Rheological Chaos in a Scalar Shear-Thickening Model

We study a simple scalar constitutive equation for a shear-thickening material at zero Reynolds number, in which the shear stress \sigma is driven at a constant shear rate \dot\gamma and relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R(\sigma_1) and a linear decay at rate \lambda\sigma_2. Here \sigma_{1,2}(t) = \tau_{1,2}^{-1}\int_0^t\sigma(t')\exp[-(t-t')/\tau_{1,2}] {\rm d}t' are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when \tau_2>\tau_1 and 0>R'(\sigma)>-\lambda so that monotonicity is restored only through the strongly retarded term (which might model a slow evolution of material structure under stress). Within the unstable region we find a period-doubling sequence leading to chaos. Instability, but not chaos, persists even for the case \tau_1\to 0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows.Comment: Reference added; typos corrected. To appear in PRE Rap. Com

Stretching and squeezing of sessile dielectric drops by the optical radiation pressure

We study numerically the deformation of sessile dielectric drops immersed in a second fluid when submitted to the optical radiation pressure of a continuous Gaussian laser wave. Both drop stretching and drop squeezing are investigated at steady state where capillary effects balance the optical radiation pressure. A boundary integral method is implemented to solve the axisymmetric Stokes flow in the two fluids. In the stretching case, we find that the drop shape goes from prolate to near-conical for increasing optical radiation pressure whatever the drop to beam radius ratio and the refractive index contrast between the two fluids. The semi-angle of the cone at equilibrium decreases with the drop to beam radius ratio and is weakly influenced by the index contrast. Above a threshold value of the radiation pressure, these "optical cones" become unstable and a disruption is observed. Conversely, when optically squeezed, the drop shifts from an oblate to a concave shape leading to the formation of a stable "optical torus". These findings extend the electrohydrodynamics approach of drop deformation to the much less investigated "optical domain" and reveal the openings offered by laser waves to actively manipulate droplets at the micrometer scale

Shear induced instabilities in layered liquids

Motivated by the experimentally observed shear-induced destabilization and reorientation of smectic A like systems, we consider an extended formulation of smectic A hydrodynamics. We include both, the smectic layering (via the layer displacement u and the layer normal p) and the director n of the underlying nematic order in our macroscopic hydrodynamic description and allow both directions to differ in non equilibrium situations. In an homeotropically aligned sample the nematic director does couple to an applied simple shear, whereas the smectic layering stays unchanged. This difference leads to a finite (but usually small) angle between n and p, which we find to be equivalent to an effective dilatation of the layers. This effective dilatation leads, above a certain threshold, to an undulation instability of the layers. We generalize our earlier approach [Rheol. Acta, vol.39(3), 15] and include the cross couplings with the velocity field and the order parameters for orientational and positional order and show how the order parameters interact with the undulation instability. We explore the influence of various material parameters on the instability. Comparing our results to recent experiments and molecular dynamic simulations, we find a good qualitative agreement.Comment: 15 pages, 12 figures, accepted for publication in PR

Shear-banding in a lyotropic lamellar phase, Part 2: Temporal fluctuations

We analyze the temporal fluctuations of the flow field associated to a shear-induced transition in a lyotropic lamellar phase: the layering transition of the onion texture. In the first part of this work [Salmon et al., submitted to Phys. Rev. E], we have evidenced banded flows at the onset of this shear-induced transition which are well accounted for by the classical picture of shear-banding. In the present paper, we focus on the temporal fluctuations of the flow field recorded in the coexistence domain. These striking dynamics are very slow (100--1000s) and cannot be due to external mechanical noise. Using velocimetry coupled to structural measurements, we show that these fluctuations are due to a motion of the interface separating the two differently sheared bands. Such a motion seems to be governed by the fluctuations of $\sigma^\star$, the local stress at the interface between the two bands. Our results thus provide more evidence for the relevance of the classical mechanical approach of shear-banding even if the mechanism leading to the fluctuations of $\sigma^\star$ remains unclear

