Chapter 20
Viscous Fingering of Silica Suspensions Dispersed in Polymer Fluids Downloaded by PENNSYLVANIA STATE UNIV on September 12, 2012 | http://pubs.acs.org Publication Date: November 18, 2003 | doi: 10.1021/bk-2004-0869.ch020
Masami Kawaguchi Department of Chemistry for Materials, Faculty of Engineering, Mie University, Mie 514-8505, Japan
We make an experimental study of the viscous fingering of shear thinning silica suspensions in a radial Hele-Shaw cell and shear thickening silica suspensions in a linear Hele-Shaw cell injected by air. For the shear thinning silica suspensions, the viscous fingering instability is strongly related to the polymer concentration in the dispersant rather than the silica concentration. For the shear thickening silica suspensions, the imposed shear rate at which the viscous fingering instability is observed for the first time, is close to the critical shear rate of the corresponding shear thickening silica suspensions. The finger velocities of the shear thinning silica suspensions are in agreement with the modified Darcy's law, where the constant viscosity is replaced by the shear rate dependent viscosity. On the other hand, the finger velocities of the shear thickening silica suspensions with the silica concentrations larger than 7.5 wt % are much lower than the prediction of the modified Darcy's law.
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© 2004 American Chemical Society
In Nonlinear Dynamics in Polymeric Systems; Pojman, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.
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Downloaded by PENNSYLVANIA STATE UNIV on September 12, 2012 | http://pubs.acs.org Publication Date: November 18, 2003 | doi: 10.1021/bk-2004-0869.ch020
Introduction Motion of a fluid produces a variety of spatio-temporal shapes (pattern) in nature: flowing clouds with changes in their shapes, traveling an air bubble in a bottle filled with water, and burning flames. On the other hand, in a quasi-two dimensional space, one of the simplest problems of fluid motion is the Saffman-Taylor problem in which two fluids move in the narrow space between two plates (/), namely in a Hele-Shaw cell (2). Pressure gradient driven pattern formation of an interface between two fluids in Hele-Shaw cells, viscous fingering occurs when a more viscous fluid is displaced by a less viscous fluid injected. Viscous fingering produces pattern formation far from equilibrium, it is a model system for flow through porous media, and it can be related to the recovery of crude oils in oil wells as well as the blowing process of plastic products. Viscous fingering in Newtonian fluids has been theoretically and experimentally well understood and the developments of the viscous fingering in Newtonian fluids have been deeply reviewed (3-5). On the other hand, during recent two decades several research groups have paid much attentions to investigate the viscous fingering non-Newtonian fluids (5-7), such as polymer solutions, liquid crystals, forms, gels, and suspenstions, but our knowledge has been little in comparison with that of Newtonian ones due to their complex rheological properties. In this study, we report viscous fingering experiments of two silica suspensions dispersed in polymer fluids: one is a silica suspension dispersed in aqueous hydroxylpropyl methyl cellulose (HPMC) solution and it shows shear thinning behavior; the other is a silica suspension dispersed in poly propylene glycol (PPG) and it indicates shear thickening response. We describe their viscous fingering instabilities in terms of changes in pattern morphology and finger pattern growth by taking into account the rheological responses of two silica suspensions.
Experimental
Materials
An HPMC sample kindly supplied by Shin-Estu Chemical Co. was purified by the method described previously (8) and its molecular weight was determined to be 250x10 by the intrinsic viscosity measurement. PPG with the molecular weight of 725 was purchased from the Aldrich Chemical Co. and it was used without further purification. Silica suspensions were prepared by mechanically 3
In Nonlinear Dynamics in Polymeric Systems; Pojman, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.
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mixed Aerosil 130 silica powder supplied from the Japan Aerosil Co. with aqueous HPMC solutions of different concentrations (HPMC-silica suspension) and with PPG (PPG-silica suspension). The silica concentrations in the former suspensions were fixed at 5.0, 7.5, and 10.0 wt %, whereas the silica contents of the latter suspensions were 2.5, 5.0, 7.5, and 10.0 wt %. Moreover, the concentrations of HPMC in the supernatants of the HPMC-silica suspensions should be lower than those in the prepared HPMC solutions, since HPMC chains are adsorbed on the silica surfaces (9).
Instrumentations The viscous fingering experiments were performed at 25 °C using two HeleShaw cells: a radial cell made by using two plane-glass plates (0.8x50x35 cm ) with a silicon wafer spacer of 0.05 cm thickness clamped in between the plates (10); a linear cell made of the same two glass plates as the radial cell, clamped along their sides with a U-shaped silicone rubber sheet (0.05x50x15 cm ) and with silicon wafer spacers of 0.05 cm thickness in between the plates (//). In the linear cell, the width of the channel was fixed at 3 cm by using the rubber sheet. The HPMC-silica suspension was injected through the inlet at the center of the top plate for the radial cell to form a 10 cm sample radius, whereas for the linear cell the PPG-silica suspension was injected into the inlet at the distance L of 20 cm from the short unsealed edge of the top plate. Air was injected through the inlet at the fixed injection pressure of 5.0 kPa for the HPMC-silica suspensions, whereas for the PPG-silica suspensions the injection pressures were changed from 1.0 to 30 kPa. The generated patterns were recorded with a CCD camera-recorder method. The images of the recorded patterns were analyzed by a Himawari-60 digital image analyzer. Rheological measurements of the silica suspensions were performed using a Paar Physica MCR300 rheometer with a cone-plate geometry. 3
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Results and Discussion
HPMC-Silica Suspensions HPMC chains adsorb onto the silica surface (9) and their adsorbed amounts are determined to be ca. 0.12g/g, irrespective of the silica concentration and HPMC. Figure 1 displays steady-state shear viscosities of the 5.0, 7.5, and 10.0 wt % silica suspensions dispersed in a 1.5g/100 mL HPMC solution, where the HPMC concentrations in the supernatants are 0.90, 0.60, and 0.30 g/100 mL in
In Nonlinear Dynamics in Polymeric Systems; Pojman, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.
Downloaded by PENNSYLVANIA STATE UNIV on September 12, 2012 | http://pubs.acs.org Publication Date: November 18, 2003 | doi: 10.1021/bk-2004-0869.ch020
253 order of the silica content, as a function of the shear rate, together with that of 1.5 g/100 mL HPMC solution. The HPMC solution shows the existence of a Newtonian region followed by the weak shear thinning. The silica suspensions show shear-thinning behavior typical for aggregated suspensions. This is attributed to the mechanical strength of the aggregated silica suspensions, whose structure was a fractal-like, as determined by small-angle neutron scattering measurement (9). Moreover, the HPMC-silica suspensions show solid-like viscoelastic responses: their dynamic storage moduli G' are larger than the dynamic loss moduli G" at small and linear strain ranges. On the other hand, the HPMC solution has much larger values of G" than G' in thefrequencyranges from 0.1 to 100 rad/s due to liquid-like viscoelastic matter. 10'
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