Incoming Mass Flux Research Articles

Micrometeoroid infall onto Saturn's rings constrains their age to no more than a few hundred million years.

There is ongoing debate as to whether Saturn's main rings are relatively young or ancient- having been formed shortly after Saturn or during the Late Heavy Bombardment. The rings are mostly water-ice but are polluted by non-icy material with a volume fraction ranging from ∼0.1 to 2%. Continuous bombardment by micrometeoroids exogenic to the Saturnian system is a source of this non-icy material. Knowledge of the incoming mass flux of these pollutants allows estimation of the rings' exposure time, providing a limit on their age. Here we report the final measurements by Cassini's Cosmic Dust Analyzer of the micrometeoroid flux into the Saturnian system. Several populations are present, but the flux is dominated by low-relative velocity objects such as from the Kuiper belt. We find a mass flux between 6.9 · 10-17 and 2.7 · 10-16 kg m-2s-1 from which we infer a ring exposure time ≲100 to 400 million years in support of recent ring formation scenarios.

An approach for evaluating gas sorption in polymer matrix membranes based on balancing incoming and outgoing membrane mass fluxes

The transport of gases in polymeric membranes can be described by a solution–diffusion mechanism in which the individual transport parameters are determined from independent measurements of the gas permeability and diffusivity and further measurements of the gas solubility in the polymer of interest. Herein, we propose a new method for determining all three transport parameters from a single permeation experiment performed using a modified classical permeation cell with very small volumes above and below the membrane (1.192 and 0.658 mL, respectively). The new concept is based on the evaluation of gas sorption in the membrane determined from the balance of mass fluxes entering and leaving the membrane. The amount of gas sorbed in the membrane can then be calculated by integrating the area between the fluxes. This arrangement allows for the rapid and complex characterization of the gas transport and separation properties of polymeric materials using a single experiment. The novel approach was tested on a polydimethylsiloxane membrane for three gases having considerably different solubilities in the polymer, and the results were consistent with those obtained using classical procedures.

Size-Dependent Dried Colloidal Deposit and Particle Sorting via Saturated Alcohol Vapor-Mediated Sessile Droplet Spreading

We experimentally and theoretically investigate a distinct problem of spreading, evaporation, and the associated dried deposits of a colloidal particle-laden aqueous sessile droplet on a surface in a saturated alcohol vapor environment. In particular, the effect of particle size on monodispersed suspensions and efficient self-sorting of bidispersed particles have been investigated. The alcohol vapor diffuses toward the droplet's curved liquid-vapor interface from the far field. The incoming vapor mass flux profile assumes a nonuniform pattern across the interface. The alcohol vapor molecules are adsorbed at the liquid-vapor interface, which eventually leads to absorption into the droplet's liquid phase due to the miscibility. This phenomenon triggers a liquid-vapor interfacial tension gradient and causes a reduction in the global surface tension of the droplet. This results in a solutal Marangoni flow recirculation and spontaneous droplet spreading. The interplay between these phenomena gives rise to a complex internal fluid flow within the droplet, resulting in a significantly modified and strongly particle-size-dependent dried colloidal deposit. While the smaller particles form a multiple ring pattern, larger particles form a single ring, and additional "patchwise" deposits emerge. High-speed visualization of the internal liquid-flow revealed that initially, a ring forms at the first location of the contact line. Concurrently, the Marangoni flow recirculation drives a collection of particles at the liquid-vapor interface to form clusters. Thereafter, as the droplet spreads, the smaller particles in the cluster exhibit a "jetlike" outward flow, forming multiple ring patterns. In contrast, the larger particles tend to coalesce together in the cluster, forming the "patchwise" deposits. The widely different response of the different-sized particles to the internal fluid flow enables an efficient sorting of the smaller particles at the contact line from bidispersed suspensions. We corroborate the measurements with theoretical and numerical models wherever possible.

