Scientific and Technical Aerospace Reports Volume 39 April 6, 2001

20010025012 California Inst. of Tech., Div. of Chemistry and Chemical Engineering, Pasadena, CA USA
Inertial Effects in Suspension Dynamics
J. F. Brady, California Inst. of Tech., USA; Subramanian, G., California Inst. of Tech., USA; Proceedings of the Fifth Microgravity
Fluid Physics and Transport Phenomena Conference; December 2000, pp. 1705-1717; In English; See also 20010024890; No
Copyright; Avail: CASI; A03, Hardcopy; A10, Microfiche
The present work analyses the dynamics of a suspension of heavy particles in shear flow. The magnitude of the particle inertia
is given by the Stokes number St = m(gamma/6(pi)a, which is the ratio of the viscous relaxation time of a particle tau(sub p) =
m=6pi(eta)a to the flow time gamma(sup -1). Here, m is the mass of the particle, a is its size, eta is the viscosity of the suspending
fluid and gamma is the shear rate. The ratio of the Stokes number to the Reynolds number, Re = (rho)f(gamma)a(exp 2)/eta, is
the density ratio rho(sub p)/rho(sub f). of interest is to understand the separate roles of particle (St) and fluid (Re) inertia in the
dynamics of suspensions. In this study we focus on heavy particles, rho(sub p)/rho(sub f) much greater than 1, for which the Stokes
number is finite, but the Reynolds number is sufficiently small for inertial forces in the fluid to be neglected; thus, the fluid motion
is governed by the Stokes equations. On the other hand, the probability density governing the statistics of the suspended particles
satisfies a Fokker-Planck equation that accounts for both configuration and momentum coordinates, the latter being essential for
finite St. The solution of the Fokker-Planck equation is obtained to O(St) via a Chapman-Enskog type-procedure, and the conditional
velocity distribution so obtained is used to derive a configuration-space Smoluchowski equation with inertial corrections.
The inertial effects are responsible for asymmetry in the relative trajectories of two spheres in shear flow, in contrast to the well
known symmetric structure in the absence of inertia. Finite St open trajectories in the plane of shear suffer a downward lateral
displacement resulting from the inability of a particle of finite mass to follow the curvature of the zero-Stokes-number pathlines.
In addition to the induced asymmetry, the O(St) inertial perturbation dramatically alters the nature of the near-field trajectories.
The stable closed orbits (for St = 0) in the plane of shear now spiral in, approaching particle-particle contact in the limit. All trajectories
starting from an initial offset of O(St(sup 1/2) or less (which remain open for St = 0) also spiral in. The asymmetry of the
trajectories leads to a non-Newtonian rheology and diffusive behavior. The latter because a given particle (moving along a finite
St open trajectory) suffers a net displacement in the transverse direction after a single interaction. A sequence of such uncorrelated
displacements leads to the particle executing a random walk. The inertial diffusivity tensor is anisotropic on account of differing
strengths of interaction in the gradient and vorticity directions. Since the entire region (constituting an in finite area) of closed
orbits in the plane of shear spirals onto contact for #finite St, the latter represents a singular surface for the pair-distribution function.
The exact form of the pair-distribution function at contact is still, however, indeterminate in the absence of non-hydrodynamic
effects. It should also be noted that finite St non-rectilinear flows do not support a spatially uniform number density owing
to the cross-streamline inertial migration of particles.
Author
Curvature; Diffusivity; Displacement; Particle Mass; Velocity Distribution; Migration; Inertia
20010025013 Iowa Univ., Dept. of Physics and Astronomy, Iowa City, IA USA
Plasma Dust Crystallization
John A. Goree, Iowa Univ., USA; Proceedings of the Fifth Microgravity Fluid Physics and Transport Phenomena Conference;
December 2000, pp. 1718-1765; In English; See also 20010024890; No Copyright; Avail: CASI; A03, Hardcopy; A10, Microfiche
A dusty plasma is an ionized gas, containing small particles of solid matter, which are charged and interact through a Coulomb
repulsion. Dusty plasmas are like colloidal suspensions, except that the interparticle medium is a plasma rather than a liquid, and
therefore the damping rate is reduced as much as a factor of 10(exp 5). The particles are typically 6 microns polymer microspheres,
and they acquire a charge of approximately 10(exp 4) e. The dusty plasma is said to be ”strongly-coupled” or a ”plasma crystal”
when the interparticle potential energy Q(sup 2) /4(pi)epsilon(sub 0)a is greater than the particle kinetic energy k(sub B)T.
Expressing this as the Coulomb coupling parameter, Gamma(sub 0) = Q(sup 2)/(4(pi)epsilon(sub e)k(sub K)T a), where a is the
inter-particle spacing, the strong-coupling regime is Gamma greater than 1. Under these conditions the plasma behaves like a liquid
or solid, unlike most plasmas, which are like a gas. It is easy to attain a large value Gamma greater than 10(exp 3) in a dusty
plasma, because Q is large, while the gas background cools the particles to a low T. This yields a solid-phase suspension. The field
of dusty plasmas is growing rapidly. It shows that the publication rate in major U.S. journals is increasing at an annual rate of
approximately 25%. It is also a highly interdisciplinary field, with a mixture of astronomy, applied, and basic science. In astronomy,
the rings of Saturn, interstellar clouds, comet tails, and many other objects consist of dust particles mixed with plasma. In
industry, semiconductor and solar cell manufacturers have found that contaminating dust particles are synthesized in the chemical
plasmas used to etch and deposit thin films of materials on silicon substrates. In basic science, researchers have focussed on strongly-coupled
dusty plasmas, including structural studies like those for 2D colloids as well as dynamical studies that exploit the low
damping rates of dusty plasmas. In this project, we have been led laboratory studies of 2D strongly-coupled dusty plasmas, and
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