Abstract
The design of components for inertial microfluidic focusing and separation is primarily designed from basic geometric primitives. This paper presents a topology optimization methodology to the design synthesis of microfluidic particle manipulators. The flow is modeled by the Navier-Stokes equations in an Eulerian frame while the particle transport is modeled as a Lagrangian particle model. The model assumes that the particles are small and the suspension is dilute such that both the particle influence on the fluid motion and collisions between particles can be neglected. Two manipulator design problems are studied—one that makes particles follow a predefined trajectory, and another where particles are focused at the outlet utilizing the inertia of the particles. The latter is extracted and post-analyzed using a commercial software COMSOL verifying the method’s ability to synthesize inertial microfluidic components.
Similar content being viewed by others
References
Aage N, Andreassen E, Lazarov BS (2015) Topology optimization using PETSc: an easy-to-use, fully parallel, open source topology optimization framework. Struct Multidiscip Optim 51(3):565–572. https://doi.org/10.1007/s00158-014-1157-0
Alexandersen J, Aage N, Andreasen CS, Sigmund O (2014) Topology optimisation for natural convection problems. Int J Numer Methods Fluids 76(10):699–721. https://doi.org/10.1002/fld.3954
Alexandersen J, Sigmund O, Aage N (2016) Large scale three-dimensional topology optimisation of heat sinks cooled by natural convection. Int J Heat Mass Transf 100:876–891. https://doi.org/10.1016/j.ijheatmasstransfer.2016.05.013
Andreasen CS (2017) Topology optimization of inertia driven dosing units. Struct Multidiscip Optim 55 (4):1301–1309. https://doi.org/10.1007/s00158-016-1573-4
Andreasen CS, Gersborg AR, Sigmund O (2009) Topology optimization of microfluidic mixers. Int J Numer Methods Fluids 61(5):498–513. https://doi.org/10.1002/fld.1964
Andreasen CS, Andreassen E, Jensen JS, Sigmund O (2014) On the realization of the bulk modulus bounds for two-phase viscoelastic composites. J Mech Phys Solids 63(1):228–241. https://doi.org/10.1016/j.jmps.2013.09.007
Behrou R, Ranjan R, Guest JK (2019) Adaptive topology optimization for incompressible laminar flow problems with mass flow constraints. Comput Methods Appl Mech Eng 346:612–641. https://doi.org/10.1016/j.cma.2018.11.037
Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224. https://doi.org/10.1016/0045-7825(88)90086-2
Borrvall T, Petersson J (2003) Topology optimization of fluids in Stokes flow. Int J Numer Methods Fluids 41(1):77–107. https://doi.org/10.1002/fld.426
Chan PCH, Leal LG (1979) The motion of a deformable drop in a second-order fluid. J Fluid Mech 92 (1):131–170. https://doi.org/10.1017/S0022112079000562
Deng Y, Liu Z, Zhang P, Wu Y, Korvink JG (2010) Optimization of no-moving part fluidic resistance microvalves with low reynolds number. In: 2010 IEEE 23rd international conference on micro electro mechanical systems. https://doi.org/10.1109/MEMSYS.2010.5442565. IEEE, MEMS, pp 67–70
Deng Y, Liu Z, Zhang P, Liu Y, Wu Y (2011) Topology optimization of unsteady incompressible Navier–Stokes flows. J Comput Phys 230(17):6688–6708. https://doi.org/10.1016/j.jcp.2011.05.004
Di Carlo D, Irimia D, Tompkins RG, Toner M (2007) Continuous inertial focusing, ordering, and separation of particles in microchannels. Proceedings of the National Academy of Sciences of the United States of America 104(48):18892–18897. https://doi.org/10.1073/pnas.0704958104
Dilgen CB, Dilgen SB, Fuhrman DR, Sigmund O, Lazarov BS (2018a) Topology optimization of turbulent flows. Comput Methods Appl Mech Eng 331:363–393. https://doi.org/10.1016/j.cma.2017.11.029
