Dust Dynamics Research Articles

Dynamics of electrostatically lofted dust on airless planetary bodies

The dynamics of lofted dust on airless bodies have been the subject of much study since the 1960s, when the lunar horizon glow was first observed. Lofted dust dynamics have important implications for the evolution of an airless body's surface properties. To date, most of these studies have had to rely on assumptions of initial conditions of the lofted dust grains due to a lack of experimental results. In this paper, we present a study of lofted dust grains, making use of initial conditions obtained from recent laboratory results. Additionally, we distinguish between photoemission rates from isolated dust grains and from the bulk regolith. We explore dust lofting dynamics across a large size range of dust grains (0.1 to 10 μm) and the surface gravity of their parent bodies (0.0001 to 1 lunar g). Charging and lofting results reveal a complex interplay between the grain size, gravity, initial charge, and the various charging currents. It is shown that the sheath electric field becomes increasingly significant in the lofted dust dynamics as the gravitational field decreases. Due to the initial negative charge of dust grains lofted from a positively charged regolith surface, their lofting heights are found to be generally reduced compared to uncharged grains with similar initial speeds. We show that micron-sized dust grains can be lofted to high altitudes and even escape from smaller bodies, leading to the loss of fine-grained materials from the surface.

Late Quaternary Dust, Loess and Desert Dynamics in Upwind Areas of the Chinese Loess Plateau

As a key global climate and dust archive, the nature of Chinese loess generation, transport and deposition remains debated. The lack of consensus on dust dynamics from sources to leeward regions fundamentally limits interpretation of the preserved past climate and dust record. Here, we investigate chronostratigraphic variability of aeolian deposits in upwind regions of the modern Chinese Loess Plateau (CLP) and attempt to understand dust dynamics that potentially affects loess deposition downwind. The strata consist of alternating layers of typical loess, well-sorted sand, and sandy loess, with obvious unconformities occurring at the transitions from loess to sand. We suggest that pre-existing typical loess in regions to the northwest of the modern CLP was eroded by wind, providing a significant source of homogeneous dust for the dust deposits downwind. The sand deposits interbedded with typical loess at the study sites suggests that proximal deserts have greatly expanded and contracted repeatedly prior to the Holocene. However, the spatial extents of the deserts, as inferred from the sections here, have not markedly diminished after the major expansion during the Last Glacial Maximum. Such a pattern of proximal desert dynamics plays an important role in regulating dust emission and transport, strongly affecting dust sequences on the CLP. Our results suggest a complex scenario of dust dynamics in upwind regions of the CLP at least over the Late Quaternary; the involved processes have to be considered when using conventional proxies from Chinese loess deposits to recover the history of climate and dust changes.

On dust evolution in planet-forming discs in binary systems – I. Theoretical and numerical modelling: radial drift is faster in binary discs

ABSTRACT Many stars are in binaries or higher order multiple stellar systems. Although in recent years a large number of binaries have been proven to host exoplanets, how planet formation proceeds in multiple stellar systems has not been studied much yet from the theoretical standpoint. In this paper, we focus on the evolution of the dust grains in planet-forming discs in binaries. We take into account the dynamics of gas and dust in discs around each component of a binary system under the hypothesis that the evolution of the circumprimary and the circumsecondary discs is independent. It is known from previous studies that the secular evolution of the gas in binary discs is hastened due to the tidal interactions with their hosting stars. Here, we prove that binarity affects dust dynamics too, possibly in a more dramatic way than the gas. In particular, the presence of a stellar companion significantly reduces the amount of solids retained in binary discs because of a faster, more efficient radial drift, ultimately shortening their lifetime. We prove that how rapidly discs disperse depends both on the binary separation, with discs in wider binaries living longer, and on the disc viscosity. Although the less-viscous discs lose high amounts of solids in the earliest stages of their evolution, they are dissipated slowly, while those with higher viscosities show an opposite behaviour. The faster radial migration of dust in binary discs has a striking impact on planet formation, which seems to be inhibited in this hostile environment, unless other disc substructures halt radial drift further in. We conclude that if planetesimal formation were viable in binary discs, this process would take place on very short time-scales.

