The study of creeping motion of viscoelastic fluid
around a rotating rigid torus is investigated. The
problem is solved within the frame of slow flow
approximation. The equations of motion governing the
first and second-order are formulated and solved for
the first-order only in this paper. However, the
solution of the second-order equations will be the
subject of a part two of this series of papers.
Analytically, Laplace's equation is solved via the
usual method of separation of variables. This method
shows that, the solution is given in a form of infinite
sums over Legendre functions of the first and second
kinds. From the obtained solution it is found that, the
leading term of the velocity represents the Newtonian
flow. The second-order term shows that, the only non
vanishing term is the stream function, which describes
a secondary flow domain. The distribution of the
surface traction at the toroid surface is calculated and
discussed. Considering hydrodynamically conditions,
the effects of toroidal geometrical parameters on the
flow field are investigated in detail.