Velocity Gradient Direction Research Articles

Does dispersed phase inertia affect the shape of sheared emulsion droplets?

Inertial effects on sheared emulsion droplets are a topic of scientific and industrial interest for several applications from processing to microfluidics. Most of the literature have addressed so far the role of inertia of the continuous phase, which is known to affect shear-induced droplet deformation and migration at values of the Reynolds number of the external fluid Rec > 1. However, less attention has been paid to the case of inertial effects inside the droplets, corresponding to values of the Reynolds number of the droplet fluid Red > 1. Such a case is especially relevant when the viscosity ratio λ between the droplet and the external fluid is ≪ 1, which is typical of water-in-oil emulsions where the low values of droplet viscosity can result in Red > 1, while Rec < 1 due to the larger oil viscosity. Here, we focus on the effect of droplet inertia under shear flow at λ ≪ 1 by high-speed video microscopy experiments in a microcapillary and by numerical simulations based on a front-tracking finite-difference method. The results unveil the droplet's three-dimensional shape under shear flow at low viscosity ratios and show that droplet inertia tends to increase droplet deformation and orientation along the flow direction and to form two vortices inside the droplets even at small Rec. The latter findings are at variance with the case of external fluid inertia, where droplets become more aligned with the velocity gradient direction.

Simulation of Air Flow Field and Temperature Distribution in the Ward of a Newly-Built Hospital of Post-COVID-19

In order to solve the problem of uneven distribution of air conditioning temperature and air velocity in the ward, it is easy to produce the uncomfortable feeling of cold and hot and wind blowing. Taking the standard double room general ward of a newly built hospital as the research object, a mathematical model was established, and CFD software was used to numerically simulate the temperature field and velocity field of the air in the ward, optimize the location of the air outlet, and put forward the suggestion of the optimal installation location of the hospital bed. The results show that when the fan coiler air supply outlet is close to the west wall and the fresh air outlet is far away from the west wall, the inhomogeneity of the distribution of the temperature field and velocity field in the ward is reduced, and at this time, the temperature and velocity distribution of the air in the ward is more uniform, so that the patients’ overall feeling in the ward is more comfortable, and at this time, the installation position of the air outlet is more reasonable; and it is determined that the optimal placement of the beds in the room is at the locations of [Formula: see text] = 2 m, [Formula: see text] = 2.5 m and [Formula: see text] = 2 m, [Formula: see text] = 4.5 m, and at this time the two beds are at the same time, which is more reasonable. When [Formula: see text] = 4.5 m, the temperature difference between the two beds is less than 0.5 K, the wind speed difference is not more than 0.08 m/s, and the velocity gradient direction is the same.

Morphology of Anisotropic Banded Structures in an Emulsion under Simple Shear

The formation of flow-induced, oriented structures in two-phase systems, as in this study, is a phenomenon of considerable interest to the scientific and industrial sectors. The main difficulty in understanding the formation of bands of droplets is the simultaneous interplay of physicochemical, hydrodynamic, and mechanical effects. Additionally, banded structure materials frequently show multiple length scales covering several decades as a result of complex time-dependent stress fields. Here, to facilitate understanding a subset of these structures, we studied water in oil emulsions and focused on the effects of three variables specifically: the confinement factor (Co=2R/H), the viscosity ratio (p), and the applied shear rate (γ˙). The confinement (Co) is the ratio between the drop’s diameter (2R) and the separation of (the gap between) the circular rotating disks (H) containing the emulsion. We carried out (a) observations of the induced structure under different simple shear rates, as well as (b) statistical and morphological analysis of these bands. At low shear rates, the system self-assembles into bands along the direction of the flow and stacked normal to the velocity gradient direction. At higher shear rates is possible to observe bands normal to the vorticity direction. Here, we show that a detailed analysis of the dynamics of the band structures is amenable, as well as measurements of flow field anomalies simultaneously observed. The local emulsion viscosity varies in time, increasing in regions of higher droplet concentration and subsequently inducing velocity components perpendicular to the main flow direction. Thus, the emulsion morphology evolves and changes macroscopically. A relatively plausible explanation is attributed to the competitive effects of coalescence and the rupture of drops, where p values less than one predominate coalescence.

