Abstract
The flow structures in a novel microfluidics device (CS-MFRM) combining a cross-slot (CS) and a microfluidics four-roll mill (MFRM) have been investigated through a two-dimensional boundary element method. By changing the volume flow rates at various inlets of a CS-MFRM, diverse flow structures can be generated. Some of them are proposed to be employed to achieve some functions in the fabrication process of anisotropic particles. The stagnant points and eddies in those flows are particularly discussed since they are critical to trap and/or rotate droplets. Energy consumption of eddies generated in branches in some flow structures is also investigated in this paper.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- μ :
-
The viscosity of continuous phase
- λ :
-
The viscosity ratio of the droplet to the continuous phase
- G :
-
Shear rate
- p :
-
Pressure
- u :
-
Velocity vector
- f :
-
Surface stress
- S ij :
-
Fundamental solution of the two-dimensional Stokes equations
- T ijk :
-
Associated stress kernel of the fundamental solution
- Q :
-
Volume flow rate in a channel
- w 0 :
-
Half width of a channel
- r c :
-
Radius of central circular cavity
References
Helen S., Delai L.C., Rustem F.I.: Reactions in droplets in microfluidic channels. Angew. Chem. Int. Ed. 45, 7336–7356 (2006)
Whitesides G.M.: The origins and the future of microfluidics. Nature 442, 368–373 (2006)
Teh S.Y., Lin R., Hung L.H., Lee A.P.: Droplet microfluidics. Lab Chip 8, 198–220 (2008)
Wang J.T., Wang J., Han J.J.: Fabrication of advanced particles and particle-based materials assisted by droplet-based microfluidics. Small 7, 1728–1754 (2011)
Lingxin C., Sangyeop L., Jaebum K.L., Eun C.: Continuous dynamic flow micropumps for microfluid manipulation. J. Micromech. Microeng. 18, 013001 (2008)
Um E., Park J.K.: A microfluidic abacus channel for controlling the addition of droplets. Lab Chip 9, 207–212 (2009)
Dendukuri D., Doyle P.S.: The synthesis and assembly of polymeric microparticles using microfluidics. Adv. Mater. 21, 1–16 (2009)
Aubin J., Ferrando M., Jiricny V.: Current methods for characterising mixing and flow in microchannels. Chem. Eng. Sci. 65, 2065–2093 (2010)
Hao G., Michel H.G.D., Frieder M.: Droplets formation and merging in two-phase flow microfluidics. Int. J. Mol. Sci. 12, 2572–2597 (2011)
Seemann R., Brinkmann M., Pfohl T., Herminghaus S.: Droplet based microfluidics. Rep. Prog. Phys. 75, 016601 (2012)
Tanyeri M., Johnson-Chavarria E.M., Schroeder C.M.: Hydrodynamic trap for single particles and cells. Appl. Phys. Lett. 96, 224101 (2010)
Janssen J.J.M., Boon A., Agterof W.G.M.: Influence of dynamic interfacial properties on droplet breakup in plane hyperbolic flow. AICHE J. 43, 1436–1447 (1997)
Perkins T.T., Smith D.E., Chu S.: Single polymer dynamics in an elongational flow. Science 276, 2016–2021 (1997)
Schroeder C.M., Babcock H.P.E., Shaqfeh S.G., Chu S.: Observation of polymer conformation hysteresis in extensional flow. Science 301, 1515–1519 (2003)
Hellou M., Bach T.D.P.: Stokes flow in a junction of two-dimensional orthogonal channels. Z. Angew. Math. Phys. 62, 135–147 (2011)
Lee J.S., Dylla-Spears R., Teclemariam N.P., Muller S.J.: Microfluidic four-roll mill for all flow types. Appl. Phys. Lett. 90, 074103 (2007)
Wang J.T., Han J.J., Yu D.M.: Numerical studies of geometry effects of a two-dimensional microfluidic four-roll mill on droplet elongation and rotation. Eng. Anal. Bound. Elem. 36, 1453–1464 (2012)
Lee J.S., Shaqfeh E.S.G., Muller S.J.: Dynamics of DNA tumbling in shear to rotational mixed flows: pathways and periods. Phys. Rev. E 75, 040802 (2007)
Deschamps J., Kantsler V., Segre E., Steinberg V.: Dynamics of a vesicle in general flow. PNAS 106, 11444–11447 (2009)
Young Y.N., Blawzdziewicz J., Cristini V., Goodman R.H.: Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation. J Fluid Mech. 607, 209–234 (2008)
Wang, J.T., Tao, J., Han, J.J.: Hydrodynamic Control of Droplets Coalescence in Microfluidic Devices to Fabricate Anisotropic Particles Through Boundary Element Method (unpublished)
Shankar P.N.: The eddy structure in Stokes flow in a cavity. J. Fluid Mech. 250, 371–383 (1993)
Georgiadou M., Mohr R., Alkire R.C.: Local mass transport in two-dimensional cavities in laminar shear flow. J. Electrochem. Soc. 147, 3021–3028 (2000)
Lutz B.R., Chen J., Schwartz D.T.: Hydrodynamic Tweezers: 1. Non-contact cell trapping in a laminar oscillating flow. Anal. Chem. 78, 5429–5435 (2006)
Lin C.M., Lai Y.S., Liu H.P., Chen C.Y., Wo A.M.: Trapping of bioparticles via microvortices in a microfluidic device for bioassay applications. Anal. Chem. 80, 8937–8945 (2008)
Pozrikidis C.: Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press, Cambridge (1992)
Youngren G.K., Acrivos A.: On the shape of a gas bubble in a viscous extensional flow. J Fluid Mech. 76, 433–42 (1976)
Muldowney G.P., Higdon J.J.L.: A spectral boundary element approach to three-dimensional Stokes flow. J. Fluid Mech. 298, 167–192 (1995)
Liang J., Subramaniam S.: Computation of molecular electrostatics with boundary element methods. Biophys. J. 73, 1830–1841 (1997)
Pozrikidis C.: Interfacial dynamics for Stokes flow. J Comput. Phys. 169, 250–301 (2001)
Dimitrakopoulos P., Wang J.T.: A spectral boundary element algorithm for interfacial dynamics in two-dimensional Stokes flow based on Hermitian interfacial smoothing. Eng. Anal. Bound. Elem. 31, 646–656 (2007)
Wang J.T., Liu J.X., Han J.J., Guan J.: Effects of complex internal structures on rheology of multiple emulsions particles in 2D from a boundary integral method. Phys. Rev. Lett. 110, 066001 (2013)
Wang J.T, Liu J.X., Han J.J., Guan J.: Rheology investigation of the globule of multiple emulsions with complex internal structures through a boundary element method. Chem. Eng. Sci. 96, 87–97 (2013)
Baroud C.N., Gallaire F., Dangla R.: Dynamics of microfluidic droplets. Lab Chip 10, 2032–2045 (2010)
Stone H.A., Leal L.G.: Breakup of concentric double emulsion droplets in linear flows. J Fluid Mech. 211, 123–156 (1990)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Guan, J., Liu, J., Li, X. et al. Stokes flow in a two-dimensional micro-device combined by a cross-slot and a microfluidic four-roll mill. Z. Angew. Math. Phys. 66, 149–169 (2015). https://doi.org/10.1007/s00033-013-0396-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00033-013-0396-z