# Design Optimization of Centrifugal Microfluidic “Lab-on-a-Disc” Systems towards Fluidic Larger-Scale Integration

## Abstract

**:**

## 1. Introduction

## 2. Rotational Flow Control

#### 2.1. Pressures

#### 2.2. Critical Spin Rate

#### 2.3. Example: Centrifugo-Pneumatic Siphon Valves

#### 2.4. Operational Robustness

#### 2.5. Laboratory Unit Operations

## 3. Design Optimization

#### 3.1. Multiplexing

#### 3.2. Parameter Space

#### 3.3. Performance Metrics & Design Criteria

#### 3.3.1. Band Width

#### 3.3.2. Refined Geometry

#### 3.3.3. Retention Rate and Field Strength

#### 3.3.4. Concurrent Valving

#### 3.3.5. Radial Space

#### 3.3.6. Spatial Footprint

#### 3.3.7. Definition of Liquid Volumes

#### 3.3.8. Ambient Pressure

#### 3.3.9. Manufacturing-Process Limitations and Costs

#### 3.3.10. Multi-Parameter Optimization

#### 3.3.11. General Design Guidelines

## 4. Summary and Outlook

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Default Valve Geometry

**Table A1.**Default geometrical parameters and relationships of basic CP-DF siphon valves (Figure 1). The resulting critical spin rate $\mathsf{\Omega}\left(R,\mathsf{\Gamma},{U}_{0}\right)/2\pi \approx 25\mathrm{Hz}$ Minimum lateral dimensions are given by the smallest practical diameter of milling tools (200 µm). As tools for injection molding are often adopted from optical data storage (e.g., CD, DVD, Blu-ray), a central, 1.5-cm diameter hole and a disc radius of 6 cm with thickness around 1.2 mm, fluidic structures $\mathsf{\Gamma}$ may need to stay within the radial interval between ${R}_{\mathrm{min}}=1.5\mathrm{cm}$ and ${\mathrm{R}}_{\mathrm{max}}=5.5\mathrm{cm}$, and an upper limit for the depth of about 1 mm as chosen for the main parts of geometries $\mathsf{\Gamma}$. For large lateral extensions or small aspect ratios, sagging of the lid, which is often provided by a rather flexible foil, may significantly alter the nominal volume capacity, also in response to the pressure, and might even lead to sticking to the bottom of the cavity.

$R=3\mathrm{cm}$ | ${R}_{\mathrm{min}}=1.5\mathrm{cm}$ | ${R}_{\mathrm{max}}=5.5\mathrm{cm}$ | ${R}_{\mathrm{DF}}=3.15\mathrm{cm}R$ |

${A}_{0}={d}_{0}\xb7{w}_{0}$ | ${d}_{0}=1\mathrm{mm}$ | ${w}_{0}=5\mathrm{mm}$ | |

${U}_{0}=100\mathsf{\mu}\mathrm{L}{A}_{0}\xb7\left(R-{R}_{\mathrm{min}}\right)$ | |||

${U}_{\mathrm{iso}}={d}_{0}\xb7h\xb7L\ll {U}_{0}$ | ${d}_{\mathrm{iso}}=1\mathrm{mm}$ | ${h}_{\mathrm{iso}}=1\mathrm{mm}$ | ${L}_{\mathrm{iso}}=15\mathrm{mm}{w}_{0}+w$ |

${U}_{Z}=d\xb7w\xb7Z$ | $d=500\mathsf{\mu}\mathrm{m}$ | $w=800\mathsf{\mu}\mathrm{m}\ll {w}_{0}$ | $Z=10\mathrm{mm}$ |

${V}_{\mathrm{C},0}={d}_{\mathrm{C}}\xb7{w}_{\mathrm{C}}\xb7{h}_{\mathrm{C}}\gg {U}_{Z}$ | ${d}_{\mathrm{C}}=1\mathrm{mm}$ | ${w}_{\mathrm{C}}=20\mathrm{mm}$ | ${h}_{\mathrm{C}}=10\mathrm{mm}$ |

${V}_{\mathrm{int}}={d}_{\mathrm{int}}\xb7{h}_{\mathrm{int}}\xb7{L}_{\mathrm{int}}\ll {V}_{\mathrm{C}}$ | ${d}_{\mathrm{int}}=200\mathsf{\mu}\mathrm{m}$ | ${h}_{\mathrm{int}}=300\mathsf{\mu}\mathrm{m}$ | ${L}_{\mathrm{int}}=1\mathrm{cm}2w$ |

