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Research Papers: Flows in Complex Systems

Detailed Description of Electro-Osmotic Effect on an Encroaching Fluid Column Inside a Narrow Channel

[+] Author and Article Information
Rakhitha Udugama Sumanasekara

Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: rakhitha.udugama-arachchilage@ttu.edu

Sukalyan Bhattacharya

Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: s.bhattacharya@ttu.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 15, 2017; final manuscript received February 28, 2018; published online May 2, 2018. Assoc. Editor: Moran Wang.

J. Fluids Eng 140(9), 091105 (May 02, 2018) (12 pages) Paper No: FE-17-1276; doi: 10.1115/1.4039708 History: Received May 15, 2017; Revised February 28, 2018

This paper uses eigenexpansion technique to describe electro-osmotic effect on unsteady intrusion of a viscous liquid driven by capillary action in a narrow channel. It shows how the dynamics can be manipulated by imposing an electric field along the flow direction in the presence of free charges. Similar manipulation can generate controlled transiency in motion of a complex fluid in a tube by nondestructive forcing leading to efficient rheological measurement. Existing theories analyze similar phenomena by accounting for all involved forces among which the viscous contribution is calculated assuming a steady velocity profile. However, if the transport is strongly transient, a new formulation without an underlying quasi-steady assumption is needed for accurate prediction of the time-dependent penetration. Such rigorous mathematical treatment is presented in this paper where an eigenfunction expansion is used to represent the unsteady flow. Then, a system of ordinary differential equations is derived from which the unknown time-dependent amplitudes of the expansion are determined along with the temporal variation in encroached length. The outlined methodology is applied to solve problems with both constant and periodically fluctuating electric field. In both cases, simplified and convenient analytical models are constructed to provide physical insight into numerical results obtained from the full solution scheme. The detailed computations and the simpler reduced model corroborate each other verifying accuracy of the former and assuring utility of the latter. Thus, the theoretical findings can render a new rheometric technology for effective determination of fluid properties.