Dilgen SB, Dilgen CB, Fuhrman DR, Sigmund O, Lazarov BS (2018b) Density based topology optimization of turbulent flow heat transfer systems. Struct Multidisciplinary Optim 57(5):1905–1918. https://doi.org/10.1007/s00158-018-1967-6
Fox RW, McDonald AT, Pritchard PJ (2004) Introduction to fluid mechanics, 6th edn. John Wiley & Sons, New York
Gale B, Jafek A, Lambert C, Goenner B, Moghimifam H, Nze U, Kamarapu S (2018) A review of current methods in microfluidic device fabrication and future commercialization prospects. Inventions 3 (3):60. https://doi.org/10.3390/inventions3030060
Gersborg AR, Andreasen CS (2011) An explicit parameterization for casting constraints in gradient driven topology optimization. Struct Multidiscip Optim 44(6):875–881. https://doi.org/10.1007/s00158-011-0632-0
Gersborg-Hansen A, Sigmund O, Haber R (2005) Topology optimization of channel flow problems. Struct Multidiscip Optim 30(3):181–192. https://doi.org/10.1007/s00158-004-0508-7
Guest JK, Prėvost JH (2006) Topology optimization of creeping fluid flows using a Darcy–Stokes finite element. Int J Numer Methods Eng 66(3):461–484. https://doi.org/10.1002/nme.1560
Guo Y, Xu Y, Deng Y, Liu Z (2018) Topology optimization of passive micromixers based on lagrangian mapping method. Micromachines 9(3):137. https://doi.org/10.3390/mi9030137
Hyun Jc, Hyun J, Wang S, Yang S (2017) Improved pillar shape for deterministic lateral displacement separation method to maintain separation efficiency over a long period of time. Sep Purif Technol 172:258–267. https://doi.org/10.1016/j.seppur.2016.08.023
Kang BS, Park GJ, Arora JS (2006) A review of optimization of structures subjected to transient loads. Struct Multidiscip Optim 31(2):81–95. https://doi.org/10.1007/s00158-005-0575-4
Kim D, Kim Y, Lee D, Kim B, Lee J (2017) Electrode configuration optimization for maximizing throughput of dielectrophoretic particle separator. J Mech Sci Technol 31(12):5951–5960. https://doi.org/10.1007/s12206-017-1139-4
Kreissl S, Maute K (2012) Levelset based fluid topology optimization using the extended finite element method. Struct Multidiscip Optim 46(3):311–326. https://doi.org/10.1007/s00158-012-0782-8
Kreissl S, Pingen G, Evgrafov A, Maute K (2010) Topology optimization of flexible micro-fluidic devices. Struct Multidiscip Optim 42(4):495–516. https://doi.org/10.1007/s00158-010-0526-6
Kreissl S, Pingen G, Maute K (2011) An explicit level set approach for generalized shape optimization of fluids with the lattice Boltzmann method. Int J Numer Methods Fluids 65(5):496–519. https://doi.org/10.1002/fld.2193
Lalli F, Esposito PG, Piscopia R, Verzicco R (2005) Fluid–particle flow simulation by averaged continuous model. Comput Fluids 34(9):1040–1061. https://doi.org/10.1016/j.compfluid.2004.08.004
Langelaar M (2019) Topology optimization for multi-axis machining. Comput Methods Appl Mech Eng 351:226–252. https://doi.org/10.1016/j.cma.2019.03.037
Manninen M, Taivassalo V, Kallio S, Akademi Å (1996) On the mixture model for multiphase flow, vtt public edn. VTT
Marck G, Nemer M, Harion JL (2013) Topology optimization of heat and mass transfer problems: laminar flow. Numerical Heat Transfer Part B: Fundamentals 63(6):508–539. https://doi.org/10.1080/10407790.2013.772001
Maxey MR, Riley JJ (1983) Equation of motion for a small rigid sphere in a nonuniform flow. Phys Fluids 26(4):883–889. https://doi.org/10.1063/1.864230
Michaleris P, Tortorelli DA, Vidal CA (1994) Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications to elastoplasticity. Int J Numer Meth Engng 37(14):2471–2499. https://doi.org/10.1002/nme.1620371408
