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Predicting the behavior of microfluidic circuits made from discrete elements

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Abstract

Microfluidic devices can be used to execute a variety of continuous flow analytical and synthetic chemistry protocols with a great degree of precision. The growing availability of additive manufacturing has enabled the design of microfluidic devices with new functionality and complexity. However, these devices are prone to larger manufacturing variation than is typical of those made with micromachining or soft lithography. In this report, we demonstrate a design-for-manufacturing workflow that addresses performance variation at the microfluidic element and circuit level, in context of mass-manufacturing and additive manufacturing. Our approach relies on discrete microfluidic elements that are characterized by their terminal hydraulic resistance and associated tolerance. Network analysis is employed to construct simple analytical design rules for model microfluidic circuits. Monte Carlo analysis is employed at both the individual element and circuit level to establish expected performance metrics for several specific circuit configurations. A protocol based on osmometry is used to experimentally probe mixing behavior in circuits in order to validate these approaches. The overall workflow is applied to two application circuits with immediate use at on the bench-top: series and parallel mixing circuits that are modularly programmable, virtually predictable, highly precise, and operable by hand.

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... Both lamination and chaotic advection ultimately require the construction of multi-layer channel devices with three-dimensional features, a significant challenge for microfabrication technologies. Previously, we introduced a system of discrete elements for assembling three-dimensional microfluidic circuits with integrated process sensors [13][14][15][16]. We leveraged additive manufacturing techniques (i.e. ...
... Stereolithography enables the facile routing of microfluidic channels in three dimensions, but has much larger manufacturing tolerance than traditional micromachining. For example, in the processes used to construct devices presented in this report, tolerances can be as high as 30 µm, whereas micro CNC tolerances are often < 5 µm and semiconductor processing tolerances are submicron [14]. Variation in channel sizes in discrete microfluidic elements directly propagate fluid handling performance errors, implying the need for simple and versatile empirical device characterization methods. ...
... In designing discrete element microfluidics, two hydraulic terminal characteristics are of importance to designers: resistance to flow [13,14,17] and resident volume. The inherently parallel arrangement of the microfluidic network within both L1 and L2 elements implies that their hydraulic resistance is of minimum consequence to most networks of interest. ...
Preprint
3D printing facilitates the straightforward construction of microchannels with complex three-dimensional architectures. Here, we demonstrate 3D-printed modular mixing components that operate on the basis of splitting and recombining fluid streams to decrease interstream diffusion length. These are compared to helical mixers that operate on the principle of chaotic advection.
... Adaptation of the units presented in Section 2.1 to the building block concept introduced by Rhee and Burns (2008), Langelier et al. (2011) and Vittayarukskul and Lee (2017) would further increase the flexibility and potential of the modules as part of a multi-use "plug-andplay" platform. Fig. 8 presents another example of a modular microfluidic concept (Bhargava et al., 2015), based on 3D printed modules, which is compatible with a non-planar microfluidic circuit assembly (Bhargava et al., 2014). Another 3D printed modular-based microfluidic platform has been developed by Morgan et al. (2016). ...
... Additionally, modules to control backpressure in the pumps, or allowing pressure equalization along the module assembly can be integrated. Moreover, as demonstrated by Bhargava et al. (2014Bhargava et al. ( , 2015, for most current applications in microfluidics (incompressible flows and low Reynolds numbers), the hydraulic characteristics (especially pressure loss and obtained flow rates) of a given system can be estimated using the Kirchoff's Laws which are usually applied to electronic circuits. Coupling the electronic circuit analogy with statistical analysis methods, different fluidic networks were simulated where an expected manufacturing variation from design (calculated from knowledge both on the fabrication technique and hydraulic resistance tolerances of the developed modules) was taken into account for each of the different discrete A.C. Fernandes et al. ...
... Coupling the electronic circuit analogy with statistical analysis methods, different fluidic networks were simulated where an expected manufacturing variation from design (calculated from knowledge both on the fabrication technique and hydraulic resistance tolerances of the developed modules) was taken into account for each of the different discrete A.C. Fernandes et al. Biotechnology Advances 36 (2018) 1341-1366 passive elements developed by Bhargava et al. (Bhargava et al., 2015). In this sense, it is also relevant to highlight the importance of applying mathematical modeling and fluid dynamic simulation to the first stage of development of individual fluidic parts (Wu and Gu, 2011b). ...
