Scavenging of Gaseous Pollutants by Falling Liquid Droplets in Inhomogeneous Atmosphere With Non-Uniform Temperature and Concentration Distributions

2009 ◽  
Author(s):  
Tov Elperin ◽  
Boris Krasovitov ◽  
Andrew Fominykh
Keyword(s):  
Trace Gases ◽  
Vertical Direction ◽  
Transformation Method ◽  
Gas Absorption ◽  
Time Dependent ◽  
Shear Stresses ◽  
Liquid Droplets ◽  
Internal Circulation ◽  
Linear Convolution ◽  
Temperature Boundary

We analyze non-isothermal absorption of soluble atmospheric trace gases by the falling rain droplets with internal circulation which is caused by interfacial shear stresses. It is assumed that the concentration of soluble trace gases and temperature in the atmosphere varies in a vertical direction. In the analysis we accounted for the accumulation of the absorbate in the bulk of the falling rain droplet. The problem is solved in the approximation of a thin concentration and temperature boundary layers in the droplet and in the surrounding air. We assumed that the bulk of a droplet, beyond the diffusion boundary layer, is completely mixed and concentration of the absorbate and temperature are homogeneous and time-dependent in the bulk. By combining the generalized similarity transformation method with Duhamel’s theorem, the system of transient conjugate equations of convective diffusion and energy conservation for absorbate transport in liquid and gaseous phases with time-dependent boundary conditions is reduced to a system of linear convolution Volterra integral equations of the second kind which is solved numerically. It is shown that the non-uniform vertical distribution of absorbate and temperature in a gaseous phase strongly affects mass transfer during gas absorption by a falling droplet.

scholarly journals Effect of Altitude Concentration Gradient of Soluble Gaseous Pollutants on Their Scavenging by Falling Rain Droplets

2009 ◽  
Vol 66 (8) ◽  
pp. 2349-2358 ◽  
Author(s):  
Tov Elperin ◽  
Andrew Fominykh ◽  
Boris Krasovitov
Keyword(s):  
Boundary Layer ◽  
Trace Gases ◽  
Vertical Direction ◽  
Transformation Method ◽  
Gas Absorption ◽  
Time Dependent ◽  
Shear Stresses ◽  
Internal Circulation ◽  
Concentration Boundary ◽  
Linear Convolution

Abstract This paper analyzes absorption of soluble atmospheric trace gases by falling rain droplets with internal circulation, which is caused by interfacial shear stresses. It is assumed that the concentration of soluble trace gases in the atmosphere varies in a vertical direction. In the analysis the accumulation of the absorbate in the bulk of the falling rain droplet was accounted for. The problem is solved in the approximation of a thin concentration boundary layer in the droplet and in the surrounding air. It was assumed that the bulk of a droplet, beyond the diffusion boundary layer, is completely mixed and that concentration of the absorbate is homogeneous and time dependent in the bulk. By combining the generalized similarity transformation method with Duhamel’s theorem, the system of transient conjugate equations of convective diffusion for absorbate transport in liquid and gaseous phases with time-dependent boundary conditions is reduced to a linear-convolution Volterra integral equation of the second kind, which is solved numerically. It is shown that the nonuniform vertical distribution of absorbate in a gaseous phase strongly affects mass transfer during gas absorption by a falling droplet.

Scavenging of Soluble Gaseous Pollutants by Rain Droplets in the Atmosphere With Nocturnal Temperature Profile

2010 ◽  
Author(s):  
Andrew Fominykh ◽  
Tov Elperin ◽  
Boris Krasovitov
Keyword(s):  
Trace Gases ◽  
Vertical Direction ◽  
Temperature Inversion ◽  
Transformation Method ◽  
Time Dependent ◽  
Trace Gas ◽  
Shear Stresses ◽  
Linear Convolution ◽  
Temperature Boundary ◽  
Transfer Equations

