Active nematic turbulence: An experimental study

Abstract

[eng] One of the most striking phenomena of active fluids, i.e., fluids composed of self-propelled constituents, is the emergence of chaotic spatiotemporal flows. "This regime, reminiscent of inertial turbulence but happening at low Reynolds numbers, has become to be known as active turbulence. It has been observed in a variety of systems, such as bacterial suspensions or epithelial tissues. Despite the visual similarities, active turbulent flows possess fundamental differences from classical turbulent flows. The differences essentially emanate from the fact that active turbulence originates at vanishing Reynolds numbers from the self-organization of the fluid constituents, which move coordinately at distances much larger than their own size. As a result, active chaotic flows are endowed with a characteristic length scale. In this thesis, working with an experimental active system displaying nematic order, i.e., head-to- tail orientational order, and composed of proteins from the cytoskeleton, we address some still- standing open questions regarding active turbulence. More specifically, since our experimental system is two-dimensional and has nematic order, we study 2D active nematic turbulence. We begin this thesis by unveiling the pathway followed by the active fluid with an imposed radial alignment to its final characteristic chaotic state. More in particular, we demonstrate that the AN in the aster configuration is intrinsically unstable to buckling. In turn, a characteristic length scale already emerges at the instability's early stages. Interestingly, the instability of the aligned active nematic can be characterized in terms of a growth rate that exhibits a quadratic or quasi-quadratic dependence on the leading wavenumber. Our experimental results are then compared with predictions obtained from linear stability analysis. This enables us to see that the coupling of the active nematic with adjacent fluid layers precludes long wavelength fluctuations, imposing in this way a genuine wavelength selection mechanism. In the second project, we measure the active liquid crystal's flow field and the associated kinetic energy spectrum. In this way, we verify the existence of scaling regimes, some of which feature exponents previously predicted through theory and simulations , together with new ones. To understand the newly-discovered scaling regimes, we exploit a theory that includes the hydrodynamic coupling of the active nematic with the two contacting passive fluid layers. This theory assesses the range of validity of the identified scaling regimes, and permits to extract information on important rheological parameters of the active fluid In the final project, still in progress, we address the presence of energy cascades in active nematic turbulence. Preliminary experimental results, supported with simulations, suggest that even though the free energy balance does not entirely vanish at all length scales, we cannot indeed conclude that there is energy transfer between scales. A significant limitation we encounter when computing the free energy balance of the active nematic is that most of the material parameters

still need to be determined. Therefore, further research research devoted to the evaluation of such parameters may shed light on this respect. On top of the above fundamental studies, we also demonstrate two implementations of polarimetry measurements coupled with fluorescence imaging, with which we can simultaneously measure the director and velocity fields of the active nematic . The first arrangement is based on a liquid crystal slab, whose retardance can be easily commanded with a computer. By measuring the light intensity reaching the detector at different configurations of the liquid crystal retarder, we can unequivocally and continuously know the sample's local orientation. The alternative implementation incorporates a polarization camera, a device composed of subpixels with different polarizations. This arrangement allows us to obtain exceptional birefringence measurements at significantly high frame rates, even with very low-birefringent samples, as the active nematic.

[cat] Els fluids actius, com les suspensions de bacteris o els teixits, són fluids compostos per moltes unitats capaces de propulsar-se contínuament. Aquests fluids presenten propietats molt interessants i radicalment oposades a les que s’observen quan una d’aquestes unitats actives es mou individualment. Un exemple és el que es coneix com a turbulència activa, on els fluids actius es mouen caòticament i que emergeix inclús a números de Reynolds baixos, quan la inèrcia es menyspreable. Aquest fenomen es diu així perquè visualment recorda a la turbulència inercial clàssica. Tot i així, hi ha diferències fonamentals entre aquests dos tipus de turbulència, els quals ens interessa discernir. En aquesta tesi es presenten estudis experimentals, duts a terme amb una suspensió de proteïnes del citoesquelet, i amb els quals abordem algunes qüestions encara obertes sobre la turbulència activa i les seves similituds i diferències amb la turbulència inercial. Més concretament, com el nostre sistema experimental és 2D i presenta simetria nemàtica, nosaltres estudiem la turbulència nemàtica activa. En primer lloc, revelem el camí que segueix el nemàtic actiu alineat radialment fins que arriba al seu estat turbulent. Més concretament, demostrem que la geometria d’àster és inestable; en conseqüència, el fluid actiu comença a deformar-se i llavors emergeix una escala de longitud característica. Després duem a terme estudis on l’actiu nemàtic ja es troba plenament en el seu estat turbulent. En aquest sentit, demostrem l’existència de règims d’escala en l’espectre d’energia cinètica del nemàtic actiu i abordem la presència o no presència de cascades d’energia en el context de la turbulència nemàtica activa. Finalment, descrivim dues tècniques de polarimetria acoblades a fluorescència amb les quals podem mesurar simultàniament la orientació i el camp de velocitats del nemàtic actiu i que ens permeten dur a terme les mesures experimentals presentades en aquesta tesi.