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... Both lamination and chaotic advection ultimately require the construction of multi-layer channel devices with three-dimensional features, a significant challenge for microfabrication technologies. Previously, we introduced a system of discrete elements for assembling three-dimensional microfluidic circuits with integrated process sensors [13][14][15][16]. We leveraged additive manufacturing techniques (i.e., "3D printing") to achieve device designs with sophisticated interior architectures and create a system of interconnects based on self-aligned interference fits. ...
... Two variations of our laminator discrete element were designed and manufactured using stereolithography [13][14][15][16], as seen in Figure 1. In the first device, dubbed "L1" throughout this report (Figure 1a), a co-flow of two laminated miscible fluid streams is introduced into the element from a single inlet, split into separate channels such that each fluid stream is isolated, split again individually to duplicate each isolated flow, and merged in the outlet channel in an interdigitated fashion. ...
... Stereolithography enables the facile routing of microfluidic channels in three dimensions, but has much larger manufacturing tolerance than traditional micromachining. For example, in the processes used to construct devices presented in this report, tolerances can be as high as 30 µm, whereas micro CNC tolerances are often <5 µm and semiconductor processing tolerances are submicron [14]. Variation in channel sizes in discrete microfluidic elements directly propagates fluid handling performance errors, implying the need for simple and versatile empirical device characterization methods. ...
Article
Full-text available
3D printing facilitates the straightforward construction of microchannels with complex three-dimensional architectures. Here, we demonstrate 3D-printed modular mixing components that operate on the basis of splitting and recombining fluid streams to decrease interstream diffusion length. These are compared to helical mixers that operate on the principle of chaotic advection.
... These devices require specialized thin-film manufacturing practices such as micromachining that are costly and limit their format to planar design, making them better suited as instruments for purely analytical activities (e.g., microcalorimetery). Previously, we demonstrated a standardized system of modular, reconfigurable discrete microfluidic elements useful for constructing three-dimensional circuits [27,28]. Briefly, we constructed a library of components using stereolithography that perform simple functions in microfluidic transport and measurement. ...
... In microfluidic channels, substantial hydraulic resistances relative to macroscopic, traditional channels may also result in the generation of heat from viscous, laminar flows. These values are often in the MPa@BULLETs/m 3 to GPa@BULLETs/m 3 range, and for typical pressure-driven flow conditions they often result in a Reynold's Number less than 0.1 [27][28][29]. For a device such as that shown in Figure 2to achieve a steady-state measured temperature ( ), a balance between heat generated due to self-heating of the thermistor and microchannels and heat dissipated by the circuit overall must be established. ...
... In microfluidic channels, substantial hydraulic resistances R hyd relative to macroscopic, traditional channels may also result in the generation of heat from viscous, laminar flows. These values are often in the MPa¨s/m 3 to GPa¨s/m 3 range, and for typical pressure-driven flow conditions they often result in a Reynold's Number less than 0.1 [27][28][29]. For a device such as that shown in Figure 2to achieve a steady-state measured temperature (T m ), a balance between heat generated due to self-heating of the thermistor and microchannels and heat dissipated by the circuit overall must be established. ...
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Full-text available
A discrete microfluidic element with integrated thermal sensor was fabricated and demonstrated as an effective probe for process monitoring and prototyping. Elements were constructed using stereolithography and market-available glass-bodied thermistors within the modular, standardized framework of previous discrete microfluidic elements demonstrated in the literature. Flow rate-dependent response due to sensor self-heating and microchannel heating and cooling was characterized and shown to be linear in typical laboratory conditions. An acid-base neutralization reaction was performed in a continuous flow setting to demonstrate applicability in process management: the ratio of solution flow rates was varied to locate the equivalence point in a titration, closely matching expected results. This element potentially enables complex, three-dimensional microfluidic architectures with real-time temperature feedback and flow rate sensing, without application specificity or restriction to planar channel routing formats.
... The resistance of irregular elements such as the microfluidic traps can be estimated via the numerical simulations [34] or measurements [35,36]. The numerical simulations seem to be a most convenient tool, however, it is often very difficult to include all imperfections of the fabrication procedure as well as the material properties [34]. ...