Alignment of dense molecular core morphology and velocity gradients with ambient magnetic fields

ABSTRACT Studies of dense core morphologies and their orientations with respect to gas flows and the local magnetic field have been limited to only a small sample of cores with spectroscopic data. Leveraging the Green Bank Ammonia Survey alongside existing sub-millimeter continuum observations and Planck dust polarization, we produce a cross-matched catalogue of 399 dense cores with estimates of core morphology, size, mass, specific angular momentum, and magnetic field orientation. Of the 399 cores, 329 exhibit 2D vLSR maps that are well fit with a linear gradient, consistent with rotation projected on the sky. We find a best-fit specific angular momentum and core size relationship of J/M ∝ R1.82 ± 0.10, suggesting that core velocity gradients originate from a combination of solid body rotation and turbulent motions. Most cores have no preferred orientation between the axis of core elongation, velocity gradient direction, and the ambient magnetic field orientation, favouring a triaxial and weakly magnetized origin. We find, however, strong evidence for a preferred anti-alignment between the core elongation axis and magnetic field for protostellar cores, revealing a change in orientation from starless and prestellar populations that may result from gravitational contraction in a magnetically-regulated (but not dominant) environment. We also find marginal evidence for anti-alignment between the core velocity gradient and magnetic field orientation in the L1228 and L1251 regions of Cepheus, suggesting a preferred orientation with respect to magnetic fields may be more prevalent in regions with locally ordered fields.

Single-polymer dynamics of starch-like branched ring polymers in steady shear flow

The stretching dynamics and dynamical behaviors of individual branched ring polymer (BRP), a coarse-grained model for some types of the starch, in steady shear flow are studied by using a hybrid mesoscale simulation approach that combines multiparticle collision dynamics with standard molecular dynamics. By analyzing the stretched configuration of BRPs, we find the polymer size increases nonmonotonically with increasing branch length. Meanwhile, the decrease of the alignment angle of the stretched configuration of BRPs follows a universal power law during the first downward phase as the shear rate increases. Constructing the three-dimensional surface of the polymer's ring backbone and tracing the temporal fluctuations of the surface's normal vector along the simulation trajectory, the tumbling and tank-treading motion are clearly reflected by periodic and non-periodic changes of the normal vector. Interestingly, these temporal changes are much more regular than that of the gyration tensor. Thus, a novel cross-correlation function, which is the correlation between fluctuations of the normal vector along the flow direction and the velocity-gradient direction, is proposed to analyze the tumbling motion that usually coexists with the tank-treading motion. This function can naturally address the fails of traditional method that analyzing the tumbling motion by determining the correlation of temporal fluctuations of the gyration tensor Gαα. By analyzing the dynamical behaviors of BRPs, diverse dependences of the tumbling frequency ωTB and tank-treading frequency ωTT on the shear rate γ̇ are observed at a wide range of shear rates and polymer sizes. Furthermore, our simulations also reveal that the tank-treading motion is more stable than the tumbling motion for small-branch-size BRPs but the tumbling motion is more stable than the tank-treading motion for large-branch-size BRPs.

Shear thickening in dense bidisperse suspensions

Discrete-particle simulations of bidisperse shear thickening suspensions are reported. The work considers two packing parameters, the large-to-small particle radius ratio ranging from δ=1.4 (nearly monodisperse) to δ=4, and the large particle fraction of the total solid loading with values ζ=0.15, 0.5, and 0.85. Particle-scale simulations are performed over a broad range of shear stresses using a simulation model for spherical particles accounting for short-range lubrication forces, frictional interaction, and repulsion between particles. The variation of rheological properties and the maximum packing fraction ϕJ with shear stress σ are reported. At a fixed volume fraction ϕ, bidispersity decreases the suspension relative viscosity ηr=ηs/η0, where ηs is the suspension viscosity and η0 is the suspending fluid viscosity, over the entire range of shear stresses studied. However, under low shear stress conditions, the suspension exhibits an unusual rheological behavior: the minimum viscosity does not occur as expected at ζ≈0.5, but instead decreases with further increase of ζ to 0.85. The second normal stress difference N2 acts similarly. This behavior is caused by particles ordering into a layered structure, as is also reflected by the zero slope with respect to time of the mean-square displacement in the velocity gradient direction. The relative viscosity ηr of bidisperse rate-dependent suspensions can be predicted by a power law linking it to ϕJ, ηr=(1−ϕ/ϕJ)−2 in both low and high shear stress regimes. The agreement between the power law and experimental data from literature demonstrates that the model captures well the effect of particle size distribution, showing that viscosity roughly collapses onto a single master curve when plotted against the reduced volume fraction ϕ/ϕJ.