We analyze non-isothermal absorption of trace gases by the rain droplets with internal circulation which is caused by interfacial shear stresses. It is assumed that the temperature and concentration of soluble trace gases in the atmosphere varies in a vertical direction. The rate of scavenging of soluble trace gases by falling rain droplets is determined by solving heat and mass transfer equations. In the analysis we accounted for the accumulation of the absorbate in the bulk of the falling rain droplet. The problem is solved in the approximation of a thin concentration and temperature boundary layers in the droplet and in the surrounding air. We assumed that the bulk of a droplet, beyond the diffusion boundary layer, is completely mixed and concentration of the absorbate and temperature are homogeneous and time-dependent in the bulk. By combining the generalized similarity transformation method with Duhamel’s theorem, the system of transient conjugate equations of convective diffusion and energy conservation for absorbate transport in liquid and gaseous phases with time-dependent boundary conditions is reduced to a system of linear convolution Volterra integral equations of the second kind which is solved numerically. Calculations are performed using available experimental data on nocturnal temperature profiles in the atmosphere. It is shown than if concentration of a trace gas in the atmosphere is homogeneous and temperature in the atmosphere increases with altitude, droplet absorbs gas during all the period of its fall. Neglecting temperature inhomogenity in the atmosphere described by nocturnal temperature inversion leads to essential underestimation of the trace gas concentration in a droplet on the ground.

scholarly journals Temperature uniformity in the CERN CLOUD chamber

2017 ◽  
Vol 10 (12) ◽  
pp. 5075-5088 ◽  
Author(s):  
António Dias ◽  
Sebastian Ehrhart ◽  
Alexander Vogel ◽  
Christina Williamson ◽  
João Almeida ◽  
...  
Keyword(s):  
Steady State ◽  
Air Temperature ◽  
Elevated Temperatures ◽  
Trace Gases ◽  
Vertical Direction ◽  
Cloud Chamber ◽  
Temperature Uniformity ◽  
Atmospheric Conditions ◽  
Cloud Droplets ◽  
Experimental Conditions

Abstract. The CLOUD (Cosmics Leaving OUtdoor Droplets) experiment at CERN (European Council for Nuclear Research) investigates the nucleation and growth of aerosol particles under atmospheric conditions and their activation into cloud droplets. A key feature of the CLOUD experiment is precise control of the experimental parameters. Temperature uniformity and stability in the chamber are important since many of the processes under study are sensitive to temperature and also to contaminants that can be released from the stainless steel walls by upward temperature fluctuations. The air enclosed within the 26 m3 CLOUD chamber is equipped with several arrays (strings) of high precision, fast-response thermometers to measure its temperature. Here we present a study of the air temperature uniformity inside the CLOUD chamber under various experimental conditions. Measurements were performed under calibration conditions and run conditions, which are distinguished by the flow rate of fresh air and trace gases entering the chamber at 20 and up to 210 L min−1, respectively. During steady-state calibration runs between −70 and +20 °C, the air temperature uniformity is better than ±0.06 °C in the radial direction and ±0.1 °C in the vertical direction. Larger non-uniformities are present during experimental runs, depending on the temperature control of the make-up air and trace gases (since some trace gases require elevated temperatures until injection into the chamber). The temperature stability is ±0.04 °C over periods of several hours during either calibration or steady-state run conditions. During rapid adiabatic expansions to activate cloud droplets and ice particles, the chamber walls are up to 10 °C warmer than the enclosed air. This results in temperature differences of ±1.5 °C in the vertical direction and ±1 °C in the horizontal direction, while the air returns to its equilibrium temperature with a time constant of about 200 s.

