TY - JOUR
T1 - Macroscopic rheological behavior of suspensions of soft solid particles in yield stress fluids
AU - Avazmohammadi, Reza
AU - Ponte Castañeda, Pedro
N1 - Funding Information:
This material is based upon work supported by the National Science Foundation under Grant No. CMMI-0969570 .
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - In this study, we present a homogenization model for the macroscopic rheological behavior of non-colloidal suspensions of initially spherical, viscoelastic particles in yield stress fluids, which are subjected to uniform flow conditions. The constitutive behavior of the suspending fluid is characterized by the Herschel–Bulkley (HB) model, and the particles are assumed to be neutrally buoyant solids characterized by the finite-strain Kelvin–Voigt viscoelastic model. We make use of the “linear comparison composite” variational technique of Ponte Castañeda (1991) to approximate the instantaneous response of the suspensions of viscoelastic particles in the HB fluid by that of a fictitious suspension consisting of the same particles distributed identically in a Newtonian fluid with a suitably-chosen viscosity. The response of the latter suspension is then estimated by the homogenization model recently developed by Avazmohammadi and Ponte Castañeda (2015), which, when combined with appropriate evolution laws for the relevant microstructural variables, provides a complete characterization of the time-dependent response of the actual suspensions. With the objective of illustrating the key features of our model, we consider the particular case of suspensions of elastic particles in HB fluids under shear flow conditions. The results provide a broad picture of the influence of the HB fluid and particle constitutive properties, as well as of the particle volume fraction on the effective time-dependent and steady-state behaviors of the suspensions. For the special case of non-deformable particles, our model predicts that the suspensions behave like HB fluids with modified properties, consistent with the results of Chateau et al. (2008).
AB - In this study, we present a homogenization model for the macroscopic rheological behavior of non-colloidal suspensions of initially spherical, viscoelastic particles in yield stress fluids, which are subjected to uniform flow conditions. The constitutive behavior of the suspending fluid is characterized by the Herschel–Bulkley (HB) model, and the particles are assumed to be neutrally buoyant solids characterized by the finite-strain Kelvin–Voigt viscoelastic model. We make use of the “linear comparison composite” variational technique of Ponte Castañeda (1991) to approximate the instantaneous response of the suspensions of viscoelastic particles in the HB fluid by that of a fictitious suspension consisting of the same particles distributed identically in a Newtonian fluid with a suitably-chosen viscosity. The response of the latter suspension is then estimated by the homogenization model recently developed by Avazmohammadi and Ponte Castañeda (2015), which, when combined with appropriate evolution laws for the relevant microstructural variables, provides a complete characterization of the time-dependent response of the actual suspensions. With the objective of illustrating the key features of our model, we consider the particular case of suspensions of elastic particles in HB fluids under shear flow conditions. The results provide a broad picture of the influence of the HB fluid and particle constitutive properties, as well as of the particle volume fraction on the effective time-dependent and steady-state behaviors of the suspensions. For the special case of non-deformable particles, our model predicts that the suspensions behave like HB fluids with modified properties, consistent with the results of Chateau et al. (2008).
KW - Shear flow
KW - Soft particle
KW - Suspension
KW - Yield stress fluid
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U2 - 10.1016/j.jnnfm.2016.05.005
DO - 10.1016/j.jnnfm.2016.05.005
M3 - Article
AN - SCOPUS:84976367361
SN - 0377-0257
VL - 234
SP - 139
EP - 161
JO - Journal of Non-Newtonian Fluid Mechanics
JF - Journal of Non-Newtonian Fluid Mechanics
ER -