${V}_{\mathrm{DF}}=0.25\pi \xb7{d}_{\mathrm{DF}}\xb7{D}_{\mathrm{DF}}^{2}\ll {V}_{\mathrm{C}}$ | ${d}_{\mathrm{DF}}=190\mathsf{\mu}\mathrm{m}$ | ${D}_{\mathrm{DF}}=3\mathrm{mm}$ | $\alpha =0.45,\beta =0.5$ |

- Lateral structuring $\mathsf{\Delta}w=\mathsf{\Delta}h=20\mathsf{\mu}\mathrm{m}$;
- Vertical structuring $\mathsf{\Delta}d=30\mathsf{\mu}\mathrm{m}$;
- Precision of liquid volume $\mathsf{\Delta}{U}_{0}/{U}_{0}=1\%$;
- Ambient pressure $\mathsf{\Delta}{p}_{0}=40\mathrm{hPa}$.

#### Appendix A.2. Computation of Results

## References

- Manz, A.; Graber, N.; Widmer, H.Á. Miniaturized total chemical analysis systems: A novel concept for chemical sensing. Sens. Actuators B Chem.
**1990**, 1, 244–248. [Google Scholar] [CrossRef] - Reyes, D.R.; Iossifidis, D.; Auroux, P.A.; Manz, A. Micro total analysis systems. 1. introduction, theory, and technology. Anal. Chem.
**2002**, 74, 2623–2636. [Google Scholar] [CrossRef] [PubMed] - Auroux, P.A.; Iossifidis, D.; Reyes, D.R.; Manz, A. Micro total analysis systems. 2. analytical standard operations and applications. Anal. Chem.
**2002**, 74, 2637–2652. [Google Scholar] [CrossRef] [PubMed] - Whitesides, G.M. The origins and the future of microfluidics. Nature
**2006**, 442, 368–373. [Google Scholar] [CrossRef] [PubMed] - Craighead, H. Future lab-on-a-chip technologies for interrogating individual molecules. Nature
**2006**, 442, 387–393. [Google Scholar] [CrossRef] - Jamil, E.A.; Sorger, P.K.; Jensen, K.F. Cells on chips. Nature
**2006**, 442, 403–411. [Google Scholar] [CrossRef] - Janasek, D.; Franzke, J.; Manz, A. Scaling and the design of miniaturized chemical-analysis systems. Nature
**2006**, 442, 374–380. [Google Scholar] [CrossRef] - Schembri, C.T.; Ostoich, V.; Lingane, P.J.; Burd, T.L.; Buhl, S.N. Portable simultaneous multiple analyte whole-blood analyzer for point-of-care testing. Clin. Chem.
**1992**, 38, 1665–1670. [Google Scholar] [CrossRef] - Schembri, C.T.; Burd, T.L.; Kopf-Sill, A.R.; Shea, L.R.; Braynin, B. Centrifugation and capillarity integrated into a multiple analyte whole-blood analyzer. J. Autom. Chem.
**1995**, 17, 99–104. [Google Scholar] [CrossRef] - Abaxis (Piccolo Express). Available online: https://www.abaxis.com (accessed on 14 June 2021).
- Andersson, P.; Jesson, G.; Kylberg, G.; Ekstrand, G.; Thorsén, G. Parallel nanoliter microfluidic analysis system. Anal. Chem.
**2007**, 79, 4022–4030. [Google Scholar] [CrossRef] [Green Version] - Inganas, M.; Derand, H.; Eckersten, A.; Ekstrand, G.; Honerud, A.K.; Jesson, G.; Thorsen, G.; Soderman, T.; Andersson, P. Integrated microfluidic compact disc device with potential use in both centralized and point-of-care laboratory settings. Clin. Chem.
**2005**, 51, 1985–1987. [Google Scholar] [CrossRef] [PubMed] - Gyros Protein Technologies. Available online: https://www.gyrosproteintechnologies.com(accessed on 14 June 2021).
- Madou, M.J.; Kellogg, G.J. The LabCD (TM): A centrifuge-based microfluidic platform for diagnostics. In Systems and Technologies for Clinical Diagnostics and Drug Discovery; International Society for Optics and Photonics: Bellingham, DC, USA, 1998; Volume 3259, pp. 80–93. [Google Scholar] [CrossRef]
- Shea, M. ADMET assays on tecan’s labCD-ADMET system. J. Assoc. Lab. Autom.
**2003**, 8, 74–77. [Google Scholar] [CrossRef] - Smith, S.; Mager, D.; Perebikovsky, A.; Shamloo, E.; Kinahan, D.; Mishra, R.; Delgado, S.M.T.; Kido, H.; Saha, S.; Ducrée, J.; et al. CD-based microfluidics for primary care in extreme point-of-care settings. Micromachines
**2016**, 7, 22. [Google Scholar] [CrossRef] [Green Version] - Kong, L.X.; Perebikovsky, A.; Moebius, J.; Kulinsky, L.; Madou, M. Lab-on-a-CD: A fully integrated molecular diagnostic system. J. Assoc. Lab. Autom.
**2016**, . 