The central parsec of NGC 3783: a rotating broad emission line region, asymmetric hot dust structure, and compact coronal line region

Using VLTI/GRAVITY and SINFONI data, we investigate the subparsec gas and dust structure around the nearby type 1 active galactic nucleus (AGN) hosted by NGC 3783. The K-band coverage of GRAVITY uniquely allows simultaneous analysis of the size and kinematics of the broad line region (BLR), the size and structure of the near-infrared(near-IR)-continuum-emitting hot dust, and the size of the coronal line region (CLR). We find the BLR, probed through broad Brγ emission, to be well described by a rotating, thick disc with a radial distribution of clouds peaking in the inner region. In our BLR model, the physical mean radius of 16 light-days is nearly twice the ten-day time-lag that would be measured, which closely matches the ten-day time-lag that has been measured by reverberation mapping. We measure a hot dust full-width at half-maximum (FWHM) size of 0.74 mas (0.14 pc) and further reconstruct an image of the hot dust, which reveals a faint (5% of the total flux) offset cloud that we interpret as an accreting or outflowing cloud heated by the central AGN. Finally, we directly measure the FWHM size of the nuclear CLR as traced by the [Ca VIII] and narrow Brγ line. We find a FWHM size of 2.2 mas (0.4 pc), fully in line with the expectation of the CLR located between the BLR and narrow line region. Combining all of these measurements together with larger scale near-IR integral field unit and mid-IR interferometry data, we are able to comprehensively map the structure and dynamics of gas and dust from 0.01 to 100 pc.

Gravitoviscous Protoplanetary Disks with a Dust Component. V. The Dynamic Model for Freeze-out and Sublimation of Volatiles

Abstract The snowlines of various volatile species in protoplanetary disks are associated with abrupt changes in gas composition and dust physical properties. Volatiles may affect dust growth, as they cover grains with icy mantles that can change the fragmentation velocity of the grains. In turn, dust coagulation, fragmentation, and drift through the gas disk can contribute to the redistribution of volatiles between the ice and gas phases. Here we present the hydrodynamic model FEOSAD for protoplanetary disks with two dust populations and volatile dynamics. We compute the spatial distributions of major volatile molecules (H2O, CO2, CH4, and CO) in the gas, on small and grown dust, and analyze the composition of icy mantles over the initial 0.5 Myr of disk evolution. We show that most of the ice arrives to the surface of the grown dust through coagulation with small grains. Spiral structures and dust rings forming in the disk, as well as photodissociation in the outer regions, lead to the formation of complex snowline shapes and multiple snowlines for each volatile species. During the considered disk evolution, the snowlines shift closer to the star, with their final position being a factor of 4–5 smaller than that at the disk formation epoch. We demonstrate that volatiles tend to collect in the vicinity of their snowlines, both in the ice and gas phases, leading to the formation of thick icy mantles potentially important for dust dynamics. The dust size is affected by a lower fragmentation velocity of bare grains in the model with a higher turbulent viscosity.

Characteristics of Magnetized Dusty Plasma Sheath With Two Ion Species and q-Nonextensive Electrons

The effect of q-nonextensive electrons, nature, and magnitude of dust charge on magnetized dusty plasma sheath with two ion species has been numerically investigated via fluid model. The initial common speed of ion species at the sheath entrance has been extended, which increases from subsonic to supersonic with the decrease in nonextensive parameter q and ion-neutral drag force as well. The presence of super extensive primary electrons ( q <; 1) has significantly affected the sheath parameters characterizing the dusty plasma sheath: dust charging, potential profile, ion and electron densities profile, ion velocity profile, and dust dynamics. It is found that the negatively charged dust grains accelerate in the region of weak electric field, whereas the fluctuation decreases in the region of strong electric field. A significant change has been observed in dust dynamics with the presence of two different natures of dust charges and its magnitudes. The velocity fluctuations of negatively and positively charged grains are in opposite phase. Furthermore, the comparative study of dust velocity in the presence and absence of dust-neutral collisions has been presented.

