Numerical study of the formation process of ferrofluid droplets

This paper numerically investigates the influence of a uniform magnetic field on the dropletformation process at a microfluidicflow focusing configuration. The mathematical model was formulated by considering the balance of forces such as interfacial tension, magnetic force, and viscous stress across the liquid/liquid interface. A linearly magnetizable fluid was assumed. The magnetic force acts as a body force where the magnetic permeability jumps across the interface. The governing equations were solved with finite volume method on a Cartesian fixed staggered grid. The evolution of the interface was captured by the particle level set method. The code was validated with the equilibrium steady state of a ferrofluiddroplet exposed to a uniform magnetic field. The evolution of the dropletformation in a flow focusing configuration was discussed. The paper mainly analyzes the effects of magnetic Bond number and the susceptibility on the velocity field and the droplet size. The droplet size increased with increasing magnetic strength and susceptibility.

[1]  Helen Song,et al.  Reactions in droplets in microfluidic channels. , 2006, Angewandte Chemie.

[2]  John C. Chai,et al.  A Global Mass Correction Scheme for the Level-Set Method , 2006 .

[3]  Mario De Menech,et al.  Modeling of droplet breakup in a microfluidic T-shaped junction with a phase-field model. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  H. Udaykumar,et al.  A particle-level set-based sharp interface cartesian grid method for impact, penetration, and void collapse , 2004 .

[5]  Aya Eid,et al.  Light-driven formation and rupture of droplet bilayers. , 2010, Langmuir : the ACS journal of surfaces and colloids.

[6]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[7]  Amit Gupta,et al.  Effect of geometry on droplet formation in the squeezing regime in a microfluidic T-junction , 2010 .

[8]  N. Gershenfeld,et al.  Microfluidic Bubble Logic , 2006, Science.

[9]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[10]  R. Boom,et al.  Lattice Boltzmann simulations of droplet formation in a T-shaped microchannel. , 2006, Langmuir : the ACS journal of surfaces and colloids.

[11]  Michihisa Tsutahara,et al.  Three-dimensional lattice Boltzmann simulations of droplet formation in a cross-junction microchannel , 2008 .

[12]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[13]  Fluorescence lifetime imaging of mixing dynamics in continuous-flow microdroplet reactors. , 2008, Physical review letters.

[14]  G. Whitesides,et al.  Solvent compatibility of poly(dimethylsiloxane)-based microfluidic devices. , 2003, Analytical chemistry.

[15]  Jianhong Xu,et al.  Preparation of highly monodisperse droplet in a T‐junction microfluidic device , 2006 .

[16]  Nam-Trung Nguyen,et al.  Formation and manipulation of ferrofluid droplets at a microfluidic T-junction , 2010 .

[17]  Mario De Menech.  Modeling of droplet breakup in a microfluidic T-shaped junction with a phase-field model , 2006 .

[18]  Bogdan G. Nita,et al.  Modeling bubbles and droplets in magnetic fluids , 2008, Journal of physics. Condensed matter : an Institute of Physics journal.

[19]  J. Sethian,et al.  FRONTS PROPAGATING WITH CURVATURE DEPENDENT SPEED: ALGORITHMS BASED ON HAMILTON-JACOB1 FORMULATIONS , 2003 .

[20]  François Gallaire,et al.  Thermocapillary valve for droplet production and sorting. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Armand Ajdari,et al.  Microfluidic bypass for efficient passive regulation of droplet traffic at a junction , 2006 .

[22]  Helen Song,et al.  A microfluidic system for controlling reaction networks in time. , 2003, Angewandte Chemie.

[23]  G. Whitesides,et al.  Formation of droplets and bubbles in a microfluidic T-junction-scaling and mechanism of break-up. , 2006, Lab on a chip.

[24]  Frederick Stern,et al.  An improved particle correction procedure for the particle level set method , 2009, J. Comput. Phys..

[25]  Yuriko Renardy,et al.  Field-induced motion of ferrofluid droplets through immiscible viscous media , 2008, Journal of Fluid Mechanics.

[26]  François Gallaire,et al.  Microchannel deformations due to solvent-induced PDMS swelling. , 2010, Lab on a chip.

[27]  Andrew D Griffiths,et al.  Directed evolution by in vitro compartmentalization , 2006, Nature Methods.

