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Models for slow flow of dense granular materials often treat the medium as incompressible, thereby neglecting the role of Reynolds dilatancy. However, recent particle simulations have demonstrated the presence of a significant coupling between the volume fraction and velocity fields. The model of Dsouza & Nott (J. Fluid Mech., vol. 888, 2020, R3) incorporates dilatancy and captures the coupling, but it has thus far lacked experimental validation. In this paper, we provide the first experimental demonstration of dilatancy and its coupling to the kinematics in a two-dimensional cylindrical Couette cell. We find a shear layer near the inner cylinder within which there is significant dilation. Within the shear layer, the azimuthal velocity decays roughly exponentially and the volume fraction rises with radial distance from the inner cylinder. The predictions of the model of Dsouza & Nott (2020) are in good agreement with the experimental data for a variety of roughness features of the outer cylinder. Moreover, by comparing the steady states resulting from different initial volume fraction profiles (but having the same average), we show the inter-dependence of the velocity and volume fraction fields, as predicted by the model. Our results establish the importance of shear dilatancy even in systems of constant volume.
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Imaging of localized whispering-gallery-modes in a cylindrical fiber
Modes of a dielectric cylindrical waveguide are characterized by three numbers: azimuthal numberm, radial number,s, and a continuous propagation constantβ.1The azimuthal number determines the field dependence of the azimuthal angleφof the cylindrical coordinate system with the polar axis along the axis of the cylinder in the form of exp (imφ). The radial number characterizes the behavior of the field in the radial direction and in an ideal cylinder is given by a cylindrical Bessel functionJm(κm,sr). Discrete values of the parameterκscharacterizing the radial dependence of the field is determined by Maxwell boundary conditions. The propagation constantβdescribes the propagation of the mode along the axis of the fiber (Z-axis of the cylindrical coordinate system).
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- Award ID(s):
- 2102249
- PAR ID:
- 10598442
- Publisher / Repository:
- Optica Publishing Group
- Date Published:
- ISBN:
- 978-1-957171-39-5
- Page Range / eLocation ID:
- JW2A.66
- Format(s):
- Medium: X
- Location:
- Charlotte, North Carolina
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1364/cleo_at.2024.jw2a.66
