Nouvelles Instabilités De Cisaillement Dans Les Nématiques

Theoretical analysis of the stability of shear flow of nematic liquid crystals with a positive Leslie viscosity α3

“…We should also mention here that the first of the two equations in (5.11) has previously been presented by Pieranski et al [5] in a slightly different version. Their equation contains |α 2 | instead of |α 2 + α 3 | which is the more correct factor to use, a difference which in the limit α 3 |α 2 | is negligible.…”

“…Since these viscosities also have to satisfy α 3 − α 2 > 0 [3] this means that α 2 < 0, α 3 > 0. Compounds having these properties have been reported among others by Pieranski et al [5,6], Cladis and Torza [7,8], Kneppe et al [9] and by Carlsson and co-workers [10,11] and different propositions regarding their flow behaviour have been put forward. Among these one can find a picture of the flow described by a stable, stationary director configuration [7] as well as by the situation for which the director rotates permanently [6].…”

“…If we perform a shear flow experiment by increasing the velocity of the moving plate, we find that at a critical velocity, v c , the maximum tilt angle makes a jump and consequently the whole director configuration of the system undergoes a discontinuous transition. This transition has been named the tumbling instability and has been observed experimentally [5,7,28]. In this section we discuss the tumbling instability in the light of Eqs.…”

“…This instability is commonly referred to as tumbling. Pieranski et al [5] also question whether the flow is stable against fluctuations which tend to bring the director out of the shearing plane.…”

On the Existence of Infinitely Many Limit Points on the Solution Branch of Planar Shear Flow of Nematic Liquid Crystals

“…When ␣ -0 -␣ , the uniformly aligned configurations become unstable for sufficiently high shear rates and either tumbling regimes develop in the flow region in the w xŽ shear plane 4, 19, 20 shear plane is defined at the beginning of Sec-. tion 2 or the alignment of nematic liquid crystals takes on a component w x w perpendicular to the shear plane 19,20 . From numerical simulations 15, x 17, 23, 24 , they confirmed that the existence of limit points along the solution branch of planar shear flows and tumbling instability is characterized by the exchange of stability of the planar configuration by another planar configuration with a more distorted director field.…”