21, 323–355. [Google Scholar] [CrossRef] [Green Version] - Maguire, I.; O’Kennedy, R.; Ducrée, J.; Regan, F. A review of centrifugal microfluidics in environmental monitoring. Anal. Methods
**2018**, 10, 1497–1515. [Google Scholar] [CrossRef] - Gorkin, R.; Park, J.; Siegrist, J.; Amasia, M.; Lee, B.S.; Park, J.M.; Kim, J.; Kim, H.; Madou, M.; Cho, Y.K. Centrifugal microfluidics for biomedical applications. Lab Chip
**2010**, 10, 1758–1773. [Google Scholar] [CrossRef] [Green Version] - Burger, R.; Amato, L.; Boisen, A. Detection methods for centrifugal microfluidic platforms. Biosens. Bioelectron.
**2016**, 76, 54–67. [Google Scholar] [CrossRef] - Ducrée, J.; Haeberle, S.; Lutz, S.; Pausch, S.; von Stetten, F.; Zengerle, R. The centrifugal microfluidic Bio-Disk platform. J. Micromech. Microeng.
**2007**, 17, S103–S115. [Google Scholar] [CrossRef] - Lutz, S.; Mark, D.; Roth, G.; Zengerle, R.; von Stetten, F. Centrifugal microfluidic platforms for molecular diagnostics. Clin. Chem. Lab. Med.
**2011**, 49, S608. [Google Scholar] - Tang, M.; Wang, G.; Kong, S.-K.; Ho, H.-P. A review of biomedical centrifugal microfluidic platforms. Micromachines
**2016**, 7, 26. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Duffy, D.C.; Gillis, H.L.; Lin, J.; Sheppard, N.F.; Kellogg, G.J. Microfabricated centrifugal microfluidic systems: Characterization and multiple enzymatic assays. Anal. Chem.
**1999**, 71, 4669–4678. [Google Scholar] [CrossRef] - Azimi-Boulali, J.; Madadelahi, M.; Madou, M.J.; Martinez-Chapa, S.O. Droplet and particle generation on centrifugal microfluidic platforms: A review. Micromachines
**2020**, 11, 603. [Google Scholar] [CrossRef] [PubMed] - Strohmeier, O.; Keller, M.; Schwemmer, F.; Zehnle, S.; Mark, D.; von Stetten, F.; Zengerle, R.; Paust, N. Centrifugal microfluidic platforms: Advanced unit operations and applications. Chem. Soc. Rev.
**2015**, 44, 6187–6229. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Aeinehvand, M.M.; Magaña, P.; Aeinehvand, M.S.; Aguilar, O.; Madou, M.J.; Martinez-Chapa, S.O. Ultra-rapid and low-cost fabrication of centrifugal microfluidic platforms with active mechanical valves. Rsc. Adv.
**2017**, 7, 55400–55407. [Google Scholar] [CrossRef] - Aeinehvand, M.M.; Weber, L.; Jiménez, M.; Palermo, A.; Bauer, M.; Loeffler, F.F.; Ibrahim, F.; Breitling, F.; Korvink, J.; Madou, M.; et al. Elastic reversible valves on centrifugal microfluidic platforms. Lab Chip
**2019**, 19, 1090–1100. [Google Scholar] [CrossRef] - Hess, J.F.; Zehnle, S.; Juelg, P.; Hutzenlaub, T.; Zengerle, R.; Paust, N. Review on pneumatic operations in centrifugal microfluidics. Lab Chip
**2019**, 19, 3745–3770. [Google Scholar] [CrossRef] [PubMed] - Nguyen, H.V.; Nguyen, V.D.; Nguyen, H.Q.; Chau, T.H.T.; Lee, E.Y.; Seo, T.S. Nucleic acid diagnostics on the total integrated lab-on-a-disc for point-of-care testing. Biosens. Bioelectron.
**2019**, 141. [Google Scholar] [CrossRef] - Rombach, M.; Hin, S.; Specht, M.; Johannsen, B.; Lüddecke, J.; Paust, N.; Zengerle, R.; Roux, L.; Sutcliffe, T.; Peham, J.R.; et al. RespiDisk: A point-of-care platform for fully automated detection of respiratory tract infection pathogens in clinical samples. Analyst
**2020**, 145, 7040–7047. [Google Scholar] [CrossRef] - Homann, A.R.; Niebling, L.; Zehnle, S.; Beutler, M.; Delamotte, L.; Rothmund, M.-C.; Czurratis, D.; Beller, K.-D.; Zengerle, R.; Hoffmann, H.; et al. A microfluidic cartridge for fast and accurate diagnosis of Mycobacterium tuberculosis infections on standard laboratory equipment. Lab Chip
**2021**, 21, 1540–1548. [Google Scholar] [CrossRef] - Madadelahi, M.; Acosta-Soto, L.F.; Hosseini, S.; Martinez-Chapa, S.O.; Madou, M.J. Mathematical modeling and computational analysis of centrifugal microfluidic platforms: A review. Lab Chip
**2020**, 20, 1318–1357. [Google Scholar] [CrossRef] - Miyazaki, C.M.; Carthy, E.; Kinahan, D.J. Biosensing on the centrifugal microfluidic Lab-on-a-Disc platform. Processes
**2020**, 8, 1360. [Google Scholar] [CrossRef] - Mian , A.; Kieffer-Higgins, S.G.; Corey , G.D. Devices and Methods for Using Centripetal Acceleration to Drive Fluid Movement in a Microfluidics System. Patent No. US6319469B1, 18 December 1996. [Google Scholar]
- Burstein Technologies, Inc. [archived]. Available online: https://web.archive.org/web/20061209052345/http://www.bursteintechnologies.com (accessed on 31 May 2021).
