Second-grade nematic fluids and Nematoacoustics

Seminar 15th January 2013 noon 54/8033

Giovanni De Matteis
University of Milan

Web page: http://www.researchgate.net/profile/Giovanni_De_Matteis2/
Categories: Acoustics, Complex Systems
Submitter: Luke Goater

There is plenty of experimental evidence that the propagation of an ultrasonic wave in a nematic liquid crystal affects the director n, which represents the average molecular orientation, thus producing detectable optical effects. There have been several attempts to explain these observations on the basis of a coherent variational theory. We present here a general theory for nematoacoustics that incorporates flow effects. Applications of the proposed theory are also provided.

First, an explicit application to a simple computable case is given in order to estimate phenomenological parameters involved in the theory and by using available experimental data. In particular, propagation of plane waves is considered via linearization of the governing equations stemming from the general theory. Second, we introduce the equations that have been derived from the basic theory and that govern the nematoacoustic streaming in liquid crystals. Third, travelling wave solutions are also shown in a simple one-dimensional model. Finally, we sketch the solution for the so-called Freedericks transition by considering the coupling with an electric field.

References

[1] [E. G. Virga, Physical Review E, 80, 031705 (2009) [2] [G. De Matteis and E. G. Virga, Physical Review E, 83, 011703 (2011) [3] [G. De Matteis, Acta Applicandae Mathematicae, (2012) in press [4] [G. De Matteis and L. Martina, Journal of Mathematical Physics, 53, 033101 (2012) [5] [G. De Matteis and G. Napoli, submitted