- May 2022
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In this case, the band broadens rapidly in the first few centimeters of the channel as indicated by the asymmetry of the trace acquired 2 cm downstream from the inlet (blue trace in Fig. 4C). The traces acquired further downstream are noticeably more symmetrical; this change indicates a transition to diffusive broadening. Note that, by reducing the mixing length, the SHM will also reduce Deff(8, 26).
Compared to Poiseuille flow in a rectangular channel, the SHM achieved fluid mixing faster and within a shorter channel length. In addition, in the herringbone ridge mixer, the axial dispersion, i.e. spread of a plug introduced into the channel, is greatly reduced.
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In Fig. 3E, we see that Δy90 increases linearly with ln(Pe) for large Pe, as expected for chaotic flows.
The authors demonstrated that the channel length required to achieve 90% mixing increases with the natural logarithm of the Peclet number (as opposed to being directly proportional) at high flow rates. Since log(x) grows much slower than x, the channel length required to achieve full mixing remains small, even at high flow rates, when chaotic mixing methods (such as the one demonstrated in this work) are used.
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we use the leading edge of the fluorescent region to measure the angular displacement of the fluid in the cross section, Δφ.
Here, the authors captured optical images of the leading edge of the fluorescent solution to monitor and quantify the rotation of the fluid due to chaotic mixing by the herringbone ridge structures. The images are analyzed to determine the angular displacement Δφ as shown in Figure 1C.
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Mixing of the fluid flowing through microchannels is important in a variety of applications: e.g., in the homogenization of solutions of reagents used in chemical reactions, and in the control of dispersion of material along the direction of
Jones et al. proposed a method of controlling the spread of materials along the direction of flow as they are transported in a cylindrical pipe (Poiseuille flow).
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Figure 3D shows the evolution of σ for flows of different Pe in the SHM (open symbols), in a simple channel as in Fig. 3A (▴), and in a channel with straight ridges as in Fig. 3B (•).
The authors measured the variation in fluorescence intensity across the channel cross-section throughout its length and plotted the standard deviation as a function of the channel length. Minimal variation in fluorescence signal (σ values near zero) represents effective mixing. The staggered herringbone induces the most effective mixing because the σ values reach zero within a short distance along the channel.
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- Mar 2022
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chemical reactions
Microfluidic chemical reactors offer advantages such as reduced chemical consumption, high surface-area-to-volume ratios, and improved safety that make them superior to macroscopic reaction settings. These have been implemented in fluorination, tumor drug delivery, and various other applications.
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These stirring flows will reduce the mixing length by decreasing the average distance, Δr, over which diffusion must act in the transverse direction to homogenize unmixed volumes.
The implementation of ridges along the microchannel floor disrupts the flow of fluid, allowing diffusion to act more quickly compared to steady flow down a smooth channel.
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The mixing length in a simple microchannel would be Δym ∼ Pe ×l = 100 cm. On the basis of Fig. 3D, the mixing length in the SHM would be, Δym ∼ 1 cm. Furthermore, increasing the flow speed by a factor of 10 (i.e., toPe = 105) will increase the mixing length in the SHM to Δym ∼ 1.5 cm. With the same change in flow speed, the mixing length in the absence of stirring will increase 10-fold, to Δym ∼ 103 cm.
The SHM demonstrated a shorter mixing length and remained significantly less impacted by an increase in flow speed compared to a simple microchannel.
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lithography
The process of printing a design onto a flat surface using chemical reactions.
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Stokes flow
A form of fluid motion dominated by viscous forces. This occurs at low fluid velocities, high fluid viscosities, or very small length-scales of flow.
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- Feb 2022
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general strategies for controlling flow in microfluidic devices should not depend on inertial effects, because these only become important for
ETS1.A: Defining and Delimiting an Engineering Problem
What is a design for? What are the criteria and constraints of a successful solution?
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The diagrams in Fig. 3, A to C, show the experiments we used to characterize mixing.
ETS1.C: Optimizing the Design Solution
How can the various proposed design solutions be compared and improved?
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15. M. Volpert, I. Mezić, C. D. Meinhart, M. Dahleh, Proceedings of the First International Conference on Heat Transfer, Fluid Mechanics, and Thermodynamics, Kruger Park, South Africa, 2001.
This work lists numerous papers in the field of fluid mechanics and thermodynamics, three of which discuss the use of active mixers in microdevices for applications such as heat transfer mechanisms/analysis and flow cooling in microtechnology.
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12. J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge Univ. Press, Cambridge, 1989).
This book explores fluid mixing from a kinematic viewpoint and provides mechanisms of mixing including stretching and folding that occur in nature and technology.
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This condition is based on the following characteristic values: U < 100 cm/s, l ∼ 0.01 cm, ν = 0.01 g/cm·s. For channels, l is typically taken to be the smallest cross-sectional dimension.
Given these values, the Reynolds number for the microchannel flow described in this work would be less than 100, which indicates laminar flow and dominant viscous forces. It is nearly impossible to generate chaotic flows, which facilitates mixing, in microchannels.