Laser microfluidics: fluid actuation by light

The development of microfluidic devices is still hindered by the lack of robust fundamental building blocks that constitute any fluidic system. An attractive approach is optical actuation because light field interaction is contactless and dynamically reconfigurable, and solutions have been anticipated through the use of optical forces to manipulate microparticles in flows. Following the concept of an 'optical chip' advanced from the optical actuation of suspensions, we propose in this survey new routes to extend this concept to microfluidic two-phase flows. First, we investigate the destabilization of fluid interfaces by the optical radiation pressure and the formation of liquid jets. We analyze the droplet shedding from the jet tip and the continuous transport in laser-sustained liquid channels. In the second part, we investigate a dissipative light-flow interaction mechanism consisting in heating locally two immiscible fluids to produce thermocapillary stresses along their interface. This opto-capillary coupling is implemented in adequate microchannel geometries to manipulate two-phase flows and propose a contactless optical toolbox including valves, droplet sorters and switches, droplet dividers or droplet mergers. Finally, we discuss radiation pressure and opto-capillary effects in the context of the 'optical chip' where flows, channels and operating functions would all be performed optically on the same device

Generating Bessel beams with broad depth-of-field by using phase-only acoustic holograms

[EN] We report zero-th and high-order acoustic Bessel beams with broad depth-of-field generated using acoustic holograms. While the transverse field distribution of Bessel beams generated using traditional passive methods is correctly described by a Bessel function, these methods present a common drawback: the axial distribution of the field is not constant, as required for ideal Bessel beams. In this work, we experimentally, numerically and theoretically report acoustic truncated Bessel beams of flat-intensity along their axis in the ultrasound regime using phase-only holograms. In particular, the beams present a uniform field distribution showing an elongated focal length of about 40 wavelengths, while the transverse width of the beam remains smaller than 0.7 wavelengths. The proposed acoustic holograms were compared with 3D-printed fraxicons, a blazed version of axicons. The performance of both phase-only holograms and fraxicons is studied and we found that both lenses produce Bessel beams in a wide range of frequencies. In addition, high-order Bessel beam were generated. We report first order Bessel beams that show a clear phase dislocation along their axis and a vortex with single topological charge. The proposed method may have potential applications in ultrasonic imaging, biomedical ultrasound and particle manipulation applications using passive lenses.This work was supported by the Spanish Ministry of Economy and Innovation (MINECO) through Project TEC2016-80976-R. NJ and SJ acknowledge financial support from Generalitat Valenciana through grants APOSTD/2017/042, ACIF/2017/045 and GV/2018/11. FC acknowledges financial support from Agencia Valenciana de la Innovacio through grant INNCON00/18/9 and European Regional Development Fund (IDIFEDER/2018/022).Jiménez-Gambín, S.; Jimenez, N.; Benlloch Baviera, JM.; Camarena Femenia, F. (2019). Generating Bessel beams with broad depth-of-field by using phase-only acoustic holograms. Scientific Reports. 9:1-13. https://doi.org/10.1038/s41598-019-56369-zS1139Durnin, J. Exact solutions for nondiffracting beams. i. the scalar theory. J. Opt. Soc. Am. A 4, 651 (1987).Durnin, J., Miceli, J. Jr & Eberly, J. Diffraction-free beams. Physical review letters 58, 1499 (1987).Chu, X. Analytical study on the self-healing property of Bessel beam. Eur. Phys. J. D 66, 259 (2012).McLeod, E., Hopkins, A. B. & Arnold, C. B. Multiscale Bessel beams generated by a tunable acoustic gradient index of refraction lens. Opt. Lett. 31, 3155 (2006).Li, Z., Alici, K. B., Caglayan, H. & Ozbay, E. Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture. Phys. Rev. Lett. 102, 143901 (2009).Fahrbach, F. & Rohrbach, A. Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media. Nat. Commun. 3, 632 (2011).Lu, J.-y, Zou, H. & Greenleaf, J. F. Biomedical ultrasound beam forming. Ultrasound in medicine & biology 20, 403–428 (1994).Marston, P. L. Scattering of a Bessel beam by a sphere. J. Acous. Soc. Am. 121, 753 (2007).Marston, P. L. Scattering of a Bessel beam by a sphere: Ii. helicoidal case and spherical shell example. The Journal of the Acoustical Society of America 124, 2905–2910 (2008).Lu, J. & Greenleaf, F. Ultrasonic nondiffracting transducer for medical imaging. IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 37, 438 (1990).Lu, J.-Y. & Greenleaf, J. F. Pulse-echo imaging using a nondiffracting beam transducer. Ultrasound in medicine & biology 17, 265–281 (1991).Lu, J.-y, Song, T.-K., Kinnick, R. R. & Greenleaf, J. F. In vitro and in vivo real-time imaging with ultrasonic limited diffraction beams. IEEE transactions on medical imaging 12, 819–829 (1993).Lu, J.-y, Xu, X.-L., Zou, H. & Greenleaf, J. F. Application of Bessel beam for doppler velocity estimation. IEEE transactions on ultrasonics, ferroelectrics, and frequency control 42, 649–662 (1995).Nabavizadeh, A., Greenleaf, J. F., Fatemi, M. & Urban, M. W. Optimized shear wave generation using hybrid beamforming methods. Ultrasound in medicine & biology 40, 188–199 (2014).Marston, P. L. Axial radiation force of a Bessel beam on a sphere and direction reversal of the force. The Journal of the Acoustical Society of America 120, 3518–3524 (2006).Marston, P. L. Negative axial radiation forces on solid spheres and shells in a Bessel beam. The Journal of the Acoustical Society of America 122, 3162–3165 (2007).Marston, P. L. Radiation force of a helicoidal Bessel beam on a sphere. The Journal of the Acoustical Society of America 125, 3539–3547 (2009).Thomas, J.-L. & Marchiano, R. Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices. Physical review letters 91, 244302 (2003).Volke-Sepúlveda, K., Santillán, A. O. & Boullosa, R. R. Transfer of angular momentum to matter from acoustical vortices in free space. Phys. Rev. Lett. 100, 024302 (2008).Zhang, L. & Marston, P. L. Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres. Physical Review E 84, 035601 (2011).Courtney, C. R. et al. Dexterous manipulation of microparticles using Bessel-function acoustic pressure fields. Applied Physics Letters 102, 123508 (2013).Hong, Z., Zhang, J. & Drinkwater, B. W. Observation of orbital angular momentum transfer from Bessel-shaped acoustic vortices to diphasic liquid-microparticle mixtures. Phys. Rev. Lett. 114, 214301 (2015).Baresch, D., Thomas, J.-L. &Marchiano, R. Observation of a single-beam gradient force acoustical trap for elastic particles: Acoustical tweezers. Phys. Rev. Lett. 116 (2016).Marzo, A., Caleap, M. & Drinkwater, B. W. Acoustic virtual vortices with tunable orbital angular momentum for trapping of mie particles. Phys. Rev. Lett. 120, 044301 (2018).Li, Y. et al. Acoustic radiation torque of an acoustic-vortex spanner exerted on axisymmetric objects. Applied Physics Letters 112, 254101 (2018).Riaud, A., Baudoin, M., Thomas, J.-L. & Matar, O. B. Cyclones and attractive streaming generated by acoustical vortices. Physical Review E 90, 013008 (2014).Shi, C., Dubois, M., Wang, Y. & Zhang, X. High-speed acoustic communication by multiplexing orbital angular momentum. Proceedings of the National Academy of Sciences 114, 7250–7253 (2017).Jiang, X., Liang, B., Cheng, J.-C. & Qiu, C.