Modeling ultrasonic metafluids: The significance of discrete oscillators

Significant changes in the acoustic response of a fluid can be induced by the suspension of tiny, subwavelength-size discrete micro-oscillators in the fluid. We investigate how the topological properties of these oscillators, such as the mass distribution and connectivity of the oscillator parts, influence the effective dynamic density and compressibility of the fluid in which they are embedded. We demonstrate a superior, metamaterial-like response of the suspension when using micro-oscillators with a high density of low-frequency modes. Such low-frequency modes occur in loosely connected microstructures and make the system much more experimentally feasible due to the larger ultrasonic attenuation length at these frequencies. In addition, the absence of need for an intricately designed structure brings experimental implementation within reach.

Thermoelasticity of Injection-Molded Parts

In the realm of injection-molded parts, small length scale deformation defects such as sink marks often pose a major challenge to the aesthetics or functionality of the parts. To address this problem, we present a comprehensive thermoelastomechanical approach that calculates the deformation of injection molded plastic by solving the elastic problem at each time step. In our methodology, two treatments of the molten core are considered: one as a liquid and the other as a rubbery state. Our results suggest that the rubbery state treatment provides higher accuracy in predicting the deformation results, as it maintains the displacement of the localized thermal shrinkage in its vicinity. The validity of our method is supported by empirical measurements on produced parts from the existing literature as well as on samples that we molded independently.

Mass point versus whole-body modeling of skiers for performance evaluation in alpine skiing

The altitude differential of the specific mechanical energy, diff e mech $$ diff\ \left({e}_{mech}\right) $$ , is used to evaluate skiing performance. It is defined as the negative differential between the skier's total specific mechanical energy ( e mech $$ {e}_{mech} $$ ) and the altitude of the skier's center of mass (COM). Till now, e mech $$ {e}_{mech} $$ was obtained upon a mass-point (MP) model of the skier's COM, which neither considered the segmental energies of their relative movements to the COM, nor their rotational kinetic energies. The aims of the study were therefore: (a) to examine the deviations in diff e mech $$ diff\ \left({e}_{mech}\right) $$ between the MP and a more complex linked segment (LS) skier model consisting of 15 rigid bodies, which encountered the aforementioned defectiveness, (b) to compare the energy fluctuations of the two skier models, and (c) to investigate the influence of the gate setup on (a) and (b) in giant slalom. Three-dimensional whole-body kinematics of nine skiers was measured using a global navigation satellite system and an inertial motion capture system while skiing on a predefined course divided into a turny and open gate setup. Mechanical energies including their altitude differentials were calculated for the LS and MP models. There were no significant differences in e mech $$ {e}_{mech} $$ and diff e mech $$ diff\ \left({e}_{mech}\right) $$ ski turn averages, as in individual data points, between both skier models for both analyzed gate setups. The energies additionally considered by the LS model presented a negligible part regardless of the gate setup. In conclusion, the MP skier model is sufficiently accurate for the evaluation of the skiing performance with diff e mech $$ diff\ \left({e}_{mech}\right) $$ .

Macroscopic two-fluid effects in magnetorheological fluids

We investigate macroscopic two-fluid effects in magnetorheological fluids generalizing a one-fluid model studied before. In the bulk of the paper we use a model in which the carrier fluid, with density ρ_{1}, moves with velocity v_{1}, while the magnetic component (density ρ_{2}) and, therefore, the magnetization and the magnetic-field-induced relaxing strain field move with velocity v_{2}. In the framework of macroscopic dynamics we find, in particular, reversible dynamic and dissipative cross-coupling terms between the magnetization and the velocity difference. Experiments to detect some of these cross-coupling terms are suggested. We also compare the results of the two-fluid model presented here with two-fluid models available for electrorheological fluids. In two appendices we discuss the simplifying assumptions made to arrive at the model used in this paper and we also outline how to detect potential deviations from this model.

Continuum model of magnetic field induced viscoelasticity in magnetorheological fluids

An effective macroscopic model of magnetorheological fluids in the viscoelastic regime is proposed. Under the application of an external magnetic field, columns of magnetizable particles are formed in these systems. The columns are responsible for solidlike properties, such as the existence of elastic shear modulus and yield stress, and are captured by the strain field, while magnetic properties are described by the magnetization. We investigate the interplay of these variables when static shear or normal pressure is imposed in the presence of the external magnetic field. By assuming a relaxing strain field, we calculate the flow curves, i.e., the shear stress as a function of the imposed shear rate, for different values of the applied magnetic field. Focusing on the small amplitude oscillatory shear, we study the complex shear modulus, i.e., the storage and the loss moduli, as a function of the frequency. We demonstrate that already such a minimal model is capable of furnishing many of the key physical features of these systems, such as yield stress, enhancement of the shear yield stress by pressure, threshold behavior in the spirit of the frequently employed Bingham law, and several features in the frequency dependence of storage and loss moduli.