Aeolian dust dynamics in the Fergana Valley, Central Asia, since ~30 ka inferred from loess deposits

Knowledge of the interactions among atmospheric dynamics, dust emissions and climate system is essential to understand the physical mechanisms for the dust lifecycle, their role in loess formation as well as the predictions of future dust concentration. However, these issues still remain relatively poorly known in Central Asia (CA). The extensive loess deposits on the CA pediments provide a promising archive to explore atmospheric dust dynamics and climatic conditions in the past and their association with loess formation. This study investigates the granulometric and magnetic properties of a loess section (named Osh section) in the Fergana Valley, which provides a sensitive record of atmospheric dust dynamics since 30 ka based on radiometric (AMS 14C) dating. The frequency-dependent magnetic susceptibility (χfd) and the mean grain size are used to reconstruct the broad-scale effective moisture and summer atmospheric dynamics pattern in CA, respectively. The results show that the precession forcing exerts a huge influence on the wind-regime variabilities in CA, but with different physical processes under the impact of the Northern Hemisphere ice sheet (NHIS) before and after 15 ka. The origin of the sedimentation rate variations in the Osh loess is also linked to the NHIS-modulated changes of the atmospheric circulation patterns. Either the strengthened westerlies or the increased surface roughness from higher vegetation cover in loess-deposition areas have significantly accelerated the loess accumulation. As a result, these complicated influence factors of sedimentation rate change in the Osh loess section, especially during the Holocene epoch, may hamper accessibility of the authentic dust emission flux and atmospheric dust concentration in CA.

Restoration of the Parameters of a Gas-Dust Disk Based on Its Synthetic Images

The topic of the present study is combining a dynamic model of a protoplanetary disk with the computations of radiation transfer for obtaining synthetic spectra and disk images suitable for immediate comparison of the model with observations. Evolution of the disk was computed using the FEOSAD hydrodynamic model, which includes a self-consistent calculation of the dynamics of dust and gas in the 2D thin disk approximation. Radiation transfer was simulated by the open code RADMC-3D. Three phases of disk evolution were considered: a young gravitationally unstable disk, a disk during an accretion luminosity burst, and an evolved disk. For these stages, the influence of various processes upon the disk's thermal structure was analyzed, as well as the differences between the temperatures obtained in the initial dynamic model and in the model with a detailed calculation of the radiation transfer. It is shown that viscous heating in the inner regions and adiabatic heating in the disk spirals can be important sources of heating. On the basis of the calculated spectral energy distributions, using SED-fitter software package used for the observations, physical parameters of the model disks were reconstructed. A significant spread between reconstructed parameters and initial characteristics of the disk indicates verification necessity of the models within the framework of spatially resolved observations of disks in the different spectral ranges

On the possibility of dust acoustic waves over sunlit lunar surface

ABSTRACTThe photoelectron sheath and floating fine positively charged dust particles constitute two-component dusty plasma in the sunlit lunar regolith’s vicinity. By including the charge fluctuation into photoelectron–dust dynamics, the lunar exospheric plasma is proposed to support the propagation of long-wavelength dust acoustic (DA) modes. Using the standard approach based on the dynamical equations for continuity, momentum, plasma potential, and dust charging along with Fowler's treatment of photoemission and non-Maxwellian nature of the sheath photoelectrons, the wave dispersion is derived. The dust charge variation modifies the usual DA wave dispersion and excites the ultralow frequency modes that propagate with sufficiently low phase speed. Such ultralow frequency modes are predicted as pronounced for smaller values of dust charge and sheath potential. The DA wave dispersion is also depicted as sensitive to the photoelectrons’ energy distribution within the sheath. The quantitative estimates suggest that the nominal exospheric plasma may exhibit DA waves propagating with frequencies of the order of unity.

Investigation of particle density on dust cloud dynamics in a minimum ignition energy apparatus using digital in-line holography

Solids industries have inherent dust explosion hazards. Process risk assessment parameters include overpressure, deflagration index, and minimum ignition energy. These parameters are influenced by dust dynamics, such as turbulence and concentration. Cloud dynamics are affected by particle morphology, density, size, and polydispersity, which affect explosion parameters. Influence of properties such as density during explosion parameter measurement is often overlooked. This study examines particle density influence on dust clouds in the Kühner MIKE3. Two clouds of particles with different density, but similar particle size and morphology were examined with high-speed digital in-line holography, providing velocity and concentration measurements prior to ignition. Results show velocity and concentration of denser dust is lower compared to lighter dust after ignition delay. The results highlight the density effect on cloud dynamics and make a case for particle density to be considered in setting ignition delay in order to get consistent cloud dynamics and test results.

