluides. Les concepts fondamentaux sont présentés dans le cadre de la méthode des différences finies puis étendus à celles des éléments finis et spectraux.