Dumbbell dimer dynamics in three-dimensional chiral fluids

Abstract

We study the emergent orientational dynamics of a dumbbell dimer -- two asymmetric monomers connected by a linking spring -- in a three-dimensional chiral environment with odd viscosity. In classical systems with conserved parity symmetry, reciprocal oscillations of a dimer does not lead to rotational motion. Here, through an analytical calculation, we find that the presence of chirality in the system induces rotational dynamics as function of the expansion/contraction of the dimer. By incorporating thermal fluctuations, we further find that the rotational diffusivity is affected by the coupling between conformational fluctuations and rotational motion. Our results provide insights into problems where the parity symmetry is broken and can be used as a building block to study similar models at the collective level. These problems include multi-component molecular machines in odd-viscous fluids and systems with charged polymers where oddity is present through external magnetic fields.

Figures (2)

• Figure 1: Schematic of a dumbbell dimer immersed in a three-dimensional chiral fluid with an even (shear) viscosity and an odd viscosity, $\eta^{\rm e}$ and $\eta^\mathrm{o}$. The odd viscosity is assumed to be positive. The axis of the odd viscosity is assumed to be in the $\hat{\textbf{z}}$-direction, while the even viscosity is isotropic and thus does not have any preferred direction in the fluid. (a) The geometry of a dimer whose spherical domains have radii $a_1$ and $a_2$. The dimer length as well as the dimer orientation vary in time, which are characterized by the scalar function $L(t)$ and the unit vector $\textbf{n}(t)$, respectively. The dimer length undergoes expansions or contractions due to thermal noise or prescribed motion of the connecting shaft, which leads to the three dimensional rotational motion of the dimer. (b) To linear order in the odd viscosity, the expansion of the dimer arm creates an anti-clockwise rotation about the $\hat{\textbf{z}}$-axis by increasing the azimuthal angle $\phi(t)$ measured from the $x$-axis [see also Eq. \ref{['eq:phisol']} and Fig. \ref{['fig:fig2']}(b)]. (c) To quadratic order in the odd viscosity, in addition to the transient precession observed in panel (b), the contraction of the dimer causes the reorientation towards the $(x,y)$ plane by increasing the polar angle $\theta(t)$ measured from the $z$-axis [see also Eq. \ref{['eq:thetasol']} and Fig. \ref{['fig:fig2']}(a)].
• Figure 2: The angular dynamics of the dimer orientation as a function of time $t$ for various values of $\lambda$ when the self-mobility is taken into account up to the quadratic order in $\lambda$ and there is no hydrodynamic interaction between the domains. The dimer is initially oriented with $\theta(0) = \phi(0) = \pi/4$ and its length is prescribed as $L(t)=L_0 + \ell_0 \sin(t)$ for $L_0 = 1$ and $\ell_0=0.5$. The evolution of (a) the polar angle $\theta$ [Eq. \ref{['eq:thetasol']}] and (b) the azimuthal angle $\phi$ [Eq. \ref{['eq:phisol']}].