Modelling dust transport in DIII-D with DTOKS-Upgrade

Comprehensive upgrades to the dust transport code Dust in TOKamaks (DTOKS) that extend the plasma-dust interaction model are presented and compared with recent measurements of dust transport in DIII-D. Simulations incorporating variation in physical properties of graphite dust with temperature and size in a stationary plasma background suggest a substantial decrease in lifetimes due principally to thermal expansion. The trajectories of 53 dust grains identified from analysis of visible camera data taken across two similar shots were used to measure the dust particle velocity distributions. Dust tracks terminated mostly at the outer divertor strike point having a mean observation time of 2.1 ± 0.4 ms. Stochastic modelling of 200 graphite dust particles in the DIII-D tokamak performed with DTOKS-U using plasma simulations generated by OEDGE found similar behaviour, with particles ablating rapidly after acquiring a positive charge in the region close to the outer strike point, creating an acute source of neutral carbon atoms. The simulated mean lifetime, 11 ± 2 ms, showed approximate agreement with experimental observation when corrected by accounting for dust visibility and ignoring the longest trajectories 1.5 ± 0.2 ms. Synthetic diagnostic data generated from coupling the results of DTOKS-U with the visualisation software Calcam offers a powerful new tool for validation of simulations and predictive calculations of dust dynamics.

Dust and atmospheric influence on plasma properties observed in light gas gun hypervelocity impact experiments

Plasma and associated radio frequency (RF) emission produced by hypervelocity impacts of dust and meteoroids are a source of scientific information on stellar dust populations and a potential hazard to spacecraft electrical systems. A previously unexplored aspect of these impacts is the influence that non-vaporized ejecta, or dust, can have on both the plasma and RF emission. Although initially neutral, this dust can gain a charge through collisions with the plasma potentially forming a dusty plasma. Characterizing dust-producing impacts allows for assessing the threat they pose to spacecraft. This paper investigates the influence that a 0.5 Torr background pressure and dust had on the plume evolution of ground-based hypervelocity impact experiments. The effects of material and target charge on dust production and dynamics were explored. Faraday cup plasma sensors were designed and built specifically for these experiments to capture the distribution of charge in the plume and record highly transient charged dust detections. We found that the background gas had a significant effect on the propagation and evolution of the impact plume, slowing the plume from its jetting velocity of 16 km/s down to 10 km/s leading to a Rayleigh-Taylor instability. Charged dust was confirmed by the Faraday cup measurements. Based on high-speed imagery, we observed that plasma was dragged along the trajectory of the expanding dust curtain. The measured signal from this dragged plasma lasted for 10 times longer than plasma that did not contain dust. Plasma with dust was highly negative with current densities measured by the plasma sensors of up to 0.1 A/m2 — 10 to 1000 times more dense than measured on sensors at other elevations — putting spacecraft electronics at greater risk of RF interference and electrical discharges.

Formation of Dust Filaments in the Diffuse Envelopes of Molecular Clouds

Abstract The path to understanding star formation processes begins with the study of the formation of molecular clouds. The outskirts of these clouds are characterized by low column densities that allow the penetration of ultraviolet radiation, resulting in a nonnegligible ionization fraction and the charging of the small dust grains that are mixed with the gas; this diffuse phase is then coupled to the ambient magnetic field. Despite the general assumption that dust and gas are tightly correlated, several observational and theoretical studies have reported variations in the dust-to-gas ratio toward diffuse and cold clouds. In this work, we present the implementation of a new charged particles module for analyzing the dust dynamics in molecular cloud envelopes. We study the evolution of a single population of small charged grains (0.05 μm) in the turbulent, magnetized molecular cloud envelope using this module. We show that variations in the dust-to-gas ratio arise due to the coupling of the grains with the magnetic field, forming elongated dust structures decoupled from the gas. This emphasizes the importance of considering the dynamics of charged dust when simulating the different phases of the interstellar medium, especially for star formation studies.

Dynamics of charged dust in the orbit of Venus

We study the dynamics of co-orbital dust in the inner Solar System, that is, the role of the solar radiation pressure, the Poynting-Robertson effect, the solar wind, and the interplanetary magnetic field, on the location, width, and stability of resonant motion of charged and micron-sized dust grains situated in the 1:1 mean motion resonance with Venus. We find deviations and asymmetry between L4 and L5 in the locations of the libration centers and libration width caused by nongravitational effects with analytical and numerical methods. The triangular Lagrangian points become unstable when solar radiation pressure, the Poynting-Robertson effect, and solar wind drag are considered. The Lorentz force could further destabilize the orbits, especially for small dust particles. We also compare the circular and/or elliptic restricted three-body model and a more complete model that includes all planets.

