Abstract
A novel macromodel based on Krylov subspace projection method for micromixers with serpentine channels is presented. The physical equations are discretized using Galerkin method. The orthogonal basis is obtained and the discrete matrix is assembled with Arnoldi procedure based on Krylov subspace projection. The obtained macromodel can be used to calculate the concentration of the sample at arbitrary location of serpentine micromixers. The maximal relative deviation is 2 % between macromodel and only numerical simulation. The computational efficiency of the macromodel will be improved significantly with the numbers of serpentine channels increasing. Simulation results demonstrated that the macromodel is flexible, effective and easily operated for rapid design and computation of serpentine micromixers.
Funding statement: This work was supported by Liaoning Province Doctor Startup Fund (20141131), Fund of Liaoning Province Education Administration (L2014241), and the Fund in Liaoning University of Technology (X201301).
References
[1] O.H. Shapiro, E. Kramarsky-Winter, A.R. Gavish, et al., A coral-on-a-chip microfluidic platform enabling live-imaging microscopy of reef-building corals[J], Nat. Commun. 7 (2016), 1–9.10.1038/ncomms10860Search in Google Scholar PubMed PubMed Central
[2] M. Ballard, D. Owen, Z.G. Mills, et al., Orbiting magnetic microbeads enable rapid microfluidic mixing[J], Microfluid Nanofluidics 20(6) (2016), 1–13.10.1007/s10404-016-1750-1Search in Google Scholar
[3] Z.M. Malecha and K. Malecha, Numerical analysis of mixing under low and high frequency pulsations at serpentine micromixers[J], Chem. Process Eng. 35(3) (2014), 369–385.10.2478/cpe-2014-0028Search in Google Scholar
[4] X. Chen, T. Li, H. Zeng, et al., Numerical and experimental investigation on micromixers with serpentine microchannels[J], Int. J. Heat Mass Transf. 98 (2016), 131–140.10.1016/j.ijheatmasstransfer.2016.03.041Search in Google Scholar
[5] X. Chen, T. Li and J. Shen, CO2 laser ablation of microchannel on PMMA substrate for effective fabrication of microfluidic chips[J], Int. Polymer Process. 31(2) (2016), 233–238.10.3139/217.3184Search in Google Scholar
[6] D. Konstantinou, A. Shirazi, A. Sadri, et al., Combined hot embossing and milling for medium volume production of thermoplastic microfluidic devices[J], Sens. Actuators B Chem. 234 (2016), 209–221.10.1016/j.snb.2016.04.147Search in Google Scholar
[7] Z. Yin, E. Cheng and H. Zou, A novel hybrid patterning technique for micro and nanochannel fabrication by integrating hot embossing and inverse UV photolithography[J], Lab. Chip 14(9) (2014), 1614–1621.10.1039/C3LC51369FSearch in Google Scholar
[8] B.D. Stępak, A.J. Antończak and K.M. Abramski, Rapid fabrication of microdevices by controlling the PDMS curing conditions during replication of a laser-prototyped mould[J], J. Micromech. Microeng. 25(10) (2015), 107001.10.1088/0960-1317/25/10/107001Search in Google Scholar
[9] K. Malecha, L.J. Golonka, J. Bałdyga, et al., Serpentine microfluidic mixer made in LTCC[J], Sens. Actuators B Chem. 143(1) (2009), 400–413.10.1016/j.snb.2009.08.010Search in Google Scholar
[10] K. Malecha, D.G. Pijanowska, L.J. Golonka, et al., LTCC microreactor for urea determination in biological fluids[J], Sens. Actuators B Chem. 141(1) (2009), 301–308.10.1016/j.snb.2009.06.026Search in Google Scholar
[11] A.K. Au, N. Bhattacharjee, L.F. Horowitz, et al., 3D-printed microfluidic automation[J], Lab. Chip 15(8) (2015), 1934–1941.10.1039/C5LC00126ASearch in Google Scholar PubMed PubMed Central
[12] X. Chen and T. Li, A novel design for passive micromixers based on topology optimization method[J], Biomed, Microdevices 18(4) (2016), 1–15.10.1007/s10544-016-0082-ySearch in Google Scholar PubMed
[13] Y. Wang, H. Song and K. Pant, A reduced-order model for whole-chip thermal analysis of microfluidic lab-on-a-chip systems[J], Microfluid Nanofluidics 16(1–2) (2014), 369–380.10.1007/s10404-013-1210-0Search in Google Scholar PubMed PubMed Central
[14] X. Chen, C. Liu, Z. Xu, et al., Macro-micro modeling design in system-level and experiment for a micromixer[J], Anal. Methods 4(8) (2012), 2334–2340.10.1039/c2ay25263eSearch in Google Scholar
[15] Z. Xu, Y. Yang, D. Vadillo, et al., A mathematical model of mixing enhancement in microfluidic channel with a constriction under periodic electro-osmotic flow[J], Appl. Phys. Lett. 100(4) (2012), 041907.10.1063/1.3678037Search in Google Scholar
[16] A.N. Chatterjee and N.R. Aluru, Combined circuit/device modeling and simulation of integrated microfluidic systems[J], J. Microelectromech. Syst. 14(1) (2005), 81–95.10.1109/JMEMS.2004.839025Search in Google Scholar
[17] H. Song, Y. Wang and K. Pant, Cross-stream diffusion under pressure-driven flow in microchannels with arbitrary aspect ratios: A phase diagram study using a three-dimensional analytical model[J], Microfluid Nanofluidics 12(1–4) (2012), 265–277.10.1007/s10404-011-0870-xSearch in Google Scholar PubMed PubMed Central