Dynamical and Structural Properties of Comb Long-Chain Branched Polymer in Shear Flow.

Using hybrid multi-particle collision dynamics (MPCD) and a molecular dynamics (MD) method, we investigate the effect of arms and shear flow on dynamical and structural properties of the comb long-chain branched (LCB) polymer with dense arms. Firstly, we analyze dynamical properties of the LCB polymer by tracking the temporal changes on the end-to-end distance of both backbones and arms as well as the orientations of the backbone in the flow-gradient plane. Simultaneously, the rotation and tumbling behaviors with stable frequencies are observed. In other words, the LCB polymer undergoes a process of periodic stretched–folded–stretched state transition and rotation, whose period is obtained by fitting temporal changes on the orientation to a periodic function. In addition, the impact induced by random and fast motions of arms and the backbone will descend as the shear rate increases. By analyzing the period of rotation behavior of LCB polymers, we find that arms have a function in keeping the LCB polymer’s motion stable. Meanwhile, we find that the rotation period of the LCB polymer is mainly determined by the conformational distribution and the non-shrinkable state of the structure along the velocity-gradient direction. Secondly, structural properties are numerically characterized by the average gyration tensor of the LCB polymer. The changes in gyration are in accordance with the LCB polymer rolling when varying the shear rate. By analyzing the alignment of the LCB polymer and comparing with its linear and star counterparts, we find that the LCB polymer with very long arms, like the corresponding linear chain, has a high speed to reach its configuration expansion limit in the flow direction. However, the comb polymer with shorter arms has stronger resistance on configuration expansion against the imposed flow field. Moreover, with increasing arm length, the comb polymer in shear flow follows change from linear-polymer-like to capsule-like behavior.

Evaluation of constitutive models for shear-banding wormlike micellar solutions in simple and complex flows

Wormlike micellar solutions possess complex rheology: when exposed to a flow field, the wormlike micelles may orientate, stretch, and break into smaller micelles. Entangled wormlike micellar solutions exhibit shear banding characteristics: macroscopic bands with different local viscosities are organized and stacked along the velocity gradient direction, leading to a non-monotonic flow curve in simple shear. We present a systematic analysis of four commonly used constitutive models that can predict a non-monotonic flow curve and potentially describe the rheology of entangled wormlike micellar solutions with shear-banding characteristics: the Johnson–Segalman, the Giesekus, the thixotropic viscoelastic, and the Vasquez–Cook–McKinley (VCM) models. All four constitutive models contain a stress diffusion term, to account for a smooth transition between the shear bands and ensure a uniqueness of the numerical solution. Initially, the models are fitted to shear and extensional experimental data of a shear-banding wormlike micellar solution. Subsequently, they are employed to solve three non-homogeneous flows: the Poiseuille flow in a planar channel, the flow in a cross-slot geometry, and the flow past a cylinder in a straight channel. Each of these flows exposes the wormlike micellar solution to different flow kinematics (shear, extensional, and mixed), revealing different aspects of its rheological response. The predictive capability of each model is evaluated by directly comparing the numerical results to previously published experimental data obtained from microfluidic devices with corresponding flow configurations. While all the models can describe qualitatively the characteristic features observed experimentally in the benchmark flows, such as plug-like velocity profiles and elastic instabilities, none of them yields a quantitative agreement. Based on the overall performance of the models and also accounting for their differing numerical complexity, we conclude that the Giesekus model is at present the most suitable constitutive equation for simulating shear banding wormlike micellar solutions in flows that exhibit both shear and extensional deformations. However, the quantitative mismatch between model predictions and experiments with wormlike micellar solutions demand that improved constitutive models be developed in future works. • Comparison of popular constitutive models for wormlike micellar solutions. • Evaluation of their performance in rheometric and inhomogeneous shear flows. • Investigation of their predictions in extensional flows and elastic instabilities. • The models can only make qualitative predictions.