Kompressionswellen in einer isothermen Atmosphäre mit vertikalem Magnetfeld

1966 ◽  
Vol 21 (7) ◽  
pp. 1098-1106 ◽  
Author(s):  
R. Lust ◽  
M. Scholer
Keyword(s):  
Magnetic Field ◽  
Strong Influence ◽  
Vertical Direction ◽  
Time Dependent ◽  
Solar Chromosphere ◽  
Magnetohydrodynamic Equation ◽  
One Dimensional ◽  
Spatial Dimensions ◽  
Propagation Of Waves ◽  
The Waves

The propagation of waves in the solar atmosphere is investigated with respect to the problem of the chromospheric spiculae and of the heating of the solar chromosphere and corona. In particular the influence of external magnetic fields is considered. Waves of finite amplitudes are numerically calculated by solving the time-dependent magnetohydrodynamic equation for two spatial dimensions by assuming axial symmetry. For the case without a magnetic field the comparison between one dimensional and two dimensional treatment shows the strong influence of the radial propagation on the steepening of waves in the vertical direction. In the presence of a magnetic field it is shown that the propagation is strongly guided along the lines of force. The steepening of the waves along the field is much larger as compared to the case where no field is present.

Time-dependent lateral transmission of force in skeletal muscle

2009 ◽  
Vol 465 (2108) ◽  
pp. 2441-2460 ◽  
Author(s):  
Yingxin Gao ◽  
Alan S. Wineman ◽  
Anthony M. Waas
Keyword(s):  
Skeletal Muscle ◽  
Relaxation Time ◽  
Muscle Fibre ◽  
Composite System ◽  
Stress Transfer ◽  
Time Dependent ◽  
Muscle Fibres ◽  
Strain History ◽  
Shear Stresses ◽  
Lateral Stress

There is experimental evidence to suggest that extensible connective tissues are mechanically time-dependent. In view of this, the mechanics of time-dependent lateral stress transfer in skeletal muscle is investigated by employing a viscoelastic shear lag model for the transfer of tensile stress between muscle fibres and the surrounding extracellular matrix (ECM) by means of shear stresses at the interface between the muscle fibre and the ECM. The model allows for both mechanical strains in the muscle as well as the strain owing to muscle contraction. Both the ECM and the muscle fibre are modelled as viscoelastic solids. As a result, time-dependent lateral stress transfer can be studied under a variety of loading and muscle stimulation conditions. The results show that the larger the muscle fibre creep time relative to the ECM relaxation time, the longer it takes for the muscle fibre stress to relax. It also shows that the response of the muscle–ECM composite system also depends on the characteristic time of a strain history relative to the characteristic relaxation time of the ECM. The results from the present model provide significant insight into the role of the parameters that characterize the response of the muscle composite system.

scholarly journals On the formation of radiation fogs under heavily polluted conditions

2003 ◽  
Vol 3 (3) ◽  
pp. 581-589 ◽  
Author(s):  
H. Kokkola ◽  
S. Romakkaniemi ◽  
A. Laaksonen
Keyword(s):  
Liquid Phase ◽  
Gas Phase ◽  
Trace Gases ◽  
Time Dependent ◽  
Droplet Growth ◽  
Gaseous Pollutants ◽  
Thermodynamical Equilibrium ◽  
Sulfate Production ◽  
Radiation Fogs

Abstract. We have studied the effect of gaseous pollutants on fog droplet growth in heavily polluted air using a model that describes time-dependent sulfate production in the liquid phase and thermodynamical equilibrium between the droplets and the gas phase. Our research indicates that the oxidation of SO2 to sulfate has a significant effect on fog droplet growth especially when hygroscopic trace gases, for example HNO3 and NH3 are present. The increased sulfate production by dissolution of hygroscopic gases results from increased pH (caused by absorption of ammonia) and from the increased size of the fog/smog droplets. Our results indicate that unactivated fogs may become optically very thick when the droplet concentrations are on the order of several thousand per cubic centimeter of air.

scholarly journals On the formation of radiation fogs under heavily polluted conditions

2003 ◽  
Vol 3 (1) ◽  
pp. 389-411 ◽  
Author(s):  
H. Kokkola ◽  
S. Romakkaniemi ◽  
A Laaksonen
Keyword(s):  
Liquid Phase ◽  
Gas Phase ◽  
Optical Thickness ◽  
Trace Gases ◽  
Time Dependent ◽  
Droplet Growth ◽  
Gaseous Pollutants ◽  
Thermodynamical Equilibrium ◽  
Sulfate Production ◽  
Radiation Fogs

