^{1}and Nina C. Shapley

^{1}

### Abstract

This study presents an experimental investigation into particle migration behavior of concentrated suspensions of noncolloidal spheres in oscillatory torsional flows between parallel plates. Video imaging of the radial drift velocity of dyed tracer particles in a monodisperse, 0.4 bulk particle volume fraction suspension was performed during flow evolution. In conjunction with simultaneous rheological measurements, particle tracking provided insight into migration phenomena. For all of the cases studied, the average displacement of the tracer particles per cycle was directed radially outward and was approximately a linear function of the oscillatory strain amplitude while also varying with the frequency of oscillation in a nearly inverse square relationship. The measured radial migration velocity exceeded that estimated from the suspension balance continuum model for a corresponding steady flow, likely due to the increased microstructural mobility developed during oscillatory flow. Generally, the oscillatory torque increased as the flow evolved, while local minima in the torque ratio and radial drift velocity were detected at intermediate strain values, in agreement with recent studies of oscillatory flow. The results suggest the competition between radial shear-induced particle migration driven by the overall particle stress balance and rearrangement of particles into an ordered microstructure driven by local interactions.

Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for support of this research. Support for K.D. was also provided by the NSF IGERT program in Nanopharmaceutical Engineering Grant No. DGE-0504497 and the NSF ERC on Structured Organic Particulate Systems (C-SOPS) Grant No. EEC-0540855. In addition, the authors gratefully acknowledge the use of equipment (rheometer) in the Department of Chemical Engineering, Columbia University, acquired through the NSF IGERT program Grant No. RFCUNY 404340001A.

I. INTRODUCTION

II. EXPERIMENTAL METHODS

A. Materials

B. Experimental apparatus and procedure

C. Fluid rheology

D. Image analysis

III. RESULTS

A. Radial drift velocity

B. Torque evolution

IV. DISCUSSION

A. Comparison of oscillatory and steady torsional flows

B. Comparison to model calculations

C. Viscoelastic effects

D. Oscillation amplitude effects on microstructure

V. CONCLUSIONS

### Key Topics

- Suspensions
- 76.0
- Torque
- 73.0
- Radial velocities
- 36.0
- Shear rate dependent viscosity
- 22.0
- Viscosity
- 19.0

## Figures

Schematic view of the experimental setup.

Schematic view of the experimental setup.

(a) Steady shear rheology of the suspending fluid (solid diamonds) and particle volume fraction suspension (hollow triangles). (b) Elastic and loss moduli of the suspending fluid at 5% strain amplitude: (solid triangles), (solid squares), reversed (hollow triangles), and reversed (hollow squares).

(a) Steady shear rheology of the suspending fluid (solid diamonds) and particle volume fraction suspension (hollow triangles). (b) Elastic and loss moduli of the suspending fluid at 5% strain amplitude: (solid triangles), (solid squares), reversed (hollow triangles), and reversed (hollow squares).

Three images demonstrating radial particle drift during oscillatory flow with strain and . Particles used for drift velocity calculation are marked A, B, and C. The images were acquired (i) 1500 s, (ii) 6000 s, and (iii) after the start of oscillatory flow. The radial direction is vertically upward in the images.

Three images demonstrating radial particle drift during oscillatory flow with strain and . Particles used for drift velocity calculation are marked A, B, and C. The images were acquired (i) 1500 s, (ii) 6000 s, and (iii) after the start of oscillatory flow. The radial direction is vertically upward in the images.

Evolution of radial trajectories of the three particles shown in Fig. 3 at each time after the start of oscillatory flow. The time axis has the same meaning as in Fig. 3 above, without any shifting of the origin.

Evolution of radial trajectories of the three particles shown in Fig. 3 at each time after the start of oscillatory flow. The time axis has the same meaning as in Fig. 3 above, without any shifting of the origin.

(a) Radial drift velocity and (b) radial displacement per cycle as a function of strain amplitude for oscillation frequencies of (solid squares) and (hollow squares).

(a) Radial drift velocity and (b) radial displacement per cycle as a function of strain amplitude for oscillation frequencies of (solid squares) and (hollow squares).

(a) Radial drift velocity and (b) radial displacement per cycle as a function of oscillation frequency, strain amplitude . In (b), solid line represents the function and dashed line represents the function .

(a) Radial drift velocity and (b) radial displacement per cycle as a function of oscillation frequency, strain amplitude . In (b), solid line represents the function and dashed line represents the function .

Normalized torque evolution curve: strain amplitude and .

Normalized torque evolution curve: strain amplitude and .

(a) Normalized torque value as a function of strain amplitude, the ratio of final torque to initial minimum torque for (solid triangles) and (hollow squares), and the ratio of torque at a total strain of 1930 and initial minimum torque for (hollow triangles) and (x). Dashed line represents the calculated final torque ratio based on the fully developed concentration profile predicted by the suspension balance model. (b) Final/minimum torque ratio as a function of oscillation frequency, strain .

(a) Normalized torque value as a function of strain amplitude, the ratio of final torque to initial minimum torque for (solid triangles) and (hollow squares), and the ratio of torque at a total strain of 1930 and initial minimum torque for (hollow triangles) and (x). Dashed line represents the calculated final torque ratio based on the fully developed concentration profile predicted by the suspension balance model. (b) Final/minimum torque ratio as a function of oscillation frequency, strain .

Measured radial drift velocity for oscillation frequencies of (solid squares) and (hollow squares) and strain amplitude of 0.415 (stars), compared to the estimated initial migration velocity in steady flow, based on the suspension balance model, at the same average velocities corresponding to the oscillatory flows (solid line). The estimated secondary flow velocity for a Newtonian fluid at low Reynolds number in the infinite plate limit (McCoy and Denn, 1971) is also shown (dashed line).

Measured radial drift velocity for oscillation frequencies of (solid squares) and (hollow squares) and strain amplitude of 0.415 (stars), compared to the estimated initial migration velocity in steady flow, based on the suspension balance model, at the same average velocities corresponding to the oscillatory flows (solid line). The estimated secondary flow velocity for a Newtonian fluid at low Reynolds number in the infinite plate limit (McCoy and Denn, 1971) is also shown (dashed line).

## Tables

Parameters for oscillatory flow experiments.

Parameters for oscillatory flow experiments.

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