The relative motion of drops in shear flows is responsible for collisions leading to
the creation of larger drops. The collision of liquid drops in a gas is considered here.
The drops are small enough for the Reynolds number to be low (negligible fluid
motion inertia), yet large enough for the Stokes number to be possibly of order unity
(non-negligible inertia in the motion of drops). Possible concurrent effects of Van der
Waals attractive forces and drop inertia are taken into account.General expressions are first presented for the drag forces on two interacting drops
of different sizes embedded in a general linear flow field. These expressions are
obtained by superposition of solutions for the translation of drops and for steady
drops in elementary linear flow fields (simple shear flows, pure straining motions).
Earlier solutions adapted to the case of inertialess drops (by Zinchenko, Davis and
coworkers) are completed here by the solution for a simple shear flow along the line
of centres of the drops. A solution of this problem in bipolar coordinates is provided;
it is consistent with another solution obtained as a superposition of other elementary
flow fields.The collision efficiency of drops is calculated neglecting gravity effects, that is
for strongly sheared linear flow fields. Results are presented for the cases of a
simple linear shear flow and an axisymmetric pure straining motion. As expected,
the collision efficiency increases with the Stokes numbers, that is with drop inertia.
On the other hand, the collision efficiency in a simple shear flow becomes negligible
below some value of the ratio of radii, regardless of drop inertia. The value of this
threshold increases with decreasing Van der Waals forces. The concurrence between
drop inertia and attractive van der Waals forces results in various anisotropic shapes
of the collision cross-section. By comparison, results for the collision efficiency in
an axisymmetric pure straining motion are more regular. This flow field induces
axisymmetric sections of collision and strong inertial effects resulting in collision
efficiencies larger than unity. Effects of van der Waals forces only appear when one
of the drops has a very low Stokes number.
Classification of Aggregate Structure of Ferrofluids under Condition of Strong Magnetic Fields and Simple Shear Flow Fields.