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References

Kestin, J. , Sokolov, M. , and Wakeham, W. , 1973, “ Theory of Capillary Viscometers,” Appl. Sci. Res., 27(1), pp. 241–264. [CrossRef]
Boukellal, G. , Durin, A. , Valette, R. , and Agassant, J. , 2011, “ Evaluation of a Tube-Based Constitutive Equation Using Conventional and Planar Elongation Flow Optical Rheometers,” Rheol. Acta, 50(5–6), pp. 547–557. [CrossRef]
Perez-Orozco, J. , Beristain, C. , Espinosa-Paredes, G. , Lobato-Calleros, C. , and Vernon-Carter, E. , 2004, “ Interfacial Shear Rheology of Interacting Carbohydrate Polyelectrolytes at the Water-Oil Interface Using an Adapted Conventional Rheometer,” Carbohydr. Polym., 57(1), pp. 45–54. [CrossRef]
Ts, N. , 1986, “ A Comparative Study of the Extensional Rheometer Results on Rubber Compounds With Values Obtained by Conventional Industrial Measuring Methods,” Kautsch. Gummi Kunstst., 39, pp. 830–833.
Mason, T. G. , Ganeshan, K. , van Zanten, J. , Wirtz, D. , and Kuo, S. , 1997, “ Particle Tracking Microrheology of Complex Fluid,” Phys. Rev. Lett., 79(17), pp. 3282–3285. [CrossRef]
Mason, T. G. , 2000, “ Estimating the Viscoelastic Moduli of Complex Fluids Using the Generalized Stokes-Einstein Equation,” Rheol. Acta, 39(4), pp. 371–378. [CrossRef]
Squires, T. M. , 2008, “ Nonlinear Microrheology: Bulk Stresses Versus Direct Interactions,” Langmuir, 24(4), pp. 1147–1159. [CrossRef] [PubMed]
Koser, A. E. , and Pan, L. C. , 2013, “ Measuring Material Relaxation and Creep Recovery in a Microfluidic Device,” Lab Chip, 13(10), pp. 1850–1853. [CrossRef] [PubMed]
Kang, Y. J. , and Lee, S. J. , 2013, “ Blood Viscoelasticity Measurement Using Steady and Transient Flow Controls of Blood in a Microfluidic Analogue of Wheastone-Bridge Channel,” Biomicrofluidics, 7(5), p. 054122. [CrossRef]
Zilz, J. , Schafer, C. , Wagner, C. , Poole, R. J. , Alves, M. A. , and Linder, A. , 2014, “ Serpentine Channels: Micro-Rheometers for Fluid Relaxation Times,” Lab Chip, 14(2), pp. 351–358. [CrossRef] [PubMed]
Groisman, A. , Enzelberger, M. , and Quake, S. R. , 2003, “ Microfluidic Memory and Control Devices,” Science, 300(5621), pp. 955–958. [CrossRef] [PubMed]
Washburn, E. W. , 1921, “ The Dynamics of Capillary Flow,” Phys. Rev., 17(3), pp. 273–283. [CrossRef]
Lucas, R. , 1918, “ Ueber das Zeitgesetz des kapillaren Aufstiegs von Flussigkeiten,” Kolloid-Z., 23(1), pp. 15–22. [CrossRef]
Szekely, J. , Neumann, A. W. , and Chuang, Y. K. , 1970, “ The Rate of Capillary Penetration and the Applicability of the Washburn Equation,” J. Colloid Interface Sci., 35(2), pp. 273–278. [CrossRef]
Chebbi, R. , 2007, “ Dynamics of Liquid Penetration Into Capillary Tubes,” J. Colloid Interface Sci., 315(1), pp. 255–260. [CrossRef] [PubMed]
Waghmare, P. R. , and Mitra, S. K. , 2008, “ Investigation of Combined Electro-Osmotic and Pressure Driven Flow in Rough Microchannels,” ASME J. Fluids Eng., 130(6), p. 061204. [CrossRef]
Waghmare, P. R. , and Mitra, S. K. , 2010, “ On the Derivation of Pressure Field Distribution at the Entrance of a Rectangular Capillary,” ASME J. Fluids Eng., 132(5), p. 054502. [CrossRef]
Waghmare, P. R. , and Mitra, S. K. , 2010, “ Modeling of Combined Electro-Osmotic and Capillary Flow in Microchannels,” Anal. Chim. Acta, 663(2), pp. 117–126. [CrossRef] [PubMed]
Das, S. , Waghmare, P. R. , and Mitra, S. K. , 2012, “ Early Regimes of Capillary Filling,” Phys. Rev. E, 86(6), p. 067301. [CrossRef]
Bhattacharya, S. , Azese, M. N. , and Singha, S. , 2016, “ Rigorous Theory for Transient Capillary Imbibition in Channels of Arbitrary Cross Section,” Theor. Comput. Fluid Dyn., 31(2), pp. 137–157.
Ichikawa, N. , and Satoda, Y. , 1993, “ Interface Dynamics of Capillary Flow in a Tube Under Negligible Gravity Condition,” J. Colloid Interface Sci., 162(2), pp. 350–355. [CrossRef]
Marmur, A. , and Cohen, R. D. , 1997, “ Characterization of Porous Media by the Kinetics of Liquid Penetration: The Vertical Capillaries Model,” J. Colloid Interface Sci., 189(2), pp. 299–304. [CrossRef]
Barry, D. A. , Parlange, J. Y. , Sander, G. C. , and Sivaplan, M. , 1993, “ A Class of Exact Solutions of Richard's Equation,” J. Hydrol., 142(1–4), pp. 29–46. [CrossRef]
Zhmud, B. V. , Tiberg, F. , and Hallstensson, K. , 2000, “ Dynamics of Capillary Rise,” J. Colloid Interface Sci., 228(2), pp. 263–269. [CrossRef] [PubMed]
Mawardi, A. , Xiao, Y. , and Pitchumani, R. , 2008, “ Theoretical Analysis of Capillary-Driven Nanoparticulate Slurry Flow During a Micromold Filling Process,” Int. J. Multiphase Flow, 34(3), pp. 227–240. [CrossRef]
Housiadas, K. , Georgiou, G. , and Tsamopoulos, J. , 2000, “ The Steady Annular Extrusion of a Newtonian Liquid Under Gravity and Surface Tension,” Int. J. Numer. Methods Fluids, 33(8), pp. 1099–1119. [CrossRef]
Mitsoulis, E. , and Heng, F. L. , 1987, “ Extrudate Swell of Newtonian Fluids From Converging and Diverging Annular Dies,” Rheol. Acta, 26(5), pp. 414–417. [CrossRef]
Ichikawa, N. , Hosokawa, K. , and Maeda, R. , 2004, “ Interface Motion of Capillary Driven Flow in Rectangular Microchannel,” J. Colloid Interface Sci., 280(1), pp. 155–164. [CrossRef] [PubMed]
Fabiano, W. G. , Santos, L. O. E. , and Philippi, P. C. , 2010, “ Capillary Rise Between Parallel Plates Under Dynamic Conditions,” J. Colloid Interface Sci., 344(1), pp. 171–179. [CrossRef] [PubMed]
Bławzdziewicz, J. , and Bhattacharya, S. , 2003, “ Comment on ‘Drift Without Flux: Brownian Walker With a Space-Dependent Diffusion Coefficient’,” Europhys. Lett., 63(5), pp. 789–90. [CrossRef]
Bhattacharya, S. , and Blawzdziewicz, J. , 2008, “ Effect of Smaller Species on the Near-Wall Dynamics of a Large Particle in Bidispersed Solution,” J. Chem. Phys., 128(21), p. 214704. [CrossRef] [PubMed]
Navardi, S. , and Bhattacharya, S. , 2010, “ Effect of Confining Conduit on Effective Viscosity of Dilute Colloidal Suspension,” J. Chem. Phys., 132(11), p. 114114. [CrossRef] [PubMed]
Navardi, S. , and Bhattacharya, S. , 2010, “ A New Lubrication Theory to Derive Far-Field Axial Pressure-Difference Due to Force Singularities in Cylindrical or Annular Vessels,” J. Math. Phys., 51(4), p. 043102. [CrossRef]
Jong, W. R. , Kuo, T. H. , Ho, S. W. , Chiu, H. H. , and Peng, S. H. , 2007, “ Flows in Rectangular Microchannels Driven by Capillary Force and Gravity,” Int. Commun. Heat Mass Transfer, 34(2), pp. 186–196. [CrossRef]
Navardi, S. , and Bhattacharya, S. , 2010, “ Axial Pressure-Difference Between Far-Fields Across a Sphere in Viscous Flow Bounded by a Cylinder,” Phys. Fluid, 22(10), p. 103306. [CrossRef]
Bhattacharya, S. , Gurung, D. , and Navardi, S. , 2013, “ Radial Distribution and Axial Dispersion of Suspended Particles Inside a Narrow Cylinder Due to Mildly Inertial Flow,” Phys. Fluids, 25(3), p. 033304. [CrossRef]
Bhattacharya, S. , Gurung, D. , and Navardi, S. , 2013, “ Radial Lift on a Suspended Finite Sized Sphere Due to Fluid Inertia for Low Reynolds Number Flow Through a Cylinder,” J. Fluid Mech., 722, pp. 159–186. [CrossRef]
Bhattacharya, S. , and Gurung, D. , 2010, “ Derivation of Governing Equation Describing Time-Dependent Penetration Length in Channel Flows Driven by Non-Mechanical Forces,” Anal. Chim. Acta, 666(1–2), pp. 51–54. [CrossRef] [PubMed]
Azese, M. N. , 2011, “ Modified Time Dependent Penetration Length and Inlet Pressure Field in Rectangular and Cylindrical Channel Flows Driven by Non Mechanical Forces,” ASME J. Fluids Eng., 133(11), p. 111205. [CrossRef]
Sumanasekara, U. , Azese, M. , and Bhattacharya, S. , 2017, “ Transient Penetration of a Viscoelastic Fluid in a Narrow Capillary Channel,” J. Fluid Mech., 830, pp. 528–552. [CrossRef]
Stange, M. , Dreyer, M. E. , and Rath, H. J. , 2003, “ Capillary Driven Flow in Circular Cylindrical Tubes,” Phys. Fluids, 15(9), pp. 2587–2601. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