- Biosurfit, SA. Available online: https://www.biosurfit.com (accessed on 14 June 2021).
- Spindiag GmbH. Available online: http://www.spindiag.de (accessed on 14 June 2021).
- RotaPrep Inc. Available online: https://rotaprep.com/ (accessed on 19 April 2021).
- LaMotte Chemical Products, Co. Available online: https://www.lamotte.com (accessed on 14 June 2021).
- Radisens Diagnostics. Available online: http://www.radisens.com (accessed on 14 June 2021).
- Blusense Diagnostics. Available online: https://blusense-diagnostics.com (accessed on 14 June 2021).
- SpinX Technologies. Available online: https://web.archive.org/web/20040414090409/http://www.spinx-technologies.com (accessed on 14 June 2021).
- Clime, L.; Daoud, J.; Brassard, D.; Malic, L.; Geissler, M.; Veres, T. Active pumping and control of flows in centrifugal microfluidics. Microfluid. Nanofluid.
**2019**, 23, 29. [Google Scholar] [CrossRef] - Brassard, D.; Geissler, M.; Descarreaux, M.; Tremblay, D.; Daoud, J.; Clime, L.; Mounier, M.; Charlebois, D.; Veres, T. Extraction of nucleic acids from blood: Unveiling the potential of active pneumatic pumping in centrifugal microfluidics for integration and automation of sample preparation processes. Lab Chip
**2019**, 19, 1941–1952. [Google Scholar] [CrossRef] [PubMed] - Abi-Samra, K.; Hanson, R.; Madou, M.; Gorkin, R.A. Infrared controlled waxes for liquid handling and storage on a CD-microfluidic platform. Lab Chip
**2011**, 11, 723–726. [Google Scholar] [CrossRef] - Kong, L.X.; Parate, K.; Abi-Samra, K.; Madou, M. Multifunctional wax valves for liquid handling and incubation on a microfluidic CD. Microfluid. Nanofluid.
**2015**, 18, 1031–1037. [Google Scholar] [CrossRef] - Torres Delgado, S.M.; Kinahan, D.J.; Nirupa Julius, L.A.; Mallette, A.; Ardila, D.S.; Mishra, R.; Miyazaki, C.M.; Korvink, J.G.; Ducrée, J.; Mager, D. Wirelessly powered and remotely controlled valve-array for highly multiplexed analytical assay automation on a centrifugal microfluidic platform. Biosens. Bioelectron.
**2018**, 109, 214–223. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kinahan, D.J.; Renou, M.; Kurzbuch, D.; Kilcawley, N.A.; Bailey, E.; Glynn, M.T.; McDonagh, C.; Ducrée, J. Baking powder actuated centrifugo-pneumatic valving for automation of multi-step bioassays. Micromachine
**2016**, 7, 175. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Haeberle, S.; Brenner, T.; Zengerle, R.; Ducrée, J. Centrifugal extraction of plasma from whole blood on a rotating disk. Lab Chip
**2006**, 6, 776–781. [Google Scholar] [CrossRef] - Steigert, J.; Brenner, T.; Grumann, M.; Riegger, L.; Lutz, S.; Zengerle, R.; Ducrée, J. Integrated siphon-based metering and sedimentation of whole blood on a hydrophilic lab-on-a-disk. Biomed. Microdevices
**2007**, 9, 675–679. [Google Scholar] [CrossRef] [PubMed] - Kinahan, D.J.; Kearney, S.M.; Kilcawley, N.A.; Early, P.L.; Glynn, M.T.; Ducrée, J. Density-gradient mediated band extraction of leukocytes from whole blood using centrifugo-pneumatic siphon valving on centrifugal microfluidic discs. PLoS ONE
**2016**, 11. [Google Scholar] [CrossRef] - Dimov, N.; Gaughran, J.; Mc Auley, D.; Boyle, D.; Kinahan, D.J.; Ducrée, J. Centrifugally Automated Solid-Phase Purification of RNA. In Proceedings of the 2014 IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS), San Francisco, CA, USA, 26–30 January 2014; pp. 260–263. [Google Scholar] [CrossRef]
- Gaughran, J.; Boyle, D.; Murphy, J.; Kelly, R.; Ducrée, J. Phase-selective graphene oxide membranes for advanced microfluidic flow control. Microsyst. Nanoeng.