Linking planetary embryo formation to planetesimal formation

Context. The growth-timescales of planetary embryos and their formation process are imperative for our understanding on how planetary systems form and develop. They determine the subsequent growth mechanisms during the life stages of a circumstellar disk. Aims. We quantify the timescales and spatial distribution of planetary embryos through collisional growth and fragmentation of dynamically forming 100 km sized planetesimals. In our study, the formation timescales of viscous disk evolution and planetesimal formation are linked to the formation of planetary embryos in the terrestrial planet zone. Methods. We connected a one-dimensional model for viscous gas evolution, dust and pebble dynamics, and pebble flux-regulated planetesimal formation to the N-body code LIPAD. Our framework enabled us to study the formation, growth, fragmentation, and evolution of planetesimals with an initial size of 100 km in diameter for the first million years of a viscous disk. Results. Our study shows the effect of the planetesimal surface density evolution on the preferential location and timescales of planetary embryo formation. Only the innermost embryos (&lt;2 au) in our study form well within the lifetime of an active pebble flux for any disk studied. Higher planetesimal disk masses and steeper planetesimal surface density profiles result in more massive embryos within a larger area, rather than in a higher number of embryos. A one-dimensional analytically derived model for embryo formation based on the local planetesimal surface density evolution is presented. This model can reproduce the spatial distribution, formation rate, and total number of planetary embryos at a fraction of the computational cost of the N-body simulations. Conclusions. The formation of planetary embryos in the terrestrial planet zone occurs simultaneously with the formation of planetesimals. The local planetesimal surface density evolution and the orbital spacing of planetary embryos in the oligarchic regime are good constraints for modeling planetary embryo formation analytically. Our embryo formation model is a valuable asset in future studies of planet formation.

Recovery of dust particles trajectories in modeling physical processes in the near-surface exosphere of the moon

This study demonstrates the visualization and recovery of the 3D dynamic trajectories of charged microparticles in electric field conditions. The main aim of this work is to simulate plasma-dust processes above the surfaces of the Moon and other Solar system bodies without atmospheres. The experimental setup includes two parts: a vacuum chamber, in which microparticles imitate lunar dust dynamics under electrostatic field conditions, and a stereo camera system for image registration combined with laser and optics for illuminating the investigation volume. Image processing techniques for estimating the 3D particle trajectory were developed. Examples of processing results and their prospective application are discussed.

Addressing uncertainty in mouthing-mediated ingestion of chemicals on indoor surfaces, objects, and dust

In indoor environments, humans ingest chemicals present as surface residues and bound to settled particles (dust), through mouthing hands (hand-to-mouth transfer) and objects (object-to-mouth transfer). Here, we introduce a novel modeling approach in support of systematic investigation into the mouthing-mediated ingestion of chemicals present in indoor environments. This model explicitly considers the indoor dynamics of dust and chemicals, building on mechanistic links with physicochemical properties of chemicals, features of the indoor environment, and human activity patterns. The evaluation of this model demonstrates that it satisfactorily reproduces chemical hand loadings and exposure data reported in the literature. We then use the evaluated model to investigate the response of mouthing-mediated ingestion to chemical partitioning between the gas phase and solid phases, expressed as the octanol–air partition coefficient (KOA). Assuming a unit emission rate to the indoor environment, we find that low-volatility chemicals (with a KOA greater than 109) are more efficiently enriched in hand skin, resulting in higher mouthing-mediated ingestion than other compounds. For individuals living in a room with a typical level of dustiness, more than half of the chemical mass found in their hands comes from dust transfer, whereas more than half of the chemical mass ingested is the fraction present as residues on hands. We also use the new model to explore how the mouthing-mediated ingestion of chemicals is dependent on factors describing the indoor environment and human behavior. The model predicts that less frequent cleaning leads to higher accumulation of dust on indoor surfaces, thereby transferring more chemicals to hands and mouth in each contact. Introducing more dust into the room, but maintaining the same cleanup frequency, increases the dustiness of indoor surfaces, which promotes the transfer of relatively volatile chemicals (with a KOA lower than 109) to hands and mouth but decreases the transfer of chemicals with low volatility. More frequent hand contact with indoor surfaces increases both the hand loading and mouthing-mediated ingestion of chemicals, but the increases are more remarkable for adults than children because the higher surface contact frequency of children “saturates” hand loadings. An increase in handwashing frequency lowers the hand loading and mouthing-mediated ingestion of chemicals and this mitigating process is more prominent for relatively volatile chemicals. The new evaluated modeling approach can facilitate the prediction of mouthing-mediated ingestion for various age groups and the model predictions can be used to aid future fate and (bio)monitoring studies focusing on indoor contamination.