The schematic diagram of the system considered in our analysis where a horizontal capillary channel transports fluid from a drop with free surface due to the action of surface tension and electro-osmotic effects

Grahic Jump Location
Fig. 2

Penetration length is plotted as function of time for facilitating (solid line), opposing (dash-dot line) and neutral (dotted line) electric potentials with l¯=10 (a) and l¯=30 (b)

Grahic Jump Location
Fig. 3

Penetration rate is plotted as function of time for facilitating (solid line), opposing (dash-dot line) and neutral (dotted line) electric potentials with l¯=10 (a) and l¯=30 (b)

Grahic Jump Location
Fig. 4

Computed values (solid line) of first-order penetration length are compared with its approximate analytical expression in Eq. (29) (dotted line) for opposing (top) and facilitating (bottom) electric potentials with l¯=10 (left figure) and l¯=30 (right figure)

Grahic Jump Location
Fig. 5

Computed values (solid line) of first-order penetration rate are compared with its approximate analytical expression (dotted line) for opposing (top) and facilitating (bottom) electric potentials with l¯=10 (left figure) and l¯=30 (right figure)

Grahic Jump Location
Fig. 6

Penetration lengths are plotted as functions of time for Sl = 4.0 (a), 1.0 (b), and 0.25 (c) with l¯=10 (solid line), 20 (dotted line) and 30 (dashed line)

Grahic Jump Location
Fig. 7

Penetration rates are plotted as functions of time for Sl = 4.0 (a), 1.0 (b) and 0.25 (c) with l¯=10 (solid line), 20 (dotted line) and 30 (dashed line)

Grahic Jump Location
Fig. 8

Penetration length is plotted as function of renormalized t¯ for Sl = 0.25 (solid line), 1.0 (dotted line), 4.0 (dash-dot line) with l¯=20

Grahic Jump Location
Fig. 9

Penetration rate is plotted as function of renormalized t¯ for Sl = 0.25 (solid line), 1.0 (dotted line), 4.0 (dash-dot line) with l¯=20

Grahic Jump Location
Fig. 10

The amplitude (C¯), phase (θ¯), and time-dependent variable f¯k defined in Eq. (38) are presented as functions of Strouhal number

Grahic Jump Location
Fig. 11

Computed (dotted line) and analytical expressions (dashed line) in Eqs. (35)(38) for first-order penetration lengths (left panel) and penetration rates (right panel) are plotted as functions of time where Sl = 4.0 (top), 1.0 (middle), and 0.25 (bottom) with l¯=20

Grahic Jump Location
Fig. 12

Relative error for first-order penetration length (left) and penetration rate (right) in Eq. (39) are plotted as functions of time for Sl = 0.25 (dotted line), 1.0 (dashed-dotted line) and 4.0 (solid line) with l¯=20

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