Rheo-Dielectrics and Diffusion of Type-A Rouse Chain under Fast Shear Flow: Method of Evaluation of Non-Equilibrium Parameters for FENE, Friction-Reduction, and Brownian Force Intensity Variation

Rouse model is the basic molecular model for unentangled linear polymer chains in melts. Recent studies suggest that the Rouse parameters characterizing the unentangled melts, the spring strength κ , the segmental friction coefficient ζ, and the mean-square Brownian force intensity B, change under fast flow thereby providing significant rheological nonlinearities with those melts (Matsumiya et al., Macromolecules, 51, 9710 (2018)). This article theoretically analyzes effects of the flow-induced changes of these parameters on the dielectric and diffusion behavior of the Rouse chain having so-called type-A dipoles parallel along the chain backbone. It turned out that the dielectric behavior under steady shear is determined by non-equilibrium parameters, rκ = κ/κeq and rζ,ij = ζij/ζeq but irrelevant to rB,ij = B ij/Beq, where the subscript “eq” stands for the quantities at equilibrium and the subscripts “ij” denote the spatial direction under shear flow: i and/or j = x, y, and z for the velocity, velocity gradient, and vorticity directions, respectively. Specifically, the complex dielectric permittivity ε* is analytically expressed in terms of the parameters rκ and rζ,ij, which in turn enables us to evaluate these parameters from data of the dielectric relaxation time and intensity under steady shear (obtained in future experiments). In contrast, the advective diffusion behavior under steady shear is determined by rζ,ij and rB,ij but irrelevant to rκ. The mean-square displacement ‹Δr2CM› of the center of mass defined with respect to the known non-diffusive advection point is analytically expressed in terms of rζ,ij and rB,ij, thereby allowing us to evaluate rB,ij from the diffusion data under steady shear and the dielectrically determined rζ,ij. The method of experimental evaluation of the non-equilibrium parameters presented in this article provides us with a complementary basis for analyzing nonlinear rheological behavior of unentangled melts.

Kinematics of Antlia 2 and Crater 2 from the Southern Stellar Stream Spectroscopic Survey (S 5)

Abstract We present new spectroscopic observations of the diffuse Milky Way satellite galaxies Antlia 2 and Crater 2, taken as part of the Southern Stellar Stream Spectroscopic Survey (S 5). The new observations approximately double the number of confirmed member stars in each galaxy and more than double the spatial extent of spectroscopic observations in Antlia 2. A full kinematic analysis, including Gaia EDR3 proper motions, detects a clear velocity gradient in Antlia 2 and a tentative velocity gradient in Crater 2. The velocity gradient magnitudes and directions are consistent with particle stream simulations of tidal disruption. Furthermore, the orbit and kinematics of Antlia 2 require a model that includes the reflex motion of the Milky Way induced by the Large Magellanic Cloud. We also find that Antlia 2's metallicity was previously overestimated, so it lies on the empirical luminosity–metallicity relation and is likely only now experiencing substantial stellar mass loss. Current dynamical models of Antlia 2 require it to have lost over 90% of its stars to tides, in tension with the low stellar mass loss implied by the updated metallicity. Overall, the new kinematic measurements support a tidal disruption scenario for the origin of these large and extended dwarf spheroidal galaxies.