Molecular dynamics simulation of kinetic boundary conditions and evaporation/condensation coefficients of direct-contact condensation in two-phase jet

Using non-equilibrium molecular dynamics simulations, the kinetic boundary condition (KBC) for direct-contact condensation in two-phase jet and its evaporation and condensation coefficients were studied to solve the Boltzmann equation. The evaporating and reflecting molecular behaviors were studied in detail. The normalized velocity distributions of reflecting molecules in the z-direction before and after reflection fit the Maxwell velocity distribution shifted by two large macroscopic velocities toward and away from the liquid surface owing to the strong net condensation rate. A singular definition of the evaporation coefficient has not been obtained in previous studies. We used a two-boundary method to count the evaporation coefficient and define a parameter to connect our result and the spontaneous evaporation coefficient. The condensation coefficient was studied using the condensation probability and showed larger than the evaporation coefficient in direct-contact condensation states. Both the evaporation and condensation coefficients were not independent of the incoming mass flux. When the incoming mass flux was small, the values of these two coefficients were close to the values under equilibrium states. Based on these results, we constructed the KBC of direct-contact condensation.

Compressible subsonic cavity flow in a nozzle

This paper concerns the existence and uniqueness of a two-dimensional compressible subsonic cavity flow behind a given obstacle with a free surface in an infinitely long nozzle. More precisely, for any given atmospheric pressure pe > 0, we first show that there exists a critical value mcr for the incoming mass flux m0 such that if m0 < mcr, then there exists a unique smooth subsonic cavity flow behind the given obstacle, and the free surface initiates smoothly from the vertex of the obstacle and goes to infinity at the far field. Second, we establish some fundamental properties of the cavity flow, such as the positivity of the horizontal velocity and the asymptotic behavior of the flow at the far field. Finally, we obtain that the vertical velocity is positive under the corresponding assumptions on the upper nozzle wall and the upper surface of the obstacle.

Existence and optimal convergence rates of multi-dimensional subsonic potential flows through an infinitely long nozzle with an obstacle inside

In this paper, the well-posedness and optimal convergence rates of subsonic irrotational flows through a three-dimensional infinitely long nozzle with a smooth obstacle inside are established. More precisely, the global existence and uniqueness of the uniformly subsonic flow are obtained via variational formulation as long as the incoming mass flux is less than a critical value. Furthermore, with the aid of delicate choice of weight functions, we prove the optimal convergence rates of the flow at far fields via weighted energy estimates and Nash–Moser iteration.

СПОСОБ РАСЧЕТА КОМБИНИРОВАННОЙ СИСТЕМЫ ОТОПЛЕНИЯ КУЛЬТИВАЦИОННОГО СООРУЖЕНИЯ НА ПРИМЕРЕ ЗИМНЕЙ ТЕПЛИЦЫ

Modern systems of artificial heating of cultivation structures on the example of winter greenhouses intended for year-round use require the development of sufficiently accurate and reliable methods of calculation. According to the calculations, a decentralized heating system of agricultural facilities, which includes only ceiling infrared heating elements, is justified only in a moderately cold period of the year. At lower outdoor temperatures, mainly in January, the indoor temperature may drop below standard values due to the specifics of radiant heating. Therefore, the article considers the method of calculating heat power of the radiant and convective heating system that includes infrared emitters for soil heating and convective heating devices for maintaining the target indoor air temperature. The calculation procedure of radiant and convective (combined) heating system comes to the calculation of incoming and outgoing heat and mass fluxes as well as finding unknown microclimate parameters (first of all, inside air temperature) that form design heat and humidity conditions of an agrobiotechnological facility. The proposed calculation method has been tested at the industrial greenhouse “Fermer 7.5”.

Focused ion beam-induced droplet formation and motion

Nanometer-scale droplet formation and motion under the effects of a focused ion beam is described using a continuum model that combines a thin-film fluid model for dynamics with a Cahn–Hilliard type model for chemical diffusion and phase separation. The focused ion beam (FIB) is represented as a time and space dependent mass and chemical species source. Drops form and move due to the combined effects of a concentration-dependent surface energy, a concentration gradient on the edges of the droplet, and a beam angle-dependent net FIB incoming mass flux. The velocity is comparable to observations, and it has a similar dependence on the beam angle of incidence. Likewise, the ion dose at which droplets reach a width of 60 nm is in good agreement with experiments. The model also explains the biased motion of droplets under a raster-scan pattern focused ion beam.