**2016**, 2, 1–7. [Google Scholar] [CrossRef] [Green Version] - Zehnle, S.; Rombach, M.; Zengerle, R.; von Stetten, F.; Paust, N. Network simulation-based optimization of centrifugopneumatic blood plasma separation. Biomicrofluidics
**2017**, 11. [Google Scholar] [CrossRef] [Green Version] - Al-Faqheri, W.; Thio, T.H.G.; Qasaimeh, M.A.; Dietzel, A.; Madou, M.; Al-Halhouli, A. Particle/cell separation on microfluidic platforms based on centrifugation effect: A review. Microfluid. Nanofluid.
**2017**, 21. [Google Scholar] [CrossRef] - Mark, D.; Haeberle, S.; Metz, T.; Lutz, S.; Ducrée, J.; Zengerle, R.; von Stetten, F. Aliquoting structure for centrifugal microfluidics based on a new pneumatic valve. In Proceedings of the 2008 IEEE 21st International Conference on Micro Electro Mechanical Systems, Tucson, AZ, USA, 13–17 January 2008; pp. 611–614. [Google Scholar] [CrossRef] [Green Version]
- Schwemmer, F.; Hutzenlaub, T.; Buselmeier, D.; Paust, N.; von Stetten, F.; Mark, D.; Zengerle, R.; Kosse, D. Centrifugo-pneumatic multi-liquid aliquoting-parallel aliquoting and combination of multiple liquids in centrifugal microfluidics. Lab Chip
**2015**, 15, 3250–3258. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Keller, M.; Wadle, S.; Paust, N.; Dreesen, L.; Nuese, C.; Strohmeier, O.; Zengerle, R.; von Stetten, F. Centrifugo-thermopneumatic fluid control for valving and aliquoting applied to multiplex real-time PCR on off-the-shelf centrifugal thermocycler. Rsc. Adv.
**2015**, 5, 89603–89611. [Google Scholar] [CrossRef] [Green Version] - Grumann, M.; Geipel, A.; Riegger, L.; Zengerle, R.; Ducrée, J. Batch-mode mixing on centrifugal microfluidic platforms. Lab Chip
**2005**, 5, 560–565. [Google Scholar] [CrossRef] [PubMed] - Ducrée, J.; Brenner, T.; Haeberle, S.; Glatzel, T.; Zengerle, R. Multilamination of flows in planar networks of rotating microchannels. Microfluid. Nanofluid.
**2006**, 2, 78–84. [Google Scholar] [CrossRef] - Burger, R.; Kinahan, D.; Cayron, H.; Reis, N.; Garcia da Fonseca, J.; Ducrée, J. Siphon-induced droplet break-off for enhanced mixing on a centrifugal platform. Inventions
**2020**, 5, 1. [Google Scholar] [CrossRef] [Green Version] - Ducrée, J.; Haeberle, S.; Brenner, T.; Glatzel, T.; Zengerle, R. Patterning of flow and mixing in rotating radial microchannels. In Microfluid. Nanofluid.
**2006**, 2, 97–105. [Google Scholar] [CrossRef] - Strohmeier, O.; Keil, S.; Kanat, B.; Patel, P.; Niedrig, M.; Weidmann, M.; Hufert, F.; Drexler, J.; Zengerle, R.; von Stetten, F. Automated nucleic acid extraction from whole blood, B. subtilis, E. coli, and Rift Valley fever virus on a centrifugal microfluidic LabDisk. Rsc. Adv.
**2015**, 5, 32144–32150. [Google Scholar] [CrossRef] - Karle, M.; Miwa, J.; Roth, G.; Zengerle, R.; von Stetten, F. A novel microfluidic platform for continuous dna extraction and purification using laminar flow magnetophoresis. In Proceedings of the 2009 IEEE 22nd International Conference on Micro Electro Mechanical Systems, Sorrento, Italy, 25–29 January 2009; pp. 276–279. [Google Scholar] [CrossRef]
- Kido, H.; Micic, M.; Smith, D.; Zoval, J.; Norton, J.; Madou, M. A novel, compact disk-like centrifugal microfluidics system for cell lysis and sample homogenization. Colloids Surf. B Biointerfaces
**2007**, 58, 44–51. [Google Scholar] [CrossRef] [PubMed] - Haeberle, S.; Zengerle, R.; Ducrée, J. Centrifugal generation and manipulation of droplet emulsions. Microfluid. Nanofluid.
**2007**, 3, 65–75. [Google Scholar] [CrossRef] - Schuler, F.; Schwemmer, F.; Trotter, M.; Wadle, S.; Zengerle, R.; von Stetten, F.; Paust, N. Centrifugal step emulsification applied for absolute quantification of nucleic acids by digital droplet RPA. Lab Chip
**2015**, 15, 2759–2766. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Schuler, F.; Trotter, M.; Geltman, M.; Schwemmer, F.; Wadle, S.; Dominguez-Garrido, E.; Lopez, M.; Cervera-Acedo, C.; Santibanez, P.; von Stetten, F.; et al. Digital droplet PCR on disk. Lab Chip
**2016**, 16, 208–216. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Brennan, D.; Coughlan, H.; Clancy, E.; Dimov, N.; Barry, T.; Kinahan, D.; Ducrée, J.; Smith, T.J.; Galvin, P. Development of an on-disc isothermal in vitro amplification and detection of bacterial RNA. Sens. Actuators B Chem.
**2017**, 239, 235–242. [Google Scholar] [CrossRef] [Green Version] - Delgado, S.M.T.; Kinahan, D.J.; Sandoval, F.S.; Julius, L.A.N.; Kilcawley, N.A.; Ducrée, J.; Mager, D. Fully automated chemiluminescence detection using an electrified-Lab-on-a-Disc (eLoaD) platform. Lab Chip
**2016**, 16, 4002–4011. [Google Scholar] [CrossRef] [Green Version] - Zehnle, S.; Schwemmer, F.; Bergmann, R.; von Stetten, F.; Zengerle, R.; Paust, N. Pneumatic siphon valving and switching in centrifugal microfluidics controlled by rotational frequency or rotational acceleration. Microfluid. Nanofluid.
**2015**, 19, 1259–1269. [Google Scholar] [CrossRef] - Ducrée, J. Systematic review of centrifugal valving based on digital twin modelling towards highly integrated Lab-on-a-Disc systems. Nat. Microsyst. Nanoeng.
**2021**. [Google Scholar] [CrossRef] - Digital Twin. Available online: https://en.wikipedia.org/wiki/Digital_twin (accessed on 25 May 2021).
- Marr, B. What Is Digital Twin Technology-And Why Is It So Important? Available online: https://www.forbes.com/sites/bernardmarr/2017/03/06/what-is-digital-twin-technology-and-why-is-it-so-important/ (accessed on 25 May 2021).
- Grieves, M.; Vickers, J. Digital twin: Mitigating unpredictable, undesirable emergent behavior in complex systems. In Transdisciplinary Perspectives on Complex Systems: New Findings and Approaches; Kahlen, F.-J., Flumerfelt, S., Alves, A., Eds.; Springer International Publishing: Berlin, Germany, 2017; pp. 85–113. [Google Scholar] [CrossRef]
- Thorsen, T. Microfluidic Large-Scale Integration. Science
**2002**, 298, 580–584. [Google Scholar] [CrossRef] [Green Version] - Ducrée, J. Secure air traffic control at the hub of multiplexing on the centrifugo-pneumatic Lab-on-a-Disc platform. Micromachines
**2021**, 700. [Google Scholar] [CrossRef] - Ducrée, J. Efficient development of integrated Lab-On-A-Chip systems featuring operational robustness and nanufacturability. Micromachines
**2019**, 10, 886. [Google Scholar] [CrossRef] [Green Version] - Reyes, D.R.; Heeren, H.v.; Guha, S.; Herbertson, L.H.; Tzannis, A.P.; Ducrée, J.; Bissig, H.; Becker, H. Accelerating innovation and commercialization through standardization of microfluidic-based medical devices. Lab Chip
**2021**, 21, 9–21. [Google Scholar] [CrossRef] - Ducrée, J. Efficient development of microfluidic solutions for bioanalytical “point-of-use” testing towards high-technology-readiness levels—a platform-based design-for-manufacture approach. Multidiscip. Digit. Publ. Inst. Proc.
**2019**, 2, 1097. [Google Scholar] [CrossRef] [Green Version] - Ducrée, J. Anti-Counterfeit Technologies for Centrifugal Microfluidic “Lab-on-a-Disc” Systems: An Analysis. Preprints
**2021**. (in preparation). [Google Scholar] - Ducrée, J.; Etzrodt, M.; Bartling, S.; Walshe, R.; Harrington, T.; Wittek, N.; Posth, S.; Wittek, K.; Ionita, A.; Prinz, W.; et al. Unchaining collective intelligence for science, research and technology development by blockchain-boosted community participation. Front. Blockchain
**2021**, 4. [Google Scholar] [CrossRef] - Ducrée, J. Research–a blockchain of knowledge? Blockchain Res. Appl.
**2020**, 1. [Google Scholar] [CrossRef] - Ducrée, J.; Gravitt, M.; Walshe, R.; Bartling, S.; Etzrodt, M.; Harrington, T. Open platform concept for blockchain-enabled crowdsourcing of technology development and supply chains. Front. Blockchain
**2020**, 3. [Google Scholar] [CrossRef] - Ducrée, J.; Etzrodt, M.; Gordijn, B.; Gravitt, M.; Bartling, S.; Walshe, R.; Harrington, T. Blockchain for Organising Effective Grass-Roots Actions on a Global Commons: Saving The Planet. Front. Blockchain
**2020**, 3, 33. [Google Scholar] [CrossRef]

