Paper Number
SC17 James Swan Memorial Symposium
Session
Suspensions and Colloids
Title
Modeling unsteady motion of a spherical particle in a viscoelastic fluid
Presentation Date and Time
October 10, 2022 (Monday) 5:25
Track / Room
Track 1 / Sheraton 4
Authors
- Joens, Mary A. (Massachusetts Institute of Technology, Department of Chemical Engineering)
- Swan, James W. (Massachusetts Institute of Technology, Chemical Engineering)
Author and Affiliation Lines
Mary A. Joens and James W. Swan
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
Speaker / Presenter
Joens, Mary A.
Keywords
theoretical methods; directed systems
Text of Abstract
Understanding the unsteady motion of a spherical particle in a viscoelastic fluid is of far-reaching interest - it is used as a benchmark problem for numerical solutions, can aid our understanding the mobility of microscale swimmers, and can be used to help understand microrheology experiments. We present a method to calculate the force exerted on a sphere undergoing such motion in fluids described by the Johnson-Segalman and Giesekus constitutive models. This is done by representing the flow field as a regular perturbation series in small values of the Weisseberg number (U λ / a), where U is the maximum particle velocity, λ is the characteristic relaxation time, and a is the particle radius. The solution presented is valid for arbitrary time varying motions, and thus arbitrary values of the Deborah number (tc / λ ), where tc is a measure of how rapidly the particle velocity changes. The governing equations for this flow field are solved analytically up to second order. These analytical solutions in turn can be used to solve for the force at third order by use of the reciprocal theorem, or other values like torque and particle rotation that may be of interest for more complicated imposed particle movements. We show examples of how this form of the solution can be used, focusing on description of microrheology experiments and some instructive common flows, like a particle suddenly impelled by a constant force.