Myung JH, Hong S (2015) Microfluidic devices to enrich and isolate circulating tumor cells. Lab Chip 15 (24):4500–4511. https://doi.org/10.1039/C5LC00947B
Okkels F, Bruus H (2007) Scaling behavior of optimally structured catalytic microfluidic reactors. Phys Rev E 75(1):016301. https://doi.org/10.1103/PhysRevE.75.016301
Olhoff N (1989) Multicriterion structural optimization via bound formulation and mathematical programming. Struct Optim 1(1):11–17. https://doi.org/10.1007/BF01743805
Ȯzbey A, Karimzadehkhouei M, Akgȯnu̇l S, Gozuacik D, Koşar A (2016) Inertial focusing of microparticles in curvilinear microchannels. Sci Rep 6(1):38809. https://doi.org/10.1038/srep38809
Park J, Kim B, Choi SK, Hong S, Lee SH, Lee KI (2005) An efficient cell separation system using 3D-asymmetric microelectrodes. Lab Chip 5(11):1264. https://doi.org/10.1039/b506803g
Schott B, Ager C, Wall WA (2019) Monolithic cut finite element–based approaches for fluid-structure interaction. Int J Numer Methods Eng 119(8):757–796. https://doi.org/10.1002/nme.6072
Shampine LF, Reichelt MW (1997) The MATLAB ode suite. SIAM J Sci Comput 18(1):1–22. https://doi.org/10.1137/S1064827594276424
Stan CA, Ellerbee AK, Guglielmini L, Stone HA, Whitesides GM (2013) The magnitude of lift forces acting on drops and bubbles in liquids flowing inside microchannels. Lab Chip 13(3):365–376. https://doi.org/10.1039/C2LC41035D
Stroock AD (2002) Chaotic mixer for microchannels. Science 295(5555):647–651. https://doi.org/10.1126/science.1066238
Svanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373
Tezduyar TE, Ramakrishnan S, Sathe S (2008) Stabilized formulations for incompressible flows with thermal coupling. Int J Numer Methods Fluids 57(9):1189–1209. https://doi.org/10.1002/fld.1743
Villanueva CH, Maute K (2017) CutFEM topology optimization of 3D laminar incompressible flow problems. Comput Methods Appl Mech Eng 320:444–473. https://doi.org/10.1016/j.cma.2017.03.007
Wang F, Jensen JS, Sigmund O (2011) Robust topology optimization of photonic crystal waveguides with tailored dispersion properties. J Opt Soc Am B 28(3):387. https://doi.org/10.1364/JOSAB.28.000387
White FM (1991) Viscous fluid flow, 2nd edn. McGraw-Hill Book Co, New York
Yoon GH (2010) Topology optimization for stationary fluid-structure interaction problems using a new monolithic formulation. Int J Numer Methods Eng 82(5):591–616. https://doi.org/10.1002/nme.2777
Yoon GH, Park J (2010) Topological design of electrode shapes for dielectrophoresis based devices. J Electrost 68(6):475–486. https://doi.org/10.1016/J.ELSTAT.2010.06.008
Acknowledgements
The author would like to thank the audience at WCSMO13 for constructive comments on the part of the work presented there. Furthermore, M.Sc. Jeppe Alexander Christensen, Associate Professor Niels Aage, and the TopOpt group at the Technical University of Denmark are acknowledged for fruitful discussions on the work.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author declares no conflict of interest.
Additional information
Responsible Editor: YoonYoung Kim
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Replication of results
Many details have been given in the relevant sections; however, for completeness, the details/parameters used are listed in this section.
Rights and permissions
About this article
Cite this article
Andreasen, C.S. A framework for topology optimization of inertial microfluidic particle manipulators. Struct Multidisc Optim 61, 2481–2499 (2020). https://doi.org/10.1007/s00158-019-02483-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-019-02483-5