**Figure 1.**Centrifugo-pneumatic (CP) dissolvable-film (DF) siphon valve structure structure $\mathsf{\Gamma}$ (linearized display, dimensions not to scale with typical measures listed in the Appendix A.1). The depths ${d}_{0}={d}_{\mathrm{iso}}=d$ of all components upstream of the crest point at $r={R}_{\mathrm{crest}}$ amount to $1\mathrm{mm}$, and $200\mathsf{\mu}\mathrm{m}$ thereafter. (

**a**) In a first step, a liquid volume ${U}_{\mathrm{iso}}$ is loaded to the basic structure $\mathsf{\Gamma}$ which pneumatically isolates the inlet reservoir that is open to atmosphere at ${p}_{0}$ from the downstream compression chamber. For instance, due to dynamic effects, the actual pressure ${p}_{0}^{\prime}$ in the enclosed volume can (slightly) deviate from ${p}_{0}$. (

**b**) The liquid volume ${U}_{0}\gg {U}_{\mathrm{iso}}$ is retained upstream of the crest point at ${R}_{\mathrm{crest}}=R-Z$ for spin rates $\omega <\mathsf{\Omega}$. (

**c**) The high-pass CP-DF siphon valve opens for $\omega >{\mathsf{\Omega}}^{*}\approx \mathsf{\Omega}$ upon arrival of a minimum volume ${U}_{\mathrm{DF}}$ in the shallow DF chamber (${d}_{\mathrm{DF}}\ll d$). (

**d**) Multi-segmented version for illustrating the key geometrical features for enhanced design optimization according to a given set of metrics.

**Figure 2.**Standard deviation $\mathsf{\Delta}\mathsf{\Omega}/2\pi $ for CP-DF siphon valves (with default parameters, see Appendix A.1) as a function of (

**a**) the volume of the main compression chamber ${V}_{\mathrm{C},0}$, and (

**b**) the radial position $R$ for typical dimensional (manufacturing) tolerances (see Appendix A.1). The dotted horizontal and vertical lines indicate the standard deviation of $\mathsf{\Omega}$ and the volume of main compression chamber ${V}_{\mathrm{C},0}$ in the default geometry and parameters.

