Particle transport in flow through a ratchet-like channel
2011, Microfluidics and Nanofluidics
https://doi.org/10.1007/S10404-010-0688-YAbstract
We present a fluidic device that shows ratchetlike characteristics for particle transport at low Reynolds. The ratchet consists of a two-dimensional saw-tooth channel, within which a laminar flow is generated by imposing a longitudinal pressure gradient. Particle trajectories are calculated by solving the continuity and Navier-Stokes equations for the fluid flow and the equations for particle transport in both flow directions. The ratchet-like effect is connected with a large asymmetry in the mean transit time, with regard to flow direction, due to particle motion within zones of low flow velocity near the asymmetric wall profile. We show how to obtain ratchet of particles with select Stokes under given flow conditions by adjusting the geometry of the ratchet channel.
References (38)
- Adjari A (2002) Electrokinetic 'ratchet' pumps for microfluidics. Appl Phys A 75:271-274
- Almeida MP, Andrade JS Jr, Herrmann HJ (2006) Aeolian transport layer. Phys Rev Lett 96:018001
- Almeida MP, Parteli EJR, Andrade JS Jr, Herrmann HJ (2008) Giant saltation on Mars. Proc Natl Acad Sci 105:6222-6226
- Arau ´jo AD, Andrade JS Jr, Herrmann HJ (2006) Critical role of gravity in filters. Phys Rev Lett 97:138001
- Austin RH, Darnton N, Huang R, Sturm J, Bakajin O, Duke T (2002) Ratchets: the problems with boundary conditions in insulating fluids. Appl Phys A 75:279-284
- Bader JS, Hammond RW, Henck SA, Deem MW, McDermott GA, Bustillo JM, Simpson JW, Mulhern GT, Rothbert JM (1999) DNA transport by a micromachined Brownian ratchet device. Proc Natl Acad Sci 96:13165-13169
- Buguin A, Talini L, Silberzan P (2002) Ratchet-like topological structures for the control of microdrops. Appl Phys A 75: 207-212
- Comer JK, Kleinstreuer C, Kim CS (2001a) Flow structures and particle deposition patterns in double-bifurcation airway models. Part 1. Air flow fields. J Fluid Mech 435:25-54
- Comer JK, Kleinstreuer C, Kim CS (2001b) Flow structures and particle deposition patterns in double-bifurcation airway models. Part 2. Aerosol transport and deposition. J Fluid Mech 435: 25-54
- Dean Astumian R (1997) Thermodynamics and Kinetics of a Brownian motor. Science 276:917:922
- Dere ´nyi I, Dean Astumian R (1998) ac separation of particles by biased Brownian motion in a two-dimensional sieve. Phys Rev E 58:7781-7784
- Di Carlo D, Edd JF, Irimia D, Tompkins RG, Toner M (2008) Equilibrium separation and filtration of particles using differen- tial inertial focusing. Anal Chem 80:2204-2211
- Effenhauser CS, Manz A, Michael Widmer H (1995) Manipulation of sample fractions on a capillary electrophoresis chip. Anal Chem 67:2284-2287
- Ertas ¸D (1998) Lateral separation of macromolecules and polyelec- trolytes in microlithographiic arrays. Phys Rev Lett 80: 1548-1551
- Faucheux LP, Bourdieu LS, Kaplan PD, Libchaber AJ (1995) Optical thermal ratchet. Phys Rev Lett 74:1504-1507
- Gorre-Talini S, Jeanjean S, Silberzan P (1997) Sorting of Brownian particles by the pulsed application of an asymmetric potential. Phys Rev E 56:2025-2034
- Grimm A, Stark H, van Maarel JRC (2009) Model for a Brownian ratchet with improved characteristics for particle separation. Phys Rev E 79:061102
- Herrmann HJ, Andrade JS Jr, Arau ´jo AD, Almeida MP (2006) Transport of particles in fluids. Phys A 372:374-386
- Huang LR, Silberzan P, Tegenfeldt JO, Cox EC, Sturm JC, Austin RH, Craighead H (2002) Role of molecular size in ratchet fractionation. Phys Rev Lett 89:178301
- Huang LR, Cox EC, Austin RH, Sturm JC (2004) Continuous particle separation through deterministic lateral displacement. Science 304:987-990
- Imdakm AO, Sahimi M (1987) Transport of large particles in flow through porous media. Phys Rev A 36:5304-5309
- Keller C, Marquardt F, Bruder C (2002) Separation quality of a geometric ratchet. Phys Rev E 65:041927
- Kettner C, Reimann P, Ha ¨nggi P, Mu ¨ller F (2000) Drift ratchet. Phys Rev E 61:312-323
- Kralj JG, Lis MTW, Schmidt MA, Jensen KF (2006) Continuous dielectrophoretic size-based particle sorting. Anal Chem 78: 5019-5025
- Loutherback K, Puchalla J, Austin RH, Sturm JC (2009) Determin- istic microfluidic ratchet. Phys Rev Lett 102:045301
- Magnasco MO (1993) Forced thermal ratchets. Phys Rev Lett 71:1477-1481
- Matthias S, Mu ¨ller F (2003) Asymmetric pores in a silicon membrane acting as massively parallel brownian ratchets. Nature 424: 53-57
- Morsi SA, Alexander AJ (1972) An investigation of particle trajectories in two-phase flow systems. J Fluid Mech 55:193-208
- Patankar SV (1980) Numerical heat transfer and fluid flow. Hemi- sphere, Washington
- Reimann P (2002) Brownian motors: noisy transport far from equilibrium. Phys Rep 361:57-265
- Sahimi M (1995) Flow and transport in porous media and fractured rock. VCH, Boston
- Smith KA, Alexeev A, Verberg R, Balazs AC (2006) Designing a simple ratcheting system to sort microcapsules by mechanical properties. Langmuir 22:6739-6742
- Takagi J, Yamada M, Yasuda M, Seki M (2005) Continuous particle separation in a microchannel having asymmetrically arranged multiple branches. Lab Chip 5:778-784
- van Oudenaarden A, Boxer SG (1999) Brownian ratchet: molecular separations in liquid bilayers supported on patterned arrays. Science 285:1046-1048
- Vasconcelos TF, Arau ´jo AD, Almeida MP, Andrade JS Jr (2009) Particle transport in rough channels. Int J Mod Phys C 20:1199-1209
- Vasconcelos TF, Morais AF, Cisne RLC Jr, Parteli EJR, Andrade JS Jr (2010) Particle separation in a ramified structure. Chem Eng Sci 65:1400-1406
- Wickramasinghe SR, Lin WC, Dandy DS (2001) Separation of different sized particles by inertial migration. Biotech Lett 23:1417-1422
- Yamada M, Nakashima M, Seki M (2004) Pinched flow fractionation: continuous size separation of particles utilizing a laminar flow profile in a pinched microchannel. Anal Chem 76:5465-5471