One-step fabrication of transparent three-dimensional (3D) microfluidic to millifluidic devices was demonstrated using a commercial 3D printer costing $2300 with 500 mL of clear resin for $138. It employs dynamic mask projection stereolithography, allowing fast concept-to-chip time. The fully automated system allows fabrication of models of up to 43 mm × 27 mm × 180 mm (x × y × z) at printing speeds of 20 mm/h in height regardless of the design complexity. The minimal cross sectional area of 250 μm was achieved for monolithic microchannels and 200 μm for positive structures (templates for soft lithography). The colorless resin’s good light transmittance (>60% transmission at wavelengths of >430 nm) allows for on-chip optical detection, while the electrically insulating material allows electrophoretic separations. To demonstrate its applicability in microfluidics, the printer was used for the fabrication of a micromixer, a gradient generator, a droplet extractor, and a device for isotachophoresis. The mixi...

Cost-Effective Three-Dimensional Printing of Visibly Transparent Microchips within Minutes

The creation of complex three-dimensional (3D) microfluidic systems has attracted significant attention from both scientific and applied research communities. However, it is still a formidable challenge to build 3D microfluidic structures with arbitrary configurations using conventional planar lithographic fabrication methods. Here, we demonstrate rapid fabrication of high-aspect-ratio microfluidic channels with various 3D configurations in glass substrates by femtosecond laser direct writing. Based on this approach, we demonstrate a 3D passive microfluidic mixer and characterize its functionalities. This technology will enable rapid construction of complex 3D microfluidic devices for a wide array of lab-on-a-chip applications.

Rapid prototyping of three-dimensional microfluidic mixers in glass by femtosecond laser direct writing.

Preconditioned iterative methods for Stokes flow problems arising in computational geodynamics

3D printing has emerged as a valuable approach for the fabrication of fluidic devices and may replace soft-lithography as the method of choice for rapid prototyping. The potential of this disruptive technology is much greater than this - it allows for functional integration in a single, highly automated manufacturing step in a cost and time effective manner. Integration of functionality with a 3D printer can be done through spatial configuration of a single material, inserting pre-made components mid-print in a print-pause-print approach, and/or through the precise spatial deposition of different materials with a multimaterial printer. This review provides an overview on the ways in which 3D printing has been exploited to create and use fluidic devices with different functionality, which provides a basis for critical reflection on the current deficiencies and future opportunities for integration by 3D printing.

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Increasing the functionalities of 3D printed microchemical devices by single material, multimaterial, and print-pause-print 3D printing

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Strange eigenmodes and decay of variance in the mixing of diffusive tracers

A three-dimensional, steady flow configuration intended to mimic the baker’s map is studied by means of numerical simulation The Poincare sections computed from a finite element solution of the velocity field show that the behavior is dominated by chaotic advection The value obtained for the Lyapunov exponent is very close to the theoretical value of ln2 predicted by the baker’s map

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On a three-dimensional implementation of the baker’s transformation

Results of numerical simulation of the advection‐diffusion equation at large Peclet number are reported, describing the mixing of a scalar field under the action of diffusion and of a class of steady, bounded, three‐dimensional flows, which can have chaotic streamlines. The time evolution of the variance of scalar field is calculated for different flow parameters and shown to undergo modulated exponential decay, with a decay rate which is a maximum for certain values of the flow parameters, corresponding to cases in which the streamlines are chaotic everywhere. If such global chaos is present, the decay rate tends to oscillate, whereas the presence of regular regions produces a more constant decay rate. Significantly different decay rates are obtained depending on the detailed properties of the chaotic streamlines. The relationship between the decay rate and the characteristic Lyapunov exponents of the flow is also investigated.

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A numerical Eulerian approach to mixing by chaotic advection

In this paper we take a closer look at the decay phase of a passive, diffusing, scalar field undergoing steady, three-dimensional chaotic advection. The energy spectrum of the scalar is obtained by numerical simulation of the advection–diffusion equation at high Peclet number. At large times, the spectral decay is found to be exponential and self-similar. It is emphasized that the asymptotic decay-time is an important measure of mixing efficiency, alongside the time required for diffusion to first become effective. The large-wavenumber spectral form, representing the distribution of scalar energy over small scales, is analyzed. Power-law behavior is found at scales intermediate between the large ones, comparable in size with the entire flow volume, and the smallest ones, at which diffusion is effective and the spectrum falls off exponentially with increasing wavenumber. Fitting of the numerical results allows the exponent of the power-law to be estimated. It is observed to vary with the parameters of the flow, taking negative values which can be either less than or greater than −1. This implies that the dominant spectral energy at high P may be either at small, large or intermediate scales, depending on the flow. In consequence, the qualitative nature of the scalar field during the decay phase varies from flow to flow, resulting in differing behavior of the predicted decay times in the large P limit obtained by asymptotic analysis. The case in which the spectral exponent exceeds −1 is shown to produce more rapid mixing and the corresponding asymptotic expression for the decay time, independent of P and involving two spectral parameters, is suggested as a quantitative means for optimizing the flow.

Spectral decay of a passive scalar in chaotic mixing

Numerical studies for two protocols of micromixing based on chaotic advection to improve DNA chip hybridization are presented. The first protocol uses syringes; the other one, pumps. For both protocols, numerical Poincare sections and Lyapunov exponents of the three-dimensional, time-periodic flow are investigated as functions of the period. Model experiments also confirm numerical results. Homogeneity of the dispersion of particles inside the chamber is of primary importance to achieve best chip reliability: although global chaos was obtained for both protocols, we find that the one employing the pumps is more likely to achieve better and more rapid hybridization.

https://hal.archives-ouvertes.fr/hal-00272171/document

Philippe Carrière

Papers

On a three-dimensional implementation of the baker’s transformation

A numerical Eulerian approach to mixing by chaotic advection

Spectral decay of a passive scalar in chaotic mixing

Towards better DNA chip hybridization using chaotic advection

Chaotic mixing efficiency in different geometries of Hele-Shaw cells