@article{discovery10193263,
            note = {Copyright {\copyright} 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).},
       publisher = {Elsevier BV},
         journal = {Journal of Non-Newtonian Fluid Mechanics},
          volume = {330},
            year = {2024},
           title = {Rheology of a suspension of deformable spheres in a weakly viscoelastic fluid},
           month = {August},
            issn = {0377-0257},
        keywords = {Dilute suspension, Second-order fluid, Elastic solid, Cell model, Solid-fluid interactions, Constitutive model, Angle of inclination},
             url = {https://doi.org/10.1016/j.jnnfm.2024.105262},
        abstract = {In this work, we consider a suspension of weakly deformable solid particles within a weakly viscoelastic fluid.
The fluid phase is modelled as a second-order fluid, and particles within the suspended phase are assumed
linearly elastic and relatively dilute. We apply a cell model as a proxy for mean field flow, and solve analytically
within a cellular fluid layer and its enclosed particle. We use an ensemble averaging process to derive analytical
results for the bulk stress in suspension, and evaluate the macroscopic properties in both shear and extensional
flow. Our viscometric functions align with existing literature over a surprisingly broad range of fluid and solid
elasticities.
The suspension behaves macroscopically as a second-order fluid, and we give simple formulae by which
the reader can calculate the parameters of this effective fluid, for use in more complex simulations. We
additionally calculate the particle shape and orientation, and in simple shear flow show that the leadingorder modifications to the angle of inclination },
          author = {Escott, Liam J and Wilson, Helen J}
}