(432a) Unsteady, Lineal Translation of a Spherical Particle in a Viscoleastic Fluid
AIChE Annual Meeting
2021
2021 Annual Meeting
Engineering Sciences and Fundamentals
Microfluidic and Microscale Flows: Separations and Particulates
Wednesday, November 10, 2021 - 8:00am to 8:15am
Understanding the unsteady, lineal translation of a spherical particle in a viscoelastic fluid is of far-reaching interest for its use both as a benchmark problem in numerical studies of fluids and as a model system for studying sedimentation and other modes of particle mobility in suspensions. It also has the potential to aid in design of 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 Weissenberg number (Uλ/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 (λ/tc), 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, which in turn can be used to solve for the force at third order by use of the reciprocal theorem.
Ultimately, the unsteady force is presented as a Volterra series expansion, where material functions have been derived to describe the first- and third-order relationships between the time course of the velocity and the force. We show examples of how this form of the solution can be used, focusing on description of microrheology experiments and calculation the time-dependent velocity of a particle suddenly impelled by a constant force, identifying the critical Weissenberg number at which overshoots in particle velocity begin to occur.
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 Weissenberg number (Uλ/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 (λ/tc), 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, which in turn can be used to solve for the force at third order by use of the reciprocal theorem.
Ultimately, the unsteady force is presented as a Volterra series expansion, where material functions have been derived to describe the first- and third-order relationships between the time course of the velocity and the force. We show examples of how this form of the solution can be used, focusing on description of microrheology experiments and calculation the time-dependent velocity of a particle suddenly impelled by a constant force, identifying the critical Weissenberg number at which overshoots in particle velocity begin to occur.