Active nematic gels as active relaxing solids

Abstract

I propose a continuum theory for active nematic gels, defined as fluids or suspensions of orientable rodlike objects endowed with active dynamics, that is based on symmetry arguments and compatibility with thermodynamics. The starting point is our recent theory that models (passive) nematic liquid crystals as relaxing nematic elastomers. The interplay between viscoelastic response and active dynamics of the microscopic constituents is naturally taken into account. By contrast with standard theories, activity is not introduced as an additional term of the stress tensor, but it is added as an external remodeling force that competes with the passive relaxation dynamics and drags the system out of equilibrium. In a simple one-dimensional channel geometry, we show that the interaction between nonuniform nematic order and activity results in either a spontaneous flow of particles or a self-organization into subchannels flowing in opposite directions.

Active viscoelastic nematics with partial degree of order

“…The equations of motions can now be derived following the thermodynamic procedure outlined in [56]. The details of this derivation when the tensor Q is employed are reported in Appendix A.…”

“…The last term in Eq. ( 24) represents the power expended by the remodelling generalised force T a [56]. It must be noted that T a is the only term conjugate to the remodelling velocity field B e .…”

“…It is interesting to note that a term of the type σ active , proportional to Q, is indeed thermodynamically correct at first order. More precisely, it is possible to put forth a thermodynamically consistent theory of active nematics based on nematic elastomer energy and microscopic relaxation dynamics [56], where activity is represented as an external remodelling force, which clearly distinguishes it from the commonly used time-reversible representation. When this latter theory is approximated under the assumption of fast material remodelling times and low activity, the first order contribution to the stress tensor turns out to be proportional to Q, exactly as in the classical theories inspired by liquid crystal physics.…”

“…In turn, this implies that there is no chemical fuel consumption when v = 0. However, chemical fuel (e.g., ATP molecules) can also be used for mesoscopic motion such as material reorganization at the microscale, or for polymer stiffening, without any visible macroscopic velocity [56,57,1]. The transduction of chemical energy into mechanical work is thus internal to the material and is more related to the evolution of the physical cross-links and their reorganization rather than to the generation of macroscopic flow.…”

A Design Principle for Actuation of Nematic Glass Sheets

“…For the purpose of finding equilibrium configurations of the sheet, A nem (z) will be considered as a given field (unlike in the nematic elastomer case). Note that A nem is analogous to the plastic distortion tensor F p in elastoplasticity theory (see, e.g., [13,14] for applications to soft materials), but now in the context of 2-d bodies occupying non-Euclidean subsets of E 3 ; the main modeling hypothesis is that, to the extent allowed by compatibility and displacement boundary conditions, the 'total' deformation gradient F field attempts to generate a right stretch tensor field that equals that of A nem pointwise in order to attain minimum energy in the body.…”