Imaging the Dusty Substructures due to Terrestrial Planets in Planet-forming Disks with ALMA and the Next-generation Very Large Array

Abstract We present simulations of the capabilities of the Atacama Large Millimeter/submillimeter Array (ALMA) and of a next-generation Very Large Array (ngVLA) to detect and resolve substructures due to terrestrial planets and super-Earths in nearby planet-forming disks. We adopt the results of global 2D hydrodynamical planet–disk simulations that account for the dynamics of gas and dust in a disk with an embedded planet. Our simulations follow the combined evolution of gas and dust for several thousand planetary orbits. We show that long integrations (several tens of hours) with the ngVLA can detect and spatially resolve dust structures due to low-mass rocky planets in the terrestrial planet formation regions of nearby disks (stellocentric radii r = 1–3 au), under the assumption that the disk viscosity in those regions is low (α ≤ 10−5). ALMA is instead unable to resolve these structures in these disk regions. We also show that high-resolution ngVLA observations separated by several days to a few weeks would allow us to detect the proper motion of the azimuthally asymmetric structures expected in the disk regions of terrestrial planet formation.

Dust delivery and entrainment in photoevaporative winds

ABSTRACT We model the gas and dust dynamics in a turbulent protoplanetary disc undergoing extreme-UV photoevaporation in order to better characterize the dust properties in thermal winds (e.g. size distribution, flux rate, trajectories). Our semi-analytic approach allows us to rapidly calculate these dust properties without resorting to expensive hydrodynamic simulations. We find that photoevaporation creates a vertical gas flow within the disc that assists turbulence in supplying dust to the ionization front. We examine both the delivery of dust to the ionization front and its subsequent entrainment in the overlying wind. We derive a simple analytic criterion for the maximum grain size that can be entrained and show that this is in good agreement with the results of previous simulations where photoevaporation is driven by a range of radiation types. We show that, in contrast to the case for magnetically driven winds, we do not expect large-scale dust transport within the disc to be effected by photoevaporation. We also show that the maximum size of grains that can be entrained in the wind (smax) is around an order of magnitude larger than the maximum size of grains that can be delivered to the front by advection alone ($s_{\mathrm{crit}}\lesssim 1 \,\, \mu {\mathrm{m}}$ for Herbig Ae/Be stars and $\lesssim 0.01 \,\, \mu {\mathrm{m}}$ for T Tauri stars). We further investigate how larger grains, up to a limiting size slimit, can be delivered to the front by turbulent diffusion alone. In all cases, we find smax ≳ slimit so that we expect that any dust that is delivered to the front can be entrained in the wind and that most entrained dust follows trajectories close to that of the gas.

Dust dynamics in planet-driven spirals

Context. Protoplanetary disks are known to host spiral features that are observed in scattered light, the ALMA continuum, and more recently in CO gas emission and gas dynamics. However, it is unknown whether spirals in gas and dust trace the same morphology. Aims. We aim to study the morphology and amplitude of dusty spirals as function of the Stokes number and the underlying mechanisms that cause a difference between dusty spirals and gas spirals. We then construct a model to relate the deviation from Keplerian rotation in the gas to a perturbation in surface density of the gas and dust. Methods. We used FARGO-3D with dust implementation to numerically study the spirals, after which the results were interpreted using a semi-analytical model. This model was tested on observational data to predict the perturbation of the spiral in gas dynamics based on the continuum data. Results. We find that the pitch angle of a spiral does not differ significantly between gas and dust. The amplitude of the dust spiral decreases with the Stokes number (St) and starts to fade out at a typical St &gt; 0.1 as the dust becomes decoupled from the gas. The semi-analytical model provides an accurate and fast representation of the difference in the surface density of the spiral in dust and gas. We find a spiral in the TW Hya velocity residual map, never seen before, which is a feature in the vertical velocity and has a kink at the continuum gap, yielding strong evidence for a planet at 99 au. Conclusions. We built a model that gives an estimate of the underlying dynamics of dust in a spiral, which can serve as evidence of the planetary origin of spirals and can be a probe for the Stokes number in the disk.