... The resistance of irregular elements such as the microfluidic traps can be estimated via the numerical simulations [34] or measurements [35,36]. The numerical simulations seem to be a most convenient tool, however, it is often very difficult to include all imperfections of the fabrication procedure as well as the material properties [34]. Hence the measurements of the hydraulic resistance of irregular elements are of high importance. ...
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... Previously, we have demonstrated initiated chemical vapor deposition (iCVD) as a useful process for coating discrete microfluidic elements fabricated using stereolithography (SLA) (Bhargava et al. 2014) as well as traditional microfluidic devices fabricated using soft lithography (PDMS) . Vapor-phase coating has limitations with post-assembly process workflows due to the distance that vapor can diffuse into microchannels; this inherently limits the size and complexity of devices to which this technique can be applied (Bhargava et al. 2015). Here, however, we assemble devices from SLAfabricated discrete elements. ...
... By creating a library of elements with different surface chemistries, we introduce surface functionality as a selectable control parameter for device construction. This allows users to reimagine the type and amount of systems that can be quickly assembled, with deep understanding as to the performance of terminal characteristics (Bhargava et al. 2015). In this communication, we demonstrate microfluidic circuits with abrupt changes in surface wettability through the use of discrete microfluidic elements with hydrophobic and hydrophilic iCVD coatings. ...
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Microfluidic device fabrication has classically utilized methods that have limited devices to specific applications. More recently, discrete microfluidic elements have reimagined the design process of microfluidic device fabrication to that of building blocks that can be constructed in various forms to produce devices of many applications. Here, surface modification of discrete microfluidic elements via initiated chemical vapor deposition is demonstrated. Coated modular elements can quickly assemble to form complex 2-D or 3-D structures with step-like surface energy gradients for applications requiring discrete control of channel surface wettability. This platform is applied toward the generation of double emulsions to show the ease of design and manufacturing over existing methods developed to manage two-phase flows.
... Bhargava et al. demonstrated an approach to microfluidic device design based on discrete elements. These components were connected by a convex block embedded in a concave block to complete the assembly of the entire microfluidic system [7][8][9]. The aforementioned microfluidic devices were adopted self-aligning structures for attaining the interblock sealing at block junctions. ...
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... Due to its convenience, this methodology is very commonly applied in microfluidics (Oh et al. 2012), e.g.: in the design of concentration-dependent microfluidic networks (Dertinger et al. 2001;Yamada et al. 2006;Lee et al. 2009Lee et al. , 2010, prediction of flow distribution in hierarchical networks (Hulme et al. 2007) design of systems built with combinations of discrete 3D modules (Bhargava et al. 2015), investigation of systems for filtering particles (Stiles et al. 2005), analysis of hydrodynamic trapping of droplets (Bithi and Vanapalli 2010;Korczyk et al. 2013;Zaremba et al. 2018), prediction of flow of droplets in microfluidics networks (Engl et al. 2005;Fuerstman et al. 2007;Cybulski et al. 2015Cybulski et al. , 2019Zaremba et al. 2019), description of formation of droplets in microfluidic systems (van Steijn et al. 2013;Korczyk et al. 2019) and the generation of concentration gradation in droplets (Wegrzyn et al. 2012). ...
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... 4 For example, inherent variations in both conventional and soft lithographic fabrication methods introduce discrepancies and variations between microfluidic device sets. 7,8 The use of machine learning can help achieve consistent operation between different devices, reducing manual intervention and ensuring consistency in information quality. More importantly, by their very nature microfluidic systems have characteristics that vary with time. ...
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... 1-5 The capability to perform rapid design troubleshooting and fabricate monolithic devices without any need of assembly processes is a convincing reason towards a wider adoption of additive manufacturing in the Lab-on-a-Chip field. [6][7][8][9][10][11] In this regard, biocompatibility of currently available 3D printed polymers is critical for any biological and biomedical applications. 10,11 Bioassays on living cells and tissues are conducted in aqueous media. ...
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We have devised a microfluidic mixer design that produces all the mixture combinations of a given number of dilutions of the input compounds. As proof of the concept, we present a device that generates four titrations of two dye solutions, blue and yellow, and combinatorially mixes the blue titrations with the yellow titrations to deliver the sixteen mixture combinations in separate outlet microchannels. Our device features four different flow levels made by stacking nine laser-cut Mylar laminates. The fluidic network has a symmetric design that guarantees that the flow rates are the same at all the outlets, with deviations attributable to imperfections in the fabrication, assembly, or perfusion processes. Design rules for scaling up the number of compounds and/or dilutions are presented. The mixing scheme has broad applicability in high-throughput combinatorial testing applications such as drug screening, cell-based biochemical assays, lab-on-a-chip devices, and biosensors.