Two-phase fluids in collision of incompressible inviscid fluids effluxing from two nozzles

This paper is devoted to the mathematical theory of two-dimensional injection of incompressible, irrotational, and inviscid fluids issuing from two infinitely long nozzles into a free stream. In general, there is a free interface with constant jump of the Bernoulli constant on it, which is different and more difficult than the previous related works. Physically, it is called the collision fluid. The main result in this paper is that for given two co-axis symmetric infinitely long nozzles, imposing the incoming mass fluxes in the two nozzles, there exists a unique piecewise smooth collision fluid, such that the free interface of the collision fluid is a C1 curve, and the pressure is continuous across the interface. As byproducts, the asymptotic behaviors, the positivity of the vertical velocity, monotone relationship between the location of the interface and the incoming mass fluxes are also established.

On an Elliptic Free Boundary Problem and Subsonic Jet Flows for a Given Surrounding Pressure

This paper concerns compressible subsonic jet flows for a given surrounding pressure from a two-dimensional finitely long convergent nozzle with straight solid wall, which are governed by a free boundary problem for a quasilinear elliptic equation. For a given surrounding pressure and a given incoming mass flux, we seek a subsonic jet flow with the given incoming mass flux such that the flow velocity at the inlet is along the normal direction, the flow satisfies the slip condition at the wall, and the pressure of the flow at the free boundary coincides with the given surrounding pressure. In general, the free boundary contains two parts: one is the particle path connected with the wall and the other is a level set of the velocity potential. We identify a suitable space of flows in terms of the minimal speed and the maximal velocity potential difference for the well-posedness of the problem. It is shown that there is an optimal interval such that there exists a unique subsonic jet flow in the space iff the length of the nozzle belongs to this interval. Furthermore, the optimal regularity and other properties of the flows are shown.

Incompressible Jet Flows in a de Laval Nozzle with Smooth Detachment

In this paper, we are concerned with the well-posedness theory of steady incompressible jet flow in a de Laval type nozzle with given end pressure at the outlet. The main results show that for any given incoming mass flux Q > 0 in the upstream and end pressure at the outlet, there exists an admissible interval to the Bernoulli’s constant, if the Bernoulli’s constant lies in the interval, there exists a unique smooth incompressible jet flow issuing from the nozzle. Moreover, the free boundary of the jet flow initiates smoothly from the surface of the divergent area of the de Laval nozzle. In particular, it is shown that the initial point of the free boundary lies behind the throat of the de Laval nozzle wall and varies continuously and monotonically with respect to the Bernoulli’s constant. As a direct corollary, imposing initial point of the free boundary on the divergent part of nozzle wall, there exists a unique incompressible jet for given incoming mass flux Q > 0 and pressure Pe at the outlet. This work is inspired by the significant works (Alt et al. in Commun Pure Appl Math 35:29–68, 1982; Arch Rational Mech Anal 81:97–149, 1983) for the incompressible jet flow imposing the initial point of the free boundary at the endpoint of the nozzle.

Sensitivity of Glacier Runoff to Winter Snow Thickness Investigated for Vatnajökull Ice Cap, Iceland, Using Numerical Models and Observations

Several simulations of the surface climate and energy balance of Vatnajökull ice cap, Iceland, are used to estimate the glacier runoff for the period 1980–2015 and the sensitivity of runoff to the spring conditions (e.g., snow thickness). The simulations are calculated using the snow pack scheme from the regional climate model HIRHAM5, forced with incoming mass and energy fluxes from the numerical weather prediction model HARMONIE-AROME. The modeled runoff is compared to available observations from two outlet glaciers to assess the quality of the simulations. To test the sensitivity of the runoff to spring conditions, simulations are repeated for the spring conditions of each of the years 1980–2015, followed by the weather of all summers in the same period. We find that for the whole ice cap, the variability in runoff as a function of varying spring conditions was on average 31% of the variability due to changing summer weather. However, some outlet glaciers are very sensitive to the amount of snow in the spring, as e.g., the variation in runoff from Brúarjökull due to changing spring conditions was on average 50% of the variability due to varying summer weather.