-W. Twisted acoustics: metasurface-enabled multiplexing and demultiplexing. Advanced Materials 30, 1800257 (2018).Hsu, D., Margetan, F. & Thompson, D. O. Bessel beam ultrasonic transducer: fabrication method and experimental results. Appl. Phys. Lett. 55, 2066 (1989).Campbell, J. A. & Soloway, S. Generation of a nondiffracting beam with frequency-independent beamwidth. The Journal of the Acoustical Society of America 88, 2467–2477 (1990).Masuyama, H., Yokoyama, T., Nagai, K. & Mizutani, K. Generation of Bessel beam from equiamplitude-driven annular transducer array consisting of a few elements. Jpn. J. Appl. Phys. 38, 3080 (1999).Fjield, T., Fan, X. & Hynynen, K. A parametric study of the concentric-ring transducer design for mri guided ultrasound surgery. J. Acoust. Soc. Am. 100, 1220 (1996).Chillara, V. K., Pantea, C. & Sinha, D. N. Low-frequency ultrasonic Bessel-like collimated beam generation from radial modes of piezoelectric transducers. Applied Physics Letters 110, 064101 (2017).Burckhardt, C., Hoffmann, H. & Grandchamp, P.-A. Ultrasound axicon: A device for focusing over a large depth. The Journal of the Acoustical Society of America 54, 1628–1630 (1973).Foster, F., Patterson, M., Arditi, M. & Hunt, J. The conical scanner: a two transducer ultrasound scatter imaging technique. Ultrasonic imaging 3, 62–82 (1981).McLeod, J. H. The axicon: A new type of optical element. J. Opt. Soc. Am. 44, 592 (1954).Arlt, J. & Dholakia, K. Generation of high-order Bessel beams by use of an axicon. Optics Communications 177, 297–301 (2000).Golub, I. Fresnel axicon. Optics letters 31, 1890–1892 (2006).Lirette, R. & Mobley, J. Broadband wave packet dynamics of minimally diffractive ultrasonic fields from axicon and stepped fraxicon lenses. The Journal of the Acoustical Society of America 146, 103–108 (2019).Jiménez, N. et al. Acoustic Bessel-like beam formation by an axisymmetric grating. Europhys. Lett. 106, 24005 (2014).Xu, Z., Xu, W., Qian, M., Cheng, Q. & Liu, X. A flat acoustic lens to generate a Bessel-like beam. Ultrasonics 80, 66–71 (2017).Li, Y., Liang, B., Gu, Z.-M., Zou, X.-Y. & Cheng, J.-C. Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces. Scientific Reports 3, 2546 (2013).Nye, J. & Berry, M. Dislocations in wave trains. Proc. R. Soc. London, Ser. A 336, 165–190 (1974).Jiménez, N. et al. Formation of high-order acoustic Bessel beams by spiral diffraction gratings. Physical Review E 94, 053004 (2016).Wang, T. et al. Particle manipulation with acoustic vortex beam induced by a brass plate with spiral shape structure. Applied Physics Letters 109, 123506 (2016).Jia, Y.-R., Wei, Q., Wu, D.-J., Xu, Z. & Liu, X.-J. Generation of fractional acoustic vortex with a discrete archimedean spiral structure plate. Applied Physics Letters 112, 173501 (2018).Jiménez, N., Romero-Garca, V., Garca-Raffi, L. M., Camarena, F. & Staliunas, K. Sharp acoustic vortex focusing by fresnel-spiral zone plates. Applied Physics Letters 112, 204101 (2018).Baudoin, M. et al. Folding a focalized acoustical vortex on a flat holographic transducer: miniaturized selective acoustical tweezers. Science advances 5, eaav1967 (2019).Muelas-Hurtado, R. D., Ealo, J. L., Pazos-Ospina, J. F. & Volke-Sepúlveda, K. Acoustic analysis of a broadband spiral source for the simultaneous generation of multiple Bessel vortices in air. The Journal of the Acoustical Society of America 144, 3252–3261 (2018).Muelas-Hurtado, R. D., Ealo, J. L., Pazos-Ospina, J. F. & Volke-Sepúlveda, K. Generation of multiple vortex beam by means of active diffraction gratings. Applied Physics Letters 112, 084101 (2018).Wunenburger, R., Lozano, J. I. V. & Brasselet, E. Acoustic orbital angular momentum transfer to matter by chiral scattering. New Journal of Physics 17, 103022 (2015).Terzi, M., Tsysar, S., Yuldashev, P., Karzova, M. & Sapozhnikov, O. Generation of a vortex ultrasonic beam with a phase plate with an angular dependence of the thickness. Moscow University Physics Bulletin 72, 61–67 (2017).Hefner, B. T. & Marston, P. L. An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems. Jour. Acous. Soc. Am. 106, 3313–3316 (1999).Ealo, J. L., Prieto, J. C. & Seco, F. Airborne ultrasonic vortex generation using flexible ferroelectrets. IEEE transactions on ultrasonics, ferroelectrics, and frequency control 58, 1651–1657 (2011).Naify, C. J. et al. Generation of topologically diverse acoustic vortex beams using a compact metamaterial aperture. Applied Physics Letters 108, 223503 (2016).Ye, L. et al. Making sound vortices by metasurfaces. AIP Advances 6, 085007 (2016).Jiang, X., Li, Y., Liang, B., Cheng, J.