A dynamic preferred direction model for the self-organization dynamics of bacterial microfluidic pumping

It is known that some flagellated bacteria like Serratia marcescens, when deposited and affixed onto a surface to form a "bacterial carpet", self-organize in a collective motion of the flagella that is capable of pumping fluid through microfluidic channels. We set up a continuum model comprising two macroscopic variables that is capable of describing this self-organization mechanism as well as quantifying it to the extent that an agreement with the experimentally observed channel width dependence of the pumping is reached. The activity is introduced through a collective angular velocity of the helical flagella rotation, which is an example of a dynamic macroscopic preferred direction. Our model supports and quantifies the view that the self-coordination is due to a positive feedback loop between the bacterial flagella and the local flow generated by their rotation. Moreover, our results indicate that this biological active system is operating close to the self-organization threshold.

Splay-density coupling in semiflexible main-chain nematic polymers with hairpins

A main-chain nematic polymer melt/solution exhibits macroscopic orientational order of main polymer chains, i.e., a preferred (nematic) direction. It has long been known that in such polymeric liquid crystals spatial density/concentration variations and distortions of the nematic direction are coupled, obeying a vectorial continuity constraint whose rigidity increases with chain length. Its vectorial nature precludes the application to flexible chains, where backfolds (hairpins) are present and apolar nematic symmetry is manifest, which has been its puzzling feature from the beginning. We now establish a description of the splay-density coupling in the case of arbitrary backfolding, devising a continuity constraint for the "recovered" polar order of the chain tangents and introducing hairpins as its new type of sources. Performing detailed Monte Carlo simulations of nematic monodomain melts of "soft" worm-like chains with variable length and flexibility, we show via their structure factors that the weakening of the coupling due to the backfolding can be consistently quantified on the macroscopic level.

Effects of flow on the dynamics of a ferromagnetic nematic liquid crystal

We investigate the effects of flow on the dynamics of ferromagnetic nematic liquid crystals. As a model, we study the coupled dynamics of the magnetization, M, the director field, n, associated with the liquid crystalline orientational order, and the velocity field, v. We evaluate how simple shear flow in a ferromagnetic nematic is modified in the presence of small external magnetic fields, and we make experimentally testable predictions for the resulting effective shear viscosity: an increase by a factor of 2 in a magnetic field of about 20 mT. Flow alignment, a characteristic feature of classical uniaxial nematic liquid crystals, is analyzed for ferromagnetic nematics for the two cases of magnetization in or perpendicular to the shear plane. In the former case, we find that small in-plane magnetic fields are sufficient to suppress tumbling and thus that the boundary between flow alignment and tumbling can be controlled easily. In the latter case, we furthermore find a possibility of flow alignment in a regime for which one obtains tumbling for the pure nematic component. We derive the analogs of the three Miesowicz viscosities well-known from usual nematic liquid crystals, corresponding to nine different configurations. Combinations of these can be used to determine several dynamic coefficients experimentally.

Magneto-optic dynamics in a ferromagnetic nematic liquid crystal

We investigate dynamic magneto-optic effects in a ferromagnetic nematic liquid crystal experimentally and theoretically. Experimentally we measure the magnetization and the phase difference of the transmitted light when an external magnetic field is applied. As a model we study the coupled dynamics of the magnetization, M, and the director field, n, associated with the liquid crystalline orientational order. We demonstrate that the experimentally studied macroscopic dynamic behavior reveals the importance of a dynamic cross-coupling between M and n. The experimental data are used to extract the value of the dissipative cross-coupling coefficient. We also make concrete predictions about how reversible cross-coupling terms between the magnetization and the director could be detected experimentally by measurements of the transmitted light intensity as well as by analyzing the azimuthal angle of the magnetization and the director out of the plane spanned by the anchoring axis and the external magnetic field. We derive the eigenmodes of the coupled system and study their relaxation rates. We show that in the usual experimental setup used for measuring the relaxation rates of the splay-bend or twist-bend eigenmodes of a nematic liquid crystal one expects for a ferromagnetic nematic liquid crystal a mixture of at least two eigenmodes.