Compressible subsonic jet flows issuing from a nozzle of arbitrary cross-section

We are concerned with the well-posedness theory of two-dimensional compressible subsonic jet flow issuing from a semi-infinitely long nozzle of arbitrary cross-section. Given any atmospheric pressure p0, we show that there exists a critical mass flux mcr depending on p0 and Ω, such that if the incoming mass flux m0 is less than the critical value, then there exists a unique smooth subsonic jet flow, issuing from the given nozzle. The jet boundary is a free streamline, which initiates from the end point of the nozzle smoothly and extends to the infinity. One of the key observations in this paper is that the restriction of the incoming mass flux guarantees completely the subsonicity of the compressible jet in the whole flow field, which coincides with the observation on the compressible subsonic flows in an infinitely long nozzle without free boundary in [8].

Collision of incompressible inviscid fluids effluxing from two nozzles

This paper concerns the mathematical theory of the collision problem of two-dimensional incompressible inviscid fluids issuing from two given nozzles. The main result reads that for given two co-axis symmetric semi-infinitely long nozzles with arbitrary variable sections, imposing the incoming mass fluxes in two nozzles, there exists a smooth impinging outgoing jet, such that the two free boundaries of the impinging jet initiate smoothly at the endpoints of the nozzles and approach to some asymptotic direction in downstream, and the pressure on the free surface remains a constant. Furthermore, we show that there exists a unique smooth surface separating the two nonmiscible fluids and there exists a unique stagnation point in the fluid region and its closure. Moreover, some results on the uniqueness and the estimates of the location of the impinging outgoing jet are also established. Finally, the asymptotic behaviors, the precise estimate to the deflection angle and other properties to the impinging outgoing jet are also considered.

The steady state collision of two compressible subsonic perfect flows

This paper is devoted to the mathematical theory for the steady state collision of two compressible subsonic irrotational flows issuing from two infinitely long nozzles. We established the existence, uniqueness and asymptotic behavior of the subsonic collision flow with a smooth interface for the steady Euler system in an important physical regime. More precisely, there exists a critical value, if the summation of the incoming mass fluxes in the inlets of the nozzles is less than the critical value, then there exists a unique smooth subsonic compressible collision flow. And furthermore, there exists a smooth interface which separates the two non-miscible compressible subsonic flows. In particular, a key observation is that the location of the interface can be determined uniquely by the incoming mass fluxes in the inlets of the nozzles. Finally, we showed some monotonic relationship between the location of the interface and the incoming mass fluxes.

Radar Detectability Studies of Slow and Small Zodiacal Dust Cloud Particles. III. The Role of Sodium and the Head Echo Size on the Probability of Detection

Abstract We present a path forward on a long-standing issue concerning the flux of small and slow meteoroids, which are believed to be the dominant portion of the incoming meteoric mass flux into the Earth’s atmosphere. Such a flux, which is predicted by dynamical dust models of the Zodiacal Cloud, is not evident in ground-based radar observations. For decades this was attributed to the fact that the radars used for meteor observations lack the sensitivity to detect this population, due to the small amount of ionization produced by slow-velocity meteors. Such a hypothesis has been challenged by the introduction of meteor head echo (HE) observations with High Power and Large Aperture radars, in particular the Arecibo 430 MHz radar. Janches et al. developed a probabilistic approach to estimate the detectability of meteors by these radars and initially showed that, with the current knowledge of ablation and ionization, such particles should dominate the detected rates by one to two orders of magnitude compared to the actual observations. In this paper, we include results in our model from recently published laboratory measurements, which showed that (1) the ablation of Na is less intense covering a wider altitude range; and (2) the ionization probability, β ip , for Na atoms in the air is up to two orders of magnitude smaller for low speeds than originally believed. By applying these results and using a somewhat smaller size of the HE radar target we offer a solution that reconciles these observations with model predictions.