Searching for Local Counterparts of High-redshift Poststarburst Galaxies in Integral Field Unit Spectroscopic Surveys of Nearby Galaxies

Abstract Searching in the MaNGA IFU survey, I identify nine galaxies that have strong Balmer absorption lines and weak nebular emission lines measured from the spectra integrated over the entire IFU. The spectral features measured from the bulk of the stellar light make these galaxies local analogs of high-redshift spectroscopically selected poststarburst galaxies and thus proxies to understand the mechanisms producing poststarburst galaxies at high redshifts. I present the distributions of absorption line indices and emission line strengths, as well as the stellar kinematics of these local poststarburst galaxies. Almost all local poststarburst galaxies have central compact emission line regions at the central <1 kpc, mostly powered by weak star formation activities. The age-sensitive absorption line indices EW(Hδ) and D n 4000 indicate that the stellar populations at the outskirts are older. Toy stellar population synthesis models suggest that the galaxies as a whole are experiencing a rapid decline of star formation with residual star formation activities at the centers. These features indicate that most poststarburst galaxies are the aftermath of highly dissipative processes that drive gas into centers, invoke centrally concentrated star formation, and then quench the galaxies. Meanwhile, when measurable, poststarburst galaxies have the directions of maximum stellar velocity gradients aligned with photometric major axes, which suggest against major mergers being the principal driving mechanism, while gas-rich minor mergers are plausible. While directly obtaining the same quality of spatially resolved spectra of high-redshift poststarburst galaxies is very difficult, finding proper local counterparts provides an alternative to understand quenching processes in the distant universe.

On the magnetization of dilute ferrofluid emulsions in shear flows

A 3D numerical investigation on the magnetization of dilute magnetic emulsions subjected to shear flows and external magnetic fields is carried out. The present study is an extension of the previous work of Cunha et al. [“Effects of external magnetic fields on the rheology and magnetization of dilute emulsions of ferrofluid droplets in shear flows,” Phys. Fluids 32, 073306 (2020)] for the 2D analogous system. The ferrofluid is assumed superparamagnetic such as the bulk magnetization depends on droplet shape and orientation. The magnetic field is applied in the main flow, main velocity gradient, and main vorticity directions. For the two former cases, the emulsion magnetization does not perfectly align with the external field, such stronger shear rates leading to larger misalignment angles. For fields parallel with flow direction, stronger fields lead to a decrease in this misalignment angle, while for external magnetic fields in the main velocity gradient direction, stronger magnetic fields lead to an increase in misalignment angle. Although these results are qualitatively similar to those presented by Cunha et al. [“Effects of external magnetic fields on the rheology and magnetization of dilute emulsions of ferrofluid droplets in shear flows,” Phys. Fluids 32, 073306 (2020)], the misalignment angles observed are significantly smaller than those of the analogous 2D. The magnetic forces at the droplet interface create a magnetic torque in the emulsion, resulting in asymmetries of the bulk stress tensor. For external magnetic fields in the main velocity gradient direction, magnetic torques increase monotonically with increasing field intensities, while for external fields in the main velocity direction, magnetic torques are smaller and remain roughly constant for Camag > 8. We observed that the magnetic field applied in the main vorticity direction may lead to oblate droplets, rather than the more conventional prolate one.

Possible Break-down of Up–Down Symmetry for Propagation of Parallel Velocity Gradient Driven Mode near Edge Transport Barrier

The propagation direction of parallel velocity gradient driven mode in the edge of H-mode plasmas is investigated. We study the possibility to observe a preferential propagation (either up-ward or down-ward) direction, simultaneously in the low-field as well as high-field sides of torus. The condition to observe such an up–down preferential propagation is derived. The proximity of the barrier to the separatrix is found to be the key for such preferential propagations. This result provides a hypothesis, which will be tested by future experiments, and a step forward to understand the broken up–down symmetry in the H-mode plasmas.

Advancing the Velocity Gradient Technique: Using Gradient Amplitudes and Handling Thermal Broadening

Abstract The recent development of the velocity gradient technique allows observers to map magnetic field orientations and magnetization using the direction of velocity gradients. Aside from the directions, amplitudes of velocity gradients also contain valuable information about the underlying properties of magnetohydrodynamic (MHD) turbulence. In this paper, we explore what physical information is contained in the amplitudes of velocity gradients and discuss how this information can be used to diagnose properties of turbulence in both diffuse and self-gravitating interstellar media. We identify the relations between amplitudes of both intensity and velocity centroid gradients and the sonic Mach number M s , and they are consistent with the theory’s predictions. We test the robustness of the method and discuss how to utilize the amplitudes of gradients into self-gravitating media. To extend the velocity gradient technique, we also discuss the usage of amplitude method to position–position–velocity space as a possible way to retrieve the velocity channel maps before the contamination of thermal broadening. We discuss that the velocity gradient technique with these advancements could potentially give a significantly more accurate statistical insight into the properties of magnetized turbulence.

