A Smoluchowski equation for a sheared suspension of frictionally interacting rods
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914217880190976 |
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| author | Quiñones, Chris Olmsted, Peter D. |
| author_facet | Quiñones, Chris Olmsted, Peter D. |
| contents | In this work we develop constitutive equations for a dense, sheared suspension of frictionally interacting rods by applying Onsager's variational method as formulated by Doi. We treat both solid friction, of the Amontons-Coulomb form; and lubricated friction, which scales with relative tangential velocity at the contact point. Dissipation functions in terms of the rod angular velocity are derived via a mean field approach for each form of friction, and from these, a Rayleighian for dense suspensions of rigid rods under shear constructed. Derivatives of this Rayleighian with respect to rod angular velocity and velocity gradient give a Smoluchowski equation and stress tensor, respectively. We show that these are representable as perturbations to Doi's model for a sheared liquid crystal. We also suggest a form for the average number of contacts between rods as a function of volume fraction, aspect ratio, and nematic order parameter, generalizing Philipse's random contact equation for disordered packings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_19149 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Smoluchowski equation for a sheared suspension of frictionally interacting rods Quiñones, Chris Olmsted, Peter D. Soft Condensed Matter In this work we develop constitutive equations for a dense, sheared suspension of frictionally interacting rods by applying Onsager's variational method as formulated by Doi. We treat both solid friction, of the Amontons-Coulomb form; and lubricated friction, which scales with relative tangential velocity at the contact point. Dissipation functions in terms of the rod angular velocity are derived via a mean field approach for each form of friction, and from these, a Rayleighian for dense suspensions of rigid rods under shear constructed. Derivatives of this Rayleighian with respect to rod angular velocity and velocity gradient give a Smoluchowski equation and stress tensor, respectively. We show that these are representable as perturbations to Doi's model for a sheared liquid crystal. We also suggest a form for the average number of contacts between rods as a function of volume fraction, aspect ratio, and nematic order parameter, generalizing Philipse's random contact equation for disordered packings. |
| title | A Smoluchowski equation for a sheared suspension of frictionally interacting rods |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2512.19149 |