Circular‐Disk Viscometer and Related Electrostatic Problems

The method of matched asymptotic expansions is applied to the problem of determining the azimuthal velocity field due to the opposing slow rotations of a pair of thin coaxial disks in a homogeneous, incompressible, viscous fluid. An asymptotic expansion for the velocity field, which is uniformly valid as the ratio e of the separation between the disks to the disk diameter approaches zero, is given and integrated to obtain an asymptotic expansion for the turning moment which contains the full second approximation including terms of the orders e log2e, e loge, and e. Corresponding results are given for the electrostatic condenser. The plane counterparts of the circular‐disk viscometer and condenser are also considered.