Continuous subsonic-sonic flows in convergent nozzles with straight solid walls

This paper concerns continuous subsonic-sonic potential flows in a two-dimensional convergent nozzle with straight solid walls. It is shown that for the given inlet, which is a perturbation of an arc centered at the vertex of the nozzle, and the given incoming flow angle which is a perturbation of the angle of the inner normal of the inlet, and the given incoming mass flux belonging to an open interval depending only on the adiabatic exponent and the length of the arc, there is a unique continuous subsonic-sonic flow from the given inlet with the given incoming flow angle and the given incoming mass flux. Furthermore, the sonic curve of this flow is a free boundary, where the flow is singular in the sense that the speed is only Hölder continuous and the acceleration blows up at the sonic state. The perturbation problem is solved in the potential plane, where the flow is governed by a degenerate elliptic problem with two free boundaries, on one of which the equation is degenerate and on the other of which the boundary condition is nonlocal.

Subsonic Irrotational Flows in a Finitely Long Nozzle with Variable end Pressure

In this paper, we characterize a set of physically acceptable boundary conditions that ensure the existence and uniqueness of a subsonic irrotational flow in a finitely long flat nozzle. Our results show that if the incoming flow is horizontal at the inlet and an appropriate pressure is prescribed at the exit, then there exist two positive constants m 0 and m 1 with m 0 < m 1, such that a global smooth irrotational subsonic flow exists uniquely in the nozzle, provided that the incoming mass flux m ∈ [m 0, m 1). The horizontal velocity of the flow is always positive in the whole nozzle and the maximum speed of the flow will approach the sonic speed as the mass flux m tends to m 1. The flow is governed by the steady compressible irrotational Euler equations with nonlocal and nonlinear mixed boundary conditions. A new key issue is that the Bernoulli's constant of the irrotational flow is not given a priori, which can be determined uniquely by the end pressure and the incoming mass flux. To handle the nonlocal boundary condition raised from the mass flux, we introduce an auxiliary problem with Bernoulli's constant as a parameter, instead of the mass flux. Furthermore, the monotonicity between the mass flux and the Bernoulli's constant is established for given end pressure.

On a Degenerate Free Boundary Problem and Continuous Subsonic–Sonic Flows in a Convergent Nozzle

This paper concerns the well-posedness of a boundary value problem for a quasilinear second order elliptic equation which is degenerate on a free boundary. Such problems arise when studying continuous subsonic–sonic flows in a convergent nozzle with straight solid walls. It is shown that for a given inlet being a perturbation of an arc centered at the vertex of the nozzle and a given incoming mass flux belonging to an open interval depending only on the adiabatic exponent and the length of the arc, there is a unique continuous subsonic–sonic flow from the given inlet with the angle of the velocity orthogonal to the inlet and the given incoming mass flux. Furthermore, the sonic curve of this continuous subsonic–sonic flow is a free boundary, where the flow is singular in the sense that while the speed is C1/2 Holder continuous at the sonic state, the acceleration blows up at the sonic state.

Subsonic Flows in a Multi-Dimensional Nozzle

In this paper, we study the global subsonic irrotational flows in a multi-dimensional ($n\geq 2$) infinitely long nozzle with variable cross sections. The flow is described by the inviscid potential equation, which is a second order quasilinear elliptic equation when the flow is subsonic. First, we prove the existence of the global uniformly subsonic flow in a general infinitely long nozzle for arbitrary dimension for sufficiently small incoming mass flux and obtain the uniqueness of the global uniformly subsonic flow. Furthermore, we show that there exists a critical value of the incoming mass flux such that a global uniformly subsonic flow exists uniquely, provided that the incoming mass flux is less than the critical value. This gives a positive answer to the problem of Bers on global subsonic irrotational flows in infinitely long nozzles for arbitrary dimension. Finally, under suitable asymptotic assumptions of the nozzle, we obtain the asymptotic behavior of the subsonic flow in far fields by a blow-up argument. The main ingredients of our analysis are methods of calculus of variations, the Moser iteration techniques for the potential equation and a blow-up argument for infinitely long nozzles.