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Needle domains are thin, lamellar domains that can appear as fine lines or stripes in a ferroelectric crystal. They affect the poling, switching, and other properties of ferroelectrics. A model is established to study the stress and electric fields caused by needle domains and their interaction. Considering the electrical and mechanical compatibility conditions at the tip of a needle domain, the fields are represented using equivalent edge dislocations and line charges. Accordingly, the dislocation fields derived by Barnett and Lothe for anisotropic piezoelectric media are employed. A modified Peach-Koehler force and calculations of the total energy due to the needle domains are used to study the formation, interaction and stability of needle patterns, taking full account of the strong anisotropy and electromechanical coupling present. The interaction of pairs of needle domains in an infinite piezoelectric with properties of barium titanate is found to be dominated by the electrostatic terms. This makes comb-like arrays of needle domains unstable if perfectly insulating properties are assumed. By considering redistribution of charge, stable equilibrium states for arrays of needle domains are found; these agree well with experimental observations. The model explains the stability of various observed needle patterns and also how unstable patterns evolve.

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The exit flow patterns of an axial flow fan widely used in electronics cooling are experimentally characterized both in free exit and in the presence of a flat impingement plate. The axial fan is rotated with 12.0 V input from a dc power supply, leading to a nominal Reynolds number of Re=9.0×103 based on fan diameter. One shear layer each is found to form between the exit flow from the axial fan and the surrounding fluid at rest, and between the exit flow and the flow along the fan axis. In addition to creating a highest wall pressure region (the primary stagnation region), the presence of the flat plate induces a flow recirculation zone (the secondary stagnation region) at the plate center. When the fan exit-to-plate spacing normalized by fan diameter (H/D) equals to about 0.6, the wall pressure is minimized in the secondary stagnation region due to the maximized “recirculation” as a result of intensified flow interaction. Within the range considered (0.2≤H/D≤2.0) and with the case of H/D∼0.6 serving as a reference, the flow interaction tends to be suppressed by the proximity of the plate at H/D=0.2 and weakened due to the momentum dissipation at H/D∼2.0.