-C. & Zhang, L. Convert acoustic resonances to orbital angular momentum. Physical review letters 117, 034301 (2016).Esfahlani, H., Lissek, H. & Mosig, J. R. Generation of acoustic helical wavefronts using metasurfaces. Physical Review B 95, 024312 (2017).Jiménez-Gambn, S., Jiménez, N., Benlloch, J. M. & Camarena, F. Holograms to focus arbitrary ultrasonic fields through the skull. Physical Review Applied 12, 014016 (2019).Maimbourg, G., Houdouin, A., Deffieux, T., Tanter, M. & Aubry, J.-F. 3d-printed adaptive acoustic lens as a disruptive technology for transcranial ultrasound therapy using single-element transducers. Physics in Medicine & Biology 63, 025026 (2018).Ferri, M. et al. On the evaluation of the suitability of the materials used to 3d print holographic acoustic lenses to correct transcranial focused ultrasound aberrations. Polymers 11, 1521 (2019).Melde, K., Mark, A. G., Qiu, T. & Fischer, P. Holograms for acoustics. Nature 537, 518 (2016).Brown, M. D., Cox, B. T. & Treeby, B. E. Design of multi-frequency acoustic kinoforms. Applied Physics Letters 111, 244101 (2017).Brown, M., Nikitichev, D., Treeby, B. & Cox, B. Generating arbitrary ultrasound fields with tailored optoacoustic surface profiles. Applied Physics Letters 110, 094102 (2017).Zhu, Y. et al. Fine manipulation of sound via lossy metamaterials with independent and arbitrary reflection amplitude and phase. Nature communications 9, 1632 (2018).Brown, M. D. Phase and amplitude modulation with acoustic holograms. Applied Physics Letters 115, 053701 (2019).Jiménez, N., Romero-Garca, V., Pagneux, V. & Groby, J.-P. Quasiperfect absorption by subwavelength acoustic panels in transmission using accumulation of resonances due to slow sound. Physical Review B 95, 014205 (2017).Tsang, P. W. M. & Poon, T.-C. Novel method for converting digital fresnel hologram to phase-only hologram based on bidirectional error diffusion. Optics Express 21, 23680–23686 (2013).Soret, J. Ueber die durch kreisgitter erzeugten diffractionsphänomene. Annalen der Physik 232, 99–113 (1875).Turunen, J., Vasara, A. & Friberg, A. T. Holographic generation of diffraction-free beams. Applied Optics 27, 3959–3962 (1988).Vasara, A., Turunen, J. & Friberg, A. T. Realization of general nondiffracting beams with computer-generated holograms. JOSA A 6, 1748–1754 (1989).Cunningham, K. B. & Hamilton, M. F. Bessel beams of finite amplitude in absorbing fluids. J. Acous. Soc. Am. 108, 519 (2000).Ding, D. & Y. Lu, J. Higher-order harmonics of limited diffraction Bessel beams. J. Acous. Soc. Am. 107, 1212 (2000).Skeldon, K., Wilson, C., Edgar, M. & Padgett, M. An acoustic spanner and its associated rotational Doppler shift. New J. Phys. 10, 013018 (2008).Wu, J. Acoustical tweezers. J. Acoust. Soc. Am. 89, 2140–2143 (1991).Zhang, L. & Marston, P. L. Angular momentum flux of nonparaxial acoustic vortex beams and torques on axisymmetric objects. Physical Review E 84, 065601 (2011).Yoon, C., Kang, B. J., Lee, C., Kim, H. H. & Shung, K. K. Multi-particle trapping and manipulation by a high-frequency array transducer. Appl. Phys. Lett. 105, 214103 (2014).Marzo, A. et al. Holographic acoustic elements for manipulation of levitated objects. Nat. Commun. 6 (2015).Blackstock, D. T. Fundamentals of physical acoustics (John Wiley & Sons, 2000).Treeby, B. E. & Cox, B. Modeling power law absorption and dispersion for acoustic propagation using the fractional laplacian. The Journal of the Acoustical Society of America 127, 2741–2748 (2010).Treeby, B. E., Jaros, J., Rendell, A. P. & Cox, B. Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method. The Journal of the Acoustical Society of America 131, 4324–4336 (2012).Jiménez, N. et al. Time-domain simulation of ultrasound propagation in a tissue-like medium based on the resolution of the nonlinear acoustic constitutive relations. Acta Acustica united with Acustica 102, 876–892 (2016)

