#### Date of Award

5-2017

#### Document Type

Thesis

#### Degree Name

Master of Science (MS)

#### College/School

College of Science and Mathematics

#### Department/Program

Mathematical Sciences

#### Thesis Sponsor/Dissertation Chair/Project Chair

Arup Mukherjee

#### Committee Member

Bogdan Nita

#### Committee Member

Ashwin Vaidya

#### Abstract

Previous studies of planar Couette flow of ferro-fluids in a transverse time-independent external magnetic field are extended to include the effects by spin diffusion. We numerically study the modification in the internal rotation of particles in a colloidal ferro-fluid. In particular, we consider a ferro-fluid between two concentric cylinders, and apply a radial magnetic field inversely proportional to the radial variable. We consider the influence of shear effects by assuming a constant magnetic field while varying the rotation rate of the inner cylinder, and the effects of the balance between shear and magnetic stresses by varying the values of the magnetic field while maintaining a fixed rate of rotation for the inner cylinder. We use a continuum model where the Navier-Stokes like conservation of linear momentum equation is coupled to an equation governing the angular momentum of isotropic particles and a Magnetization equation that describes the behavior of magnetic particles. We demonstrate that the internal rotation undergoes a directional reversal in the channel and study the relationship between the magnitude of the magnetic field and the location of the sign-change. Moreover, we show that there is an inverse relationship between fluid spin and where the change in direction of rotation takes place. Previous research has demonstrated that the direction of internal rotation of particles of ferrofluids flowing in a channel with parallel plates changes at some point of the channel. Our study aims to establish how this point in the channel is related to the applied magnetic field and the spin viscosity of the the ferrofluid.

#### File Format

#### Recommended Citation

Ottieri, Lucía Cataldo, "Spin Viscosity Effects in Planar Ferrofluid Couette Flow of Ferrofluids" (2017). *Theses, Dissertations and Culminating Projects*. 566.

https://digitalcommons.montclair.edu/etd/566