Dynamic Magneto-optic Coupling in a Ferromagnetic Nematic Liquid Crystal

Hydrodynamics of complex fluids with multiple order parameters is governed by a set of dynamic equations with many material constants, of which only some are easily measurable. We present a unique example of a dynamic magneto-optic coupling in a ferromagnetic nematic liquid, in which long-range orientational order of liquid crystalline molecules is accompanied by long-range magnetic order of magnetic nanoplatelets. We investigate the dynamics of the magneto-optic response experimentally and theoretically and find out that it is significantly affected by the dissipative dynamic cross-coupling between the nematic and magnetic order parameters. The cross-coupling coefficient determined by fitting the experimental results with a macroscopic theory is of the same order of magnitude as the dissipative coefficient (rotational viscosity) that governs the reorientation of pure liquid crystals.

Macroscopic behavior of polar nematic gels and elastomers

We present the derivation of the macroscopic equations for uniaxial polar nematic gels and elastomers. We include the strain field as well as relative rotations as independent dynamic macroscopic degrees of freedom. As a consequence, special emphasis is laid on possible static and dynamic cross-couplings between these macroscopic degrees of freedom associated with the network, and the other macroscopic degrees of freedom including reorientations of the macroscopic polarization. In particular, we find static and dissipative dynamic cross-couplings between strain fields and relative rotations on one hand and the macroscopic polarization on the other that allow for new possibilities to manipulate polar nematics. To give one example each for the effects of a static and a dissipative cross-coupling: we find that a static electric field applied perpendicularly to the polar preferred direction leads to relative rotations while dynamically relative rotations can lead to transverse electric currents. In addition to a permanent network, we also consider the effect of a transient network, which is particularly important for the case of gels, melts and concentrated polymer solutions. A section on the influence of macroscopic chirality is included as well.

Ray-trace modeling of acoustic Green's function based on the semiclassical (eikonal) approximation

The Green's function (GF) for the scalar wave equation is numerically constructed by an advanced geometric ray-tracing method based on the eikonal approximation related to the semiclassical propagator. The underlying theory is first briefly introduced, and then it is applied to acoustics and implemented in a ray-tracing-type numerical simulation. The so constructed numerical method is systematically used to calculate the sound field in a rectangular (cuboid) room, yielding also the acoustic modes of the room. The simulated GF is rigorously compared to its analytic approximation. Good agreement is found, which proves the devised numerical approach potentially useful also for low frequency acoustic modeling, which is in practice not covered by geometrical methods.

Generalized conservation law for main-chain polymer nematics

We explore the implications of the conservation law(s) and the corresponding so-called continuity equation(s), resulting from the coupling between the positional and the orientational order in main-chain polymer nematics, by showing that the vectorial and tensorial forms of these equations are in general not equivalent and cannot be reduced to one another, but neither are they disjoint alternatives. We analyze the relation between them and elucidate the fundamental role that the chain backfolding plays in the determination of their relative strength and importance. Finally, we show that the correct penalty potential in the effective free energy, implementing these conservation laws, should actually connect both the tensorial and the vectorial constraints. We show that the consequences of the polymer chains' connectivity for their consistent mesoscopic description are thus not only highly nontrivial but that its proper implementation is absolutely crucial for a consistent coarse-grained description of the main-chain polymer nematics.

Reversible and dissipative macroscopic contributions to the stress tensor: active or passive?

The issue of dynamic contributions to the macroscopic stress tensor has been of high interest in the field of bio-inspired active systems over the last few years. Of particular interest is a direct coupling ("active term") of the stress tensor with the order parameter, the latter describing orientational order induced by active processes. Here we analyze more generally possible reversible and irreversible dynamic contributions to the stress tensor for various passive and active macroscopic systems. This includes systems with tetrahedral/octupolar order, polar and non-polar (chiral) nematic and smectic liquid crystals, as well as active fluids with a dynamic preferred (polar or non-polar) direction. We show that it cannot a priori be seen, neither from the symmetry properties of the macroscopic variables involved, nor from the structure of the cross-coupling contributions to the stress tensor, whether the system studied is active or passive. Rather, that depends on whether the variables that give rise to those cross-couplings in the stress tensor are driven or not. We demonstrate that several simplified descriptions of active systems in the literature that neglect the necessary counter term to the active term violate linear irreversible thermodynamics and lead to an unphysical contribution to the entropy production.