Recent experimental probes of shear banding

Recent experimental techniques used to investigate shear banding are reviewed. After recalling the rheological signature of shear-banded flows, we summarize the various tools for measuring locally the microstructure and the velocity field under shear. Local velocity measurements using dynamic light scattering and ultrasound are emphasized. A few results are extracted from current works to illustrate open questions and directions for future research.Comment: Review paper, 23 pages, 11 figures, 204 reference

The Janus head of Bachelard’s phenomenotechnique: from purification to proliferation and back

The work of Gaston Bachelard is known for two crucial concepts, that of the epistemological rupture and that of phenomenotechnique. A crucial question is, however, how these two concepts relate to one another. Are they in fact essentially connected or must they be seen as two separate elements of Bachelard's thinking? This paper aims to analyse the relation between these two Bachelardian moments and the significance of the concept of phenomenotechnique for today. This will be done by examining certain historical uses of the concepts of Bachelard have been used from the 1960s on. From this historical perspective, one gets the impression that these two concepts are relatively independent from each other. The Althusserian school has exclusively focused on the concept of 'epistemological break', while scholars from Science & Technology Studies (STS), such as Bruno Latour, seem to have only taken up the concept of phenomenotechnique. It in fact leads to two different models of how to think about science, namely the model of purification and the model of proliferation. The former starts from the idea that sciences are rational to the extent that they are purified and free from (epistemological) obstacles. Scientific objectivity, within this later model, is not achieved by eradicating all intermediaries, obstacles and distortions, but rather exactly by introducing as many relevant technical mediators as possible. Finally, such a strong distinction will be criticized and the argument will be made that both in Bachelard's and Latour's thought both concepts are combined. This leads to a janus-headed view on science, where both the element of purification (the epistemological break) and the element of proliferation (phenomenotechnique) are combine

Scattering of a sound wave by a vibrating surface

We report an experimental study of the scattering of a sound wave of frequency f by a surface vibrating at frequency F. Both the Doppler shift at the vibrating surface and acoustic nonlinearities in the bulk of the fluid, generate the frequencies $f \pm n F$ (n integer) in the spectrum of the scattered wave. We show that these two contributions can be separated because they scale differently with respect to the vibration frequency and to the distance between the vibrating scatterer and the detector. We determine the parameter ranges in which one or the other mechanism dominates and present quantitative studies of these two regimes