Shear-induced deconfinement of hard disks

Using Brownian dynamics simulations, we investigate the response to shear of a two-dimensional system of quasi-hard disks that are confined in the velocity gradient direction by a smooth external potential. Shearing the confined system leads to a homogenization of the one-body density profile. In order to rationalize this deconfinement effect, we split the internal one-body force field into adiabatic and superadiabatic contributions. We demonstrate that the superadiabatic force field consists of viscous and of structural contributions. We give an empirical scaling law that yields results for the superadiabatic force profiles both in the flow and in the gradient direction, in excellent agreement with the simulation data.

Angular momentum profiles of Class 0 protostellar envelopes

Context. Understanding the initial properties of star forming material and how they affect the star formation process is a key question. The infalling gas must redistribute most of its initial angular momentum inherited from prestellar cores before reaching the central stellar embryo. Disk formation has been naturally considered as a possible solution to this “angular momentum problem”. However, how the initial angular momentum of protostellar cores is distributed and evolves during the main accretion phase and the beginning of disk formation has largely remained unconstrained up to now. Aims. In the framework of the IRAM CALYPSO survey, we obtained observations of the dense gas kinematics that we used to quantify the amount and distribution of specific angular momentum at all scales in collapsing-rotating Class 0 protostellar envelopes. Methods. We used the high dynamic range C18O (2−1) and N2H+ (1−0) datasets to produce centroid velocity maps and probe the rotational motions in the sample of 12 envelopes from scales ~50 to ~5000 au. Results. We identify differential rotation motions at scales ≲1600 au in 11 out of the 12 protostellar envelopes of our sample by measuring the velocity gradient along the equatorial axis, which we fit with a power-law model v ∝ rα. This suggests that coherent motions dominate the kinematics in the inner protostellar envelopes. The radial distributions of specific angular momentum in the CALYPSO sample suggest the following two distinct regimes within protostellar envelopes: the specific angular momentum decreases as j ∝ r1.6±0.2 down to ~1600 au and then tends to become relatively constant around ~6 × 10−4 km s−1 pc down to ~50 au. Conclusions. The values of specific angular momentum measured in the inner Class 0 envelopes suggest that material directly involved in the star formation process (<1600 au) has a specific angular momentum on the same order of magnitude as what is inferred in small T-Tauri disks. Thus, disk formation appears to be a direct consequence of angular momentum conservation during the collapse. Our analysis reveals a dispersion of the directions of velocity gradients at envelope scales >1600 au, suggesting that these gradients may not be directly related to rotational motions of the envelopes. We conclude that the specific angular momentum observed at these scales could find its origin in other mechanisms, such as core-forming motions (infall, turbulence), or trace an imprint of the initial conditions for the formation of protostellar cores.

Droplets. II. Internal Velocity Structures and Potential Rotational Motions in Pressure-dominated Coherent Structures

Abstract We present an analysis of the internal velocity structures of the newly identified sub-0.1 pc coherent structures, droplets, in L1688 and B18. By fitting 2D linear velocity fields to the observed maps of velocity centroids, we determine the magnitudes of linear velocity gradients and examine the potential rotational motions that could lead to the observed velocity gradients. The results show that the droplets follow the same power-law relation between the velocity gradient and size found for larger-scale dense cores. Assuming that rotational motion giving rise to the observed velocity gradient in each core is a solid-body rotation of a rotating body with a uniform density, we derive the “net rotational motions” of the droplets. We find a ratio between rotational and gravitational energies, β, of ∼0.046 for the droplets, and when including both droplets and larger-scale dense cores, we find β ∼ 0.039. We then examine the alignment between the velocity gradient and the major axis of each droplet, using methods adapted from the histogram of relative orientations introduced by Soler et al. We find no definitive correlation between the directions of velocity gradients and the elongations of the cores. Lastly, we discuss physical processes other than rotation that may give rise to the observed velocity field.

Three-dimensional observation of Brownian particles under steady shear flow by stereo microscopy.