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Losey M. W., Schmidt M. A., Jensen K. F., Ind. Eng. Chem. Res. 40, 2555 (2001).
A microchemical reactor was developed to safely and efficiently fluorinate toluene (a reactive substance found in paint products) as an alternative means to macroscale methods, which could not effectively perform this task.
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The experiments presented in Fig. 4 demonstrate that, by stirring the fluid in the cross section of the flow, the SHM (Fig. 4C) reduces the extent of the initial, rapid broadening of a band of material relative to that in an unstirred flow (Fig. 4B).
In the SHM, mixed fluid spreads less along the channel (Fig 4C) in comparison to the unstirred flow (Fig 4B).
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To quantify the degree of mixing (convection plus diffusion) as a function of the axial distance traveled in the mixer and ofPe, we measure the standard deviation of the intensity distribution in confocal images of the cross section of the flow like those in Fig. 3, A to C: σ = 〈(I − 〈I〉)2〉1/2, whereI is the grayscale value (between 0 and 1) of a pixel, and 〈 〉 means an average over all the pixels in the image. The value of σ is 0.5 for completely segregated streams and 0 for completely mixed streams.
The standard deviation (of fluorescence intensity) is determined by averaging the grayscale value of images taken and used as a metric for the degree of mixing present in each channel. Lower standard deviation values indicate less difference in the intensity values across an image and signify more complete mixing.
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confocal micrographs
Images obtained by confocal microscopy, a fluorescence imaging technique that uses lasers to create a three-dimensional image of a sample
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on the floor of the channel that are easily fabricated with commonly usedmethods of planar lithography
The authors relied on channel design rather than active components to mix fluid in microchannels.
Scientists at the National Research Council of Canada developed a mixing element within a microfluidic device consisting of slanted ridges that cause two separately-flowing fluids to intersect and travel along these ridges, providing efficient mixing of two or more fluids in the device.
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transfers of small volumes (1 to 100 nl) of materials (5).
A nonmechanical pumping mechanism was developed to move nano-liter and pico-liter sized drops of fluid within microchannels. The described system heats one end of a droplet and creates surface tension that causes a pressure difference in the channel, resulting in droplet motion.
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We used soft lithographic methods to make the channels in poly(dimethylsiloxane) (16, 17).
After designing the master mold, an elastic polymer known as polydimethylsiloxane (PDMS) is prepared and poured over it. This substance cures (becomes solid) over a short period of time and is removed from the mold, where it is bonded to a glass cover slip. The channel itself is comprised of the space between the glass surface and the patterned PDMS.
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photolithography
A microfabrication technique that uses photosensitive resin and ultraviolet light to create microscale features and devices.
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The group of Beebe has demonstrated chaotic stirring in a helical microchannel; in this design, stirring occurs as a result of eddies at the bends in the channel in flows of intermediateRe (i.e., Re > 1)
A snake-like channel with repeating C-shaped segments was developed to enhance passive fluid mixing. This design achieved significantly more thorough mixing compared to straight channels and square-wave channels.
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One way to produce a chaotic flow is to subject volumes of fluid to a repeated sequence of rotational and extensional local flows (21). This sequence of local flows is achieved in the SHM by varying the shape of the grooves as a function of axial position in the channel: The change in the orientation of the herringbones between half cycles exchanges the positions of the centers of rotation (local rotational flow, “c” in the Fig. 2A) and the up- and down-wellings (local extensional flow, “u” and “d” in Fig. 2A) in the transverse flow. Figure 2B shows the evolution of two streams through one cycle of the SHM.
To create chaotic flow, the authors inserted angled grooves that change orientation after every half cycle, which is defined as ten ridges of the same pattern. This change in orientation results in rotational flow that passively mixes streams entering the channel.
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To generate transverse flows in microchannels by using a steady axial pressure gradient, we place ridges on the floor of the channel at an oblique angle, θ, with respect to the long axis (ŷ) of the channel (Fig. 1A).
The authors implemented ridges along the bottom of microfluidic channels that extend across the length of the channel, which is labeled here as the y-axis. These ridges are set at an angle to the y-axis such that fluid flows in a rotational manner as it passes over them.
As a result, the fluid circles back on itself as it flows through the ridged channel and promotes steady mixing.
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Electroosmotic
Pertaining to the flow of fluid caused by an applied voltage across a membrane, microchannel, or porous material.
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anisotropic
Possessing a different property depending on the direction of the material.
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uniaxial
Pertaining to a single direction.
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laminar
Characterized by flow in which fluid moves smoothly along a path.
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Reynolds number
A ratio of the internal forces to the viscous forces in a fluid. A low Reynolds number indicates stronger viscous force and smoother (laminar) flow, whereas a high Reynolds number indicates greater internal forces and irregular (turbulent) flow.
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Maxwell pressure,
When a voltage between compliant electrodes causes pressure to arise, consequently causing compression of the elastomer as it expands in the plane.
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