[28]  H. Stone,et al.  Transition from squeezing to dripping in a microfluidic T-shaped junction , 2008, Journal of Fluid Mechanics.

[29]  S. Venkatraman,et al.  The deformation behavior of poly (dimethyl siloxane) networks. II: Equilibrium swelling , 1994 .

[30]  S. Osher,et al.  Regular Article: A PDE-Based Fast Local Level Set Method , 1999 .

[31]  C. Ho,et al.  Fluidics-the link between micro and nano sciences and technologies , 2001, Technical Digest. MEMS 2001. 14th IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.01CH37090).

[32]  Danping Peng,et al.  Weighted ENO Schemes for Hamilton-Jacobi Equations , 1999, SIAM J. Sci. Comput..

[33]  Andrew D Griffiths,et al.  Miniaturising the laboratory in emulsion droplets. , 2006, Trends in biotechnology.

[34]  Brian N. Johnson,et al.  An integrated nanoliter DNA analysis device. , 1998, Science.

[35]  U. Lehmann,et al.  Two dimensional magnetic manipulation of microdroplets on a chip , 2005, The 13th International Conference on Solid-State Sensors, Actuators and Microsystems, 2005. Digest of Technical Papers. TRANSDUCERS '05..

[36]  Nam-Trung Nguyen,et al.  Manipulation of ferrofluid droplets using planar coils , 2006 .

[37]  Nam-Trung Nguyen,et al.  Thermally mediated control of liquid microdroplets at a bifurcation , 2009 .

[38]  G. Luo,et al.  Microfluidic approach for rapid interfacial tension measurement. , 2008, Langmuir : the ACS journal of surfaces and colloids.

[39]  Nam-Trung Nguyen,et al.  Thermocapillary Effect of a Liquid Plug in Transient Temperature Fields , 2005 .

[40]  Nam-Trung Nguyen,et al.  Magnetowetting and sliding motion of a sessile ferrofluid droplet in the presence of a permanent magnet. , 2010, Langmuir : the ACS journal of surfaces and colloids.

[41]  Jennifer E. Curtis,et al.  Dynamic holographic optical tweezers , 2002 .

[42]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[43]  S. Cho,et al.  Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits , 2003 .

[44]  Gunar Matthies,et al.  Numerical treatment of free surface problems in ferrohydrodynamics , 2006 .

[45]  Ian M. Mitchell,et al.  A hybrid particle level set method for improved interface capturing , 2002 .

[46]  O. Séro-Guillaume,et al.  The shape of a magnetic liquid drop , 1992, Journal of Fluid Mechanics.

[47]  George M. Whitesides,et al.  Coding/Decoding and Reversibility of Droplet Trains in Microfluidic Networks , 2007, Science.

[48]  David McGloin,et al.  Thermocapillary manipulation of droplets using holographic beam shaping: Microfluidic pin ball , 2008 .

[49]  J. Brancher,et al.  Equilibrium of a magnetic liquid drop , 1987 .

[50]  S. Osher,et al.  Regular Article: A PDE-Based Fast Local Level Set Method , 1999 .

[51]  A. R. Kaiser,et al.  Microfabricated structures for integrated DNA analysis. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[52]  Fu-jun Wang,et al.  Investigation of viscosity effect on droplet formation in T-shaped microchannels by numerical and analytical methods , 2009 .

[53]  G. Whitesides.  The origins and the future of microfluidics , 2006, Nature.

[54]  D. Beebe,et al.  Controlled microfluidic interfaces , 2005, Nature.

[55]  Nam-Trung Nguyen,et al.  Thermally mediated droplet formation in microchannels , 2007 .

[56]  N. Nguyen,et al.  Motion of a droplet through microfluidic ratchets. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[57]  Jean-Pierre Delville,et al.  An optical toolbox for total control of droplet microfluidics. , 2007, Lab on a chip.

[58]  R. Austin,et al.  Hydrodynamic Focusing on a Silicon Chip: Mixing Nanoliters in Microseconds , 1998 .

[59]  Rustem F Ismagilov,et al.  A synthetic reaction network: chemical amplification using nonequilibrium autocatalytic reactions coupled in time. , 2004, Journal of the American Chemical Society.