Director turbulence

Sgalari, G. Leal, L.G. Meiberg, E. Texture evolution of sheared liquid crystalline polymers numerical predictions of roll-cells instability, director turbulence, and striped texture with a molecular model. J. Rheol. 2003, 47 (6), 1417-1444. 

Ludwig Prandtl (1875—1953) was Professor for Applied Mechanics at the University of Gottingen from 1904 until his death. He was also Director of the Kaiser-Wilhelm-Institut for Fluid Mechanics from 1925. His boundary layer theory, and work on turbulent flow, wing theory and supersonic flow are fundamental contributions to modem fluid mechanics. 

If the initial alignment of the director is homeotropic, domains as well as turbulence can be produced. The threshold voltage for the domains is somewhat higher than in the case of parallel alignment, but the patterns persist even when the voltage is reduced to a lower value. 

Theodor von Karman (11 May 1881-7 May 1963), smdied 1898-1902 in Budapest, and 1906-1908 in Gottingen, Ph.D. 1908 became Privatdozent in Gottingen in 1910, and was then professor of mechanics (as successor to Arnold Sommerfeld) and aerodynamics at the Aachen T.H. (1913-1933). He became director of the Guggenheim Aeronautical Laboratory at the California Institute of Technology in Pasadena from 1933 to 1949, where, with his theory of turbulence, he fostered the development of modem variable swept-wing aircraft. 

Brighton, P. W. M. 1987. Evaporation from a Plane Liquid Surface into a Turbulent Boundary Layer, Report No SRD R375, UK Atomic Energy Authority, Safety tmd Reliability Directorate. 

This accumulation of charge also sets up the flow pattern shown in Figure 10.16. If the electric field is not too strong, these convection cells are quite stable (Williams domains). At larger electric fields, however, the flow becomes turbulent, with a complex, fluctuating director configuration (dynamic scattering). 

Turbulent motion in nematic liquid crystals results in a nonuniform distribution of the director in the plane of the layer, which can only be described by a continuous set of wave vectors in the range 7r/d < Qx y < n/w where w is the smallest scale of the tiurbulence and d is the cell thickness. 

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