Jma. Hofman et al., Hydrodynamic interactions in colloidal crystals - (II). Application to dense cubic and tetragonal arrays, PHYSICA A, 268(3-4), 1999, pp. 353-390
Wavevector dependent friction factors, which together with the elastic prop
erties determine the hydrodynamic damping of harmonic lattice waves in coll
oidal crystals, are calculated for cubic arrays of rigid spheres at low, in
termediate and high sphere volume fractions, including simple cubic (SC), b
ody-centred cubic (BCC) and face-centred cubic (FCC) lattices. Exact numeri
cal data are presented for the rheological coefficient appropriate to pure
vortex motion of particles, the so-called spin viscosity. These results for
the spin viscosity are obtained for all three cubic lattices and for the w
hole range of volume fractions. An expression suitable for low volume fract
ions is derived that approximates the converged numerical data within an er
ror of only 3%, for volume fractions up to 75% of the close packing concent
ration for all of the three cubic packing types. Spin viscosities of extrem
ely dense cubic arrays are calculated on basis of lubrication theory which
yields new expressions for BCC and FCC lattices, while reproducing a known
result for the SC case. Constant contributions of many-particle hydrodynami
c interactions are determined that yield a first correction to the lubricat
ion expressions, appropriate for the three cubic lattices. Two types of bod
y-centred tetragonal (BCT) arrays are considered. The first type (BCT1) con
sists of aligned rows of close-touching spheres, where variations of the vo
lume fraction can be accomplished by changing the distance between these ro
ws. The second type (BCT3) has a constant structure, such that the concentr
ation can be varied by changing the size of the spheres. The two characteri
stic drag coefficients are calculated numerically for steadily sedimenting
BCT arrays of both types and at all concentrations. Likewise two characteri
stic spin viscosities are computed for these structures. Analytical results
suitable to dilute BCT3 arrays are presented for drag coefficients and spi
n viscosities. The expressions for the spin viscosities represent an approx
imation within 3%, for volume fractions up to 60% of the close packing conc
entration. (C) 1999 Elsevier Science B.V. All rights reserved.