Three-dimensional observation of Brownian particles under shear flow is performed with a stereo microscope to examine the nature of the Brownian motion that occurs in the presence of shear flow. From the three-dimensional trajectories of the particles, we clearly demonstrate the occurrence of anomalous diffusion in the flow direction and the coupling of the displacements in the flow and velocity gradient directions. Furthermore, we experimentally obtain the probability distribution function and current density, which also exhibit characteristic features, and compare the obtained results with theoretical results derived using the Fokker-Planck equation.

Inhomogeneous Flow of Wormlike Micelles: Predictions of the Generalized BMP Model with Normal Stresses

In this work, we examine the shear-banding flow in polymer-like micellar solutions with the generalized Bautista-Manero-Puig (BMP) model. The couplings between flow, structural parameters, and diffusion naturally arise in this model, derived from the extended irreversible thermodynamics (EIT) formalism. Full tensorial expressions derived from the constitutive equations of the model, in addition to the conservation equations, apply for the case of simple shear flow, in which gradients of the parameter representing the structure of the system and concentration vary in the velocity gradient direction. The model predicts shear-banding, concentration gradients, and jumps in the normal stresses across the interface in shear-banding flows.

Kinematics of dense gas in the L1495 filament

Context. Nitrogen bearing species, such as NH3, N2H+, and their deuterated isotopologues show enhanced abundances in CO-depleted gas, and thus are perfect tracers of dense and cold gas in star-forming regions. The Taurus molecular cloud contains the long L1495 filament providing an excellent opportunity to study the process of star formation in filamentary environments. Aims. We study the kinematics of the dense gas of starless and protostellar cores traced by the N2D+(2–1), N2H+(1–0), DCO+(2–1), and H13CO+(1–0) transitions along the L1495 filament and the kinematic links between the cores and surrounding molecular cloud. Methods. We measured velocity dispersions, local and total velocity gradients, and estimate the specific angular momenta of 13 dense cores in the four transitions using on-the-fly observations with the IRAM 30-m antenna. To study a possible connection to the filament gas, we used the C18O(1–0) observations. Results. The velocity dispersions of all studied cores are mostly subsonic in all four transitions and are similar and almost constant dispersion across the cores in N2D+(2–1) and N2H+(1–0). A small fraction of the DCO+(2–1) and H13CO+(1–0) lines show transonic dispersion and exhibit a general increase in velocity dispersion with line intensity. All cores have velocity gradients (0.6–6.1 km s−1 pc−1), typical of dense cores in low-mass star-forming regions. All cores show similar velocity patterns in the different transitions, simple in isolated starless cores, and complex in protostellar cores and starless cores close to young stellar objects where gas motions can be affected by outflows. The large-scale velocity field traced by C18O(1–0) does not show any perturbation due to protostellar feedback and does not mimic the local variations seen in the other four tracers. Specific angular momentum J∕M varies in a range (0.6–21.0) × 1020 cm2 s−1, which is similar to the results previously obtained for dense cores. The J∕M measured in N2D+(2–1) is systematically lower than J∕M measured in DCO+(2–1) and H13CO+(1–0). Conclusions. All cores show similar properties along the 10 pc-long filament. N2D+(2–1) shows the most centrally concentrated structure, followed by N2H+(1–0) and DCO+(2–1), which show similar spatial extent, and H13CO+(1–0). The non-thermal contribution to the velocity dispersion increases from higher to lower density tracers. The change of magnitude and direction of the total velocity gradients depending on the tracer used indicates that internal motions change at different depths within the cloud. N2D+ and N2H+ show smaller gradients than the lower density tracers DCO+ and H13CO+, implying a loss of specific angular momentum at small scales. At the level of cloud-core transition, the core’s external envelope traced by DCO+ and H13CO+ is spinning up, which is consistent with conservation of angular momentum during core contraction. C18O traces the more extended cloud material whose kinematics is not affected by the presence of dense cores. The decrease in specific angular momentum towards the centres of the cores shows the importance of local magnetic fields to the small-scale dynamics of the cores. The random distributions of angles between the total velocity gradient and large-scale magnetic field suggests that magnetic fields may become important only in high density gas within dense cores.