**Figure 3.**Comparison between structures $\mathsf{\Gamma}$ in their (

**a**) basic and (

**b**) multi-segmented versions for typical tolerances $\left\{\mathsf{\Delta}{\gamma}_{k}\right\}$ (see Appendix A.1) at identical radial position $R=3\mathrm{cm}$ and release rate $\mathsf{\Omega}/2\pi =25\mathrm{Hz}$ after optimization of $\mathsf{\Delta}\mathsf{\Omega}$. Most notably, $\mathsf{\Gamma}$ in (

**b**) displays a wider inner radial section of the reservoir and overall increased width of the inbound segment to “pin” the menisci at ${r}_{0}$ and $r={R}_{\mathrm{crest}}$, and thus $\overline{r}\mathsf{\Delta}r$, to counter variation in $\mathsf{\Omega}$ (5) and (6) via $\overline{r}\mathsf{\Delta}r$.

**Figure 4.**Optimizing the band width at (

**a**) $R=3\mathrm{cm}$ and $\mathsf{\Omega}/2\pi =40\mathrm{Hz}$ and (

**b**) at $=5\mathrm{cm}$ by reducing $\mathsf{\Omega}$ to establish the same field strength ${f}_{\omega}\propto R\xb7{\mathsf{\Omega}}^{2}$ (8), with $\mathsf{\Delta}\mathsf{\Omega}/2\pi \approx 1.03\mathrm{Hz}$.

**Figure 5.**Minimization of the standard deviation $\mathsf{\Delta}\mathsf{\Omega}$ for a set of CP-DF siphon valves $\mathsf{\Gamma}$ possessing equal retention rates $\mathsf{\Omega}/2\pi =25\mathrm{Hz}$, which are placed the radial positions (

**a**) $R=3\mathrm{cm}$ and (

**b**) $R=5.5\mathrm{cm}$.

**Figure 6.**Geometrical optimization of $\mathsf{\Gamma}$ towards minimization of $\mathsf{\Delta}\mathsf{\Omega}$ at a given $\mathsf{\Omega}/2\pi =25\mathrm{Hz}$ toward minimum radial extension $\overline{\mathsf{\Delta}R}$ (11) at the radial positions (

**a**) $R=3\mathrm{cm}$, (

**b**) $R=5\mathrm{cm}$, and (

**c**) toward smallest spatial footprint $\overline{A}$ (13) at $\mathsf{\Omega}/2\pi \approx 25\mathrm{Hz}$.

**Figure 7.**(

**a**) Spread $\mathsf{\Delta}\mathsf{\Omega}$ as a function of the precision of the loaded volume $\mathsf{\Delta}{U}_{0}$ with default other values $\left\{\mathsf{\Delta}{\gamma}_{k}\right\}$, with the dotted lines representing the values used and obtained for the default parameters (see Appendix A.1). (

**b**) Structure $\mathsf{\Gamma}$ (excerpt) optimized for minimum standard deviation $\mathsf{\Delta}\mathsf{\Omega}$ caused by a comparatively poor volume precision $\mathsf{\Delta}{U}_{0}$.

**Figure 8.**Variation of retention rate $\mathsf{\Omega}$ vs. (

**a**) actual atmospheric pressure ${p}_{0}$ and (

**b**) with the fractional deviation $\chi ={p}_{0}^{\prime}/{p}_{0}-1$ of the pressure of the enclosed gas pocket ${p}_{0}^{\prime}$ from ${p}_{0}$ at the point of isolation from atmosphere (Figure 1a). Note that variations in $\chi $ of more than a few permille have a considerable impact on $\mathsf{\Omega}$ (5), (6) and (16). The dotted lines indicate the standard deviations $\mathsf{\Delta}\mathsf{\Omega}$ obtained at ${p}_{0}={p}_{\mathrm{std}}$ (

**a**) and for $\chi =0$, (

**b**) using the standard parameter values (see Appendix A.1).

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**MDPI and ACS Style**

Ducrée, J.
Design Optimization of Centrifugal Microfluidic “Lab-on-a-Disc” Systems towards Fluidic Larger-Scale Integration. *Appl. Sci.* **2021**, *11*, 5839.
https://doi.org/10.3390/app11135839

**AMA Style**

Ducrée J.
Design Optimization of Centrifugal Microfluidic “Lab-on-a-Disc” Systems towards Fluidic Larger-Scale Integration. *Applied Sciences*. 2021; 11(13):5839.
https://doi.org/10.3390/app11135839

**Chicago/Turabian Style**

Ducrée, Jens.
2021. "Design Optimization of Centrifugal Microfluidic “Lab-on-a-Disc” Systems towards Fluidic Larger-Scale Integration" *Applied Sciences* 11, no. 13: 5839.
https://doi.org/10.3390/app11135839