Aris' use of polar is broader than the chemical/electromagnetic usage cited above, but his use may, strictly speaking, include that case as well. The distinction is mainly one of scale. In a polar fluid such as water, the polar nature comes from the molecules themselves, as opposed to, say, long polymer chains or a magnetizable suspended particles. (To cite another, very different example, a suspension of tiny pear-shaped particles, or even micro-organisms, in a gravitational field would also be polar.) If the polar nature is confined to the molecular level, as for water, then the effects at the meso/macro-scopic scales are mainly confined to that substances chemical and physical properties (viscosity, thermal conductivity, melting/boiling point, and the nature of the liquid state itself) and are not apparent as non-symmetric stresses. On the other hand, if the polar nature of the fluid is due to larger particles (or long chain molecules) then there can be non-symmetric stresses and, because the particles can transmit these stresses to the surrounding carrier fluid, the flows of this fluid will exhibit non-Newtonian flow characteristics.
So: I don't think Aris had (molecularly) polar fluids in mind, but I do think he had in mind certain suspensions (i.e. ferrofluids and MR fluids) and polymer fluids. To me what is interesting is whether a polar suspension could be used effectively as a "model system" to examine the nature of molecular polar fluids, such as water.