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Implementations of Lab-on-a-Chip technologies for in-situ analysis of small model organisms and embryos (both invertebrate and vertebrate) are attracting an increasing interest. A significant hurdle to widespread applications of microfluidic and millifluidic devices for in-situ analysis of small model organisms is the access to expensive clean room facilities and complex microfabrication technologies. Furthermore, these resources require significant investments and engineering know-how. For example, poly(dimethylsiloxane) soft lithography is still largely unattainable to the gross majority of biomedical laboratories willing to pursue development of chip-based platforms. They often turn instead to readily available but inferior classical solutions. We refer to this phenomenon as workshop-to-bench gap of bioengineering science. To tackle the above issues, we examined the capabilities of commercially available Multi-Jet Modelling (MJM) and Stereolithography (SLA) systems for low volume fabrication of optical-grade millifluidic devices designed for culture and biotests performed on millimetre-sized specimens such as zebrafish embryos. The selected 3D printing technologies spanned a range from affordable personal desktop systems to high-end professional printers. The main motivation of our work was to pave the way for off-the-shelf and user-friendly 3D printing methods in order to rapidly and inexpensively build optical-grade millifluidic devices for customized studies on small model organisms. Compared with other rapid prototyping technologies such as soft lithography and infrared laser micromachining in poly(methyl methacrylate), we demonstrate that selected SLA technologies can achieve user-friendly and rapid production of prototypes, superior feature reproduction quality, and comparable levels of optical transparency. A caution need to be, however, exercised as majority of tested SLA and MJM resins were found toxic and caused significant developmental abnormalities in zebrafish embryos. Taken together, our data demonstrate that SLA technologies can be used for rapid and accurate production of devices for biomedical research. However, polymer biotoxicity needs to be carefully evaluated.
Article
Microfluidic systems are rapidly becoming commonplace tools for high-precision materials synthesis, biochemical sample preparation, and biophysical analysis. Typically, microfluidic systems are constructed in monolithic form by means of microfabrication and, increasingly, by additive techniques. These methods restrict the design and assembly of truly complex systems by placing unnecessary emphasis on complete functional integration of operational elements in a planar environment. Here, we present a solution based on discrete elements that liberates designers to build large-scale microfluidic systems in three dimensions that are modular, diverse, and predictable by simple network analysis techniques. We develop a sample library of standardized components and connectors manufactured using stereolithography. We predict and validate the flow characteristics of these individual components to design and construct a tunable concentration gradient generator with a scalable number of parallel outputs. We show that these systems are rapidly reconfigurable by constructing three variations of a device for generating monodisperse microdroplets in two distinct size regimes and in a high-throughput mode by simple replacement of emulsifier subcircuits. Finally, we demonstrate the capability for active process monitoring by constructing an optical sensing element for detecting water droplets in a fluorocarbon stream and quantifying their size and frequency. By moving away from large-scale integration toward standardized discrete elements, we demonstrate the potential to reduce the practice of designing and assembling complex 3D microfluidic circuits to a methodology comparable to that found in the electronics industry.
Article
This work demonstrates that pressure-driven flow in a microfluidic network can solve mazelike problems by exploring all possible solutions in a parallel fashion. Microfluidic networks can be fabricated easily by soft lithography and rapid prototyping. To find the best path between the inlet and the outlet of these networks, the channels are filled with a fluid, and the path of a second, dyed fluid moving under pressure-driven flow is traced from the inlet to the outlet. Varying the viscosities of these fluids allows the behavior of the system to be tailored. For example, filling the channels with immiscible fluids of different viscosities enhances the resolution of paths of different fluidic resistances.
Article
Microfabricated devices for parallel and serial mixing of fluids are demonstrated. To simplify the voltage control hardware, electrokinetic mixing is effected using a single voltage source with the channels dimensioned to perform the desired voltage division. In addition, the number of fluid reservoirs is reduced by terminating multiple buffer, sample, or analysis channels in single reservoirs. The parallel mixing device is designed with a series of independent T-intersections, and the serial mixing device is based on an array of cross intersections and sample shunting. These devices were tested by mixing a sample with buffer in a dilution experiment. Sample fractions of 1.0, 0.84, 0.67, 0.51, 0.36, 0.19, and 0 were generated for the parallel mixing device, and sample fractions of 1.0, 0.36, 0.21, 0.12, and 0.06 for the serial mixing device.