Backflow-mediated domain switching in nematic liquid crystals

We study the dynamics of the nematic liquid crystal kickback effect upon removal of a primary electric field and its amplification by a perpendicular secondary electric field resulting in the formation of domains with a reverse director orientation. Using computational fluid dynamics, we show that the domain formation is a robust phenomenon that takes place also in the complex case of multiple irregular random Freedericksz domains in three dimension as they appear in a realistic experimental situation. We propose domain switching by kickback amplification as a tool for self-insertion of shell-like inhomogeneities into an otherwise perfectly uniform director field configuration.

Collective stop-and-go dynamics of active bacteria swarms

We set up a macroscopic model of bacterial growth and transport based on a dynamic preferred direction-the collective velocity of the bacteria. This collective velocity is subject to the isotropic-nematic transition modeling the density-controlled transformation between immotile and motile bacterial states. The choice of the dynamic preferred direction introduces a distinctive coupling of orientational ordering and transport not encountered otherwise. The approach can also be applied to other systems spontaneously switching between individual (disordered) and collective (ordered) behavior and/or collectively responding to density variations, e.g., bird flocks, fish schools, etc. We observe a characteristic and robust stop-and-go behavior. The inclusion of chirality results in a complex pulsating dynamics.

Active polar two-fluid macroscopic dynamics

We study the dynamics of systems with a polar dynamic preferred direction. Examples include the pattern-forming growth of bacteria as well as shoals of fish, flocks of birds and migrating insects. Due to the fact that the preferred direction only exists dynamically, but not statically, the macroscopic variable of choice is the macroscopic velocity associated with the motion of the active units, which are typically biological in nature. We derive the macroscopic equations for such a system and discuss novel static, reversible and irreversible cross-couplings connected to a second velocity as a variable. We analyze in detail how the macroscopic behavior of an active system with a polar dynamic preferred direction compares to other systems with two velocities including immiscible liquids and electrically neutral quantum liquids such as superfluid (4)He and (3)He . We critically discuss changes in the normal mode spectrum when comparing uncharged superfluids, immiscible liquids and active system with a polar dynamic preferred direction. We investigate the influence of a macroscopic hand (collective effects of chirality) on the macroscopic behavior of such active media.

Tensorial conservation law for nematic polymers

We derive the "conservation law" for nematic polymers in tensorial form valid for quadrupolar orientational order, in contradistinction to the conservation law in the case of polar orientational order. Due to microscopic differences in the coupling between the orientational field deformations and the density variations for polar and quadrupolar order, we find that the respective order parameters satisfy fundamentally distinct constraints. Being necessarily scalar in its form, the tensorial conservation law is obtained straightforwardly from the gradients of the polymer nematic tensor field and connects the spatial variation of this tensor field with density variations. We analyze the differences between the polar and the tensorial forms of the conservation law, present some explicit orientational fields that satisfy the tensorial constraint, and discuss the role of singular "hairpins," which do not affect the local quadrupolar order of polymer nematics, but nevertheless influence its gradients.

Lehmann effects and rotatoelectricity in liquid crystalline systems made of achiral molecules

We discuss Lehmann effects and rotato-electricity for liquid crystalline phases made of achiral molecules. We point out that for static and dynamic Lehmann effects to exist, it is not necessary to have chiral molecules provided the overall structure has macroscopic chirality. This question is of direct relevance for liquid crystalline phases formed by bent-core molecules provided they have a sufficiently low symmetry. This includes systems which break parity symmetry and have overall C(2) or C(1) symmetry. We point out that for liquid crystalline gels and elastomers one should be able to observe rotato-electricity for systems with macroscopic chirality. Rotatoelectricity is associated with the relative rotations between two subsystems, namely, between the network and the director, in an external electric field. Candidates include gels and even monolayers prepared from bent-core molecules with sufficiently low symmetry.

Macroscopic behavior of systems with an axial dynamic preferred direction

We present the derivation of the macroscopic equations for systems with an axial dynamic preferred direction. In addition to the usual hydrodynamic variables, we introduce the time derivative of the local preferred direction as a new variable and discuss its macroscopic consequences including new cross-coupling terms. Such an approach is expected to be useful for a number of systems for which orientational degrees of freedom are important including, for example, the formation of dynamic macroscopic patterns shown by certain bacteria such a Proteus mirabilis. We point out similarities in symmetry between the additional macroscopic variable discussed here, and the magnetization density in magnetic systems as well as the so-called Î vector in superfluid (3)He-A. Furthermore we investigate the coupling to a gel-like system for which one has the strain tensor and relative rotations between the new variable and the network as additional macroscopic variables.