[18] D. Vasilyev, M. Rewieński and J. White, Macromodel generation for BioMEMS components using a stabilized balanced truncation plus trajectory piecewise linear approach[M], in: Design Automation Methods and Tools for Microfluidics-Based Biochips, pp. 169–187, Cambridge, MA: Springer Netherlands, 2006.10.1007/1-4020-5123-9_7Search in Google Scholar
[19] R. Qiao and N.R. Aluru, A compact model for electroosmotic flows in microfluidic devices[J], J. Micromech. Microeng. 12(5) (2002), 625.10.1088/0960-1317/12/5/318Search in Google Scholar
[20] R. Cheng, T. Zhu and L. Mao, Three-dimensional and analytical modeling of microfluidic particle transport in magnetic fluids[J], Microfluid Nanofluidics 16(6) (2014), 1143–1154.10.1007/s10404-013-1280-zSearch in Google Scholar
[21] Y. Wang, Q. Lin and T. Mukherjee, Applications of behavioral modeling and simulation on a lab-on-a-chip: Micro-mixer and separation system[C]. Behavioral Modeling and Simulation Conference, 2004. BMAS 2004. Proceedings of the 2004 IEEE International. IEEE, 2004: 8–13.10.1109/BMAS.2004.1393974Search in Google Scholar
[22] A.S. Bedekar, Y. Wang, S. Krishnamoorthy, et al., System-level simulation of flow induced dispersion in lab-on-a-chip systems [M], in: Design Automation Methods and Tools for Microfluidics-Based Biochips, pp. 189–214, Cambridge, MA: Springer Netherlands, 2006.10.1007/1-4020-5123-9_8Search in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A Robust Algorithm for Nonlinear Variable-Order Fractional Control Systems with Delay
- Numerical Methods for the Derivative Nonlinear Schrödinger Equation
- Lax Integrability and Exact Solutions of a Variable-Coefficient and Nonisospectral AKNS Hierarchy
- Modeling of Supersonic/Hypersonic Boundary Layer Transition Using a Single-Point Approach
- A Novel Macromodel based on Krylov Subspace Projection Method for Micromixers with Serpentine Channels
- Approaches to the Numerical Estimates of Grid Convergence of NSE in the Presence of Singularities
- Numerical Solutions of Stochastic Volterra–Fredholm Integral Equations by Hybrid Legendre Block-Pulse Functions
- Positivity and Stability of Standard and Fractional Descriptor Continuous-Time Linear and Nonlinear Systems
- Dynamics of Almost Periodic Solution for a Delayed Facultative Mutualism Model Involving Negative Feedback Terms
- Controllability of Fractional Evolution Inclusions with Noninstantaneous Impulses
- Analysis of a Delayed Predator–Prey System with Harvesting
- Nonlinear Bending of Rectangular Magnetoelectroelastic Thin Plates with Linearly Varying Thickness
- Numerical Method for a Class of Nonlinear Singularly Perturbed Delay Differential Equations Using Parametric Cubic Spline
- Numerical Simulation for Shale Gas Flow in Complex Fracture System of Fractured Horizontal Well
- Real-Time Control of a Rotary Inverted Pendulum using Robust LQR-based ANFIS Controller
- A Study of an Extended Generalized (2+1)-dimensional Jaulent–Miodek Equation
- RBFPUM with QR Factorization for Solving Water Flow Problem in Multilayered Soil
- Classical Magnetism and an Integral Formula Involving Modified Bessel Functions
- Lie Symmetry Analysis of Boundary Layer Stagnation-Point Flow and Heat Transfer of Non-Newtonian Power-Law Fluids Over a Nonlinearly Shrinking/Stretching Sheet with Thermal Radiation
Articles in the same Issue
- Frontmatter
- A Robust Algorithm for Nonlinear Variable-Order Fractional Control Systems with Delay
- Numerical Methods for the Derivative Nonlinear Schrödinger Equation
- Lax Integrability and Exact Solutions of a Variable-Coefficient and Nonisospectral AKNS Hierarchy
- Modeling of Supersonic/Hypersonic Boundary Layer Transition Using a Single-Point Approach
- A Novel Macromodel based on Krylov Subspace Projection Method for Micromixers with Serpentine Channels
- Approaches to the Numerical Estimates of Grid Convergence of NSE in the Presence of Singularities
- Numerical Solutions of Stochastic Volterra–Fredholm Integral Equations by Hybrid Legendre Block-Pulse Functions
- Positivity and Stability of Standard and Fractional Descriptor Continuous-Time Linear and Nonlinear Systems
- Dynamics of Almost Periodic Solution for a Delayed Facultative Mutualism Model Involving Negative Feedback Terms
- Controllability of Fractional Evolution Inclusions with Noninstantaneous Impulses
- Analysis of a Delayed Predator–Prey System with Harvesting
- Nonlinear Bending of Rectangular Magnetoelectroelastic Thin Plates with Linearly Varying Thickness
- Numerical Method for a Class of Nonlinear Singularly Perturbed Delay Differential Equations Using Parametric Cubic Spline
- Numerical Simulation for Shale Gas Flow in Complex Fracture System of Fractured Horizontal Well
- Real-Time Control of a Rotary Inverted Pendulum using Robust LQR-based ANFIS Controller
- A Study of an Extended Generalized (2+1)-dimensional Jaulent–Miodek Equation
- RBFPUM with QR Factorization for Solving Water Flow Problem in Multilayered Soil
- Classical Magnetism and an Integral Formula Involving Modified Bessel Functions
- Lie Symmetry Analysis of Boundary Layer Stagnation-Point Flow and Heat Transfer of Non-Newtonian Power-Law Fluids Over a Nonlinearly Shrinking/Stretching Sheet with Thermal Radiation