Article
This paper describes the generation of gradients having complex shapes in solution using microfluidic networks. Flowing multiple streams of fluid each carrying different concentrations of substances laminarly and side-by-side generated step concentration gradients perpendicular to the direction of the flow. Appropriately designed networks of microchannels for controlled diffusive mixing of substances generated a range of shapes for the gradients, including linear, parabolic, and periodic. The lateral dimensions of the gradients ranged from 900 to 2200 μm. This paper also demonstrates the generation of overlapping gradients composed of different species. Since solutions in the microfluidic network exist as steady states and are continuously renewed, the gradients established in the capillaries are spatially and temporally constant and can be maintained easily for periods of hours. Using laminar flow to generate gradients should be useful in both biological and nonbiological research.
Article
A fundamental challenge in the design of microfluidic devices lies in the need to control the transport of fluid according to complex patterns in space and time, and with sufficient accuracy. Although strategies based on externally actuated valves have enabled marked breakthroughs in chip-based analysis, this requires significant off-chip hardware, such as vacuum pumps and switching solenoids, which strongly tethers such devices to laboratory environments. Severing the microfluidic chip from this off-chip hardware would enable a new generation of devices that place the power of microfluidics in a broader range of disciplines. For example, complete on-chip flow control would empower highly portable microfluidic tools for diagnostics, forensics, environmental analysis and food safety, and be particularly useful in field settings where infrastructure is limited. Here, we demonstrate an elegantly simple strategy for flow control: fluidic networks with embedded deformable features are shown to transport fluid selectively in response to the frequency of a time-modulated pressure source. Distinct fluidic flow patterns are activated through the dynamic control of a single pressure input, akin to the analog responses of passive electrical circuits composed of resistors, capacitors and diodes.
Article
We present a microfluidic parallel circuit that directly compares the test channel of an unknown hydraulic resistance with the reference channel with a known resistance, thereby measuring the unknown resistance without any measurement setup, such as standard pressure gauges. Many of microfluidic applications require the precise transport of fluid along a channel network with complex patterns. Therefore, it is important to accurately characterize and measure the hydraulic resistance of each channel segment, and determines whether the device principle works well. However, there is no fluidic device that includes features, such as the ability to diagnose microfluidic problems by measuring the hydraulic resistance of a microfluidic component in microscales. To address the above need, we demonstrate a simple strategy to measure an unknown hydraulic resistance, by characterizing the hydraulic resistance of microchannels with different widths and defining an equivalent linear channel of a microchannel with repeated patterns of a sudden contraction and expansion.
Article
The study of cellular responses to chemical gradients in vitro would greatly benefit from experimental systems that can generate precise and stable gradients comparable to chemical nonhomogeneities occurring in vivo. Recently, microfluidic devices have been demonstrated for linear gradient generation for biological applications with unmatched accuracy and stability. However, no systematic approach exists at this time for generating other gradients of target spatial configuration. Here we demonstrate experimentally and provide mathematical proof for a systematic approach to generating stable gradients of any profile by the controlled mixing of two starting solutions.
Article
In this paper, we propose a serial dilution microfluidic chip which is able to generate logarithmic or linear step-wise concentrations. These concentrations were generated via adjustments in the flow rate of two converging fluids at the channel junctions of the ladder network. The desired dilution ratios are almost independent of the flow rate or diffusion length of molecules, as the dilution device is influenced only by the ratio of volumetric flow rates. Given a set of necessary dilution ratios, whether linear or logarithmic, a serial dilution chip can be constructed via the modification of a microfluidic resistance network. The design principle was suggested and both the logarithmic and linear dilution chips were fabricated in order to verify their performance in accordance with the fluorescence intensity. The diluted concentrations of a fluorescein solution in the microfluidic device evidenced relatively high linearity, and the cytotoxicity test of MCF-7 breast cancer cells via the logarithmic dilution chip was generally consistent with the results generated with manual dilution.
Theoretical microfluidics
  • H Bruus
Bruus, H. Theoretical microfluidics (Oxford University Press, Oxford, 2008).