5 research outputs found
Monotone Solutions of a Nonautonomous Differential Equation for a Sedimenting Sphere
We study a class of integrodifferential equations and related ordinary differential equations for the initial value problem of a rigid sphere falling through an infinite fluid medium. We prove that for creeping Newtonian flow, the motion of the sphere is monotone in its approach to the steady state solution given by the Stokes drag. We discuss this property in terms of a general nonautonomous second order differential equation, focusing on a decaying nonautonomous term motivated by the sedimenting sphere proble
Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling
The amplitude equation for an unstable electrostatic wave in a multi-species
Vlasov plasma has been derived. The dynamics of the mode amplitude is
studied using an expansion in ; in particular, in the limit
, the singularities in the expansion coefficients are
analyzed to predict the asymptotic dependence of the electric field on the
linear growth rate . Generically , as
, but in the limit of infinite ion mass or for
instabilities in reflection-symmetric systems due to real eigenvalues the more
familiar trapping scaling is predicted.Comment: 13 pages (Latex/RevTex), 4 postscript encapsulated figures which are
included using the utility "uufiles". They should be automatically included
with the text when it is downloaded. Figures also available in hard copy from
the authors ([email protected]
Oscillations of a solid sphere falling through a wormlike micellar fluid
We present an experimental study of the motion of a solid sphere falling
through a wormlike micellar fluid. While smaller or lighter spheres quickly
reach a terminal velocity, larger or heavier spheres are found to oscillate in
the direction of their falling motion. The onset of this instability correlates
with a critical value of the velocity gradient scale
s. We relate this condition to the known complex rheology of wormlike
micellar fluids, and suggest that the unsteady motion of the sphere is caused
by the formation and breaking of flow-induced structures.Comment: 4 pages, 4 figure