Abstract. We have studied the effect of gaseous pollutants on fog droplet growth in heavily polluted air using a model that describes time-dependent sulfate production in the liquid phase and thermodynamical equilibrium between the droplets and the gas phase. Our research indicates that the oxidation of  SO2 to sulfate has a significant effect on fog droplet growth especially when hygroscopic trace gases, for example HNO3 andNH3 are present. The increased sulfate production by dissolution of hygroscopic gases results from increased pH (caused by absorption of ammonia) and from the increased size of the fog/smog droplets. As a result of the enhancement of the droplet growth the optical thickness of the fog will increase.

scholarly journals Live 3D imaging and mapping of shear stresses within tissues using incompressible elastic beads

2021 ◽  
Author(s):  
Alexandre SOUCHAUD ◽  
Arthur BOUTILLON ◽  
Gaëlle CHARRON ◽  
Atef ASNACIOS ◽  
Camille NOÛS ◽  
...  
Keyword(s):  
Shear Stress ◽  
Covalent Binding ◽  
Three Dimensional ◽  
Contour Method ◽  
Shear Stresses ◽  
Liquid Droplets ◽  
Mechanical Constraints

To investigate the role of mechanical constraints in morphogenesis and development, we develop a pipeline of techniques based on incompressible elastic sensors. These techniques combine the advantages of incompressible liquid droplets, which have been used as precise in situ shear stress sensors, and of elastic compressible beads, which are easier to tune and to use. Droplets of a polydimethylsiloxane (PDMS) mix, made fluorescent through specific covalent binding to a rhodamin dye, are produced by a microfluidics device. The elastomer rigidity after polymerization is adjusted to the tissue rigidity. Its mechanical properties are carefully calibrated in situ, for a sensor embedded in a cell aggregate and submitted to uniaxial compression. The local shear stress tensor is retrieved from the sensor shape, accurately reconstructed through an active contour method. In vitro, within cell aggregates, and in vivo, in the prechordal plate of the Zebrafish embryo during gastrulation, our pipeline of techniques demonstrates its efficiency to directly measure the three dimensional shear stress repartition within a tissue, and its time evolution.

On the Connection Between Geometry and Statically Determined Membrane Stresses in the Human Cornea

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
M. Angelillo ◽  
A. Montanino ◽  
A. Pandolfi
Keyword(s):  
Intraocular Pressure ◽  
Stress State ◽  
Principal Stress ◽  
Collagen Fibrils ◽  
Equilibrium Analysis ◽  
Time Dependent ◽  
Patient Specific ◽  
Shear Stresses ◽  
Human Cornea ◽  
The Matrix

Abstract Under the action of the intraocular pressure (IOP), the human cornea is stressed and deforms acquiring a quasi-spherical configuration. If the stressed configuration is known, and the cornea is regarded as a membrane, disregarding flexural behaviors with an equilibrium analysis only is possible to estimate the distribution of the average stress across the thickness. In the cornea, the action of the intraocular pressure is supported by collagen fibrils, immersed into an elastin-proteoglycan matrix, and organized in a very precise architecture to provide the necessary confinement and transparency to the light. With the goal of understanding the static consequences of shape modifications due to pathological dilatation (ectasia), we present a simplified stress analysis of the human cornea modeled as a membrane. A numerical investigation over 40 patient-specific corneas (20 normal and 20 ectatic) is carried out to establish a relationship between the physiological geometry and the distribution of the membrane stresses, and to assess the possibility to obtain information on the stress state based on topographic images only. Comparative analyses reveal that, with respect to normal corneas, in ectatic corneas the pattern of the principal stress lines is modified markedly showing a deviation from the hypothetical dominant orientation of the collagen fibrils. The rotation of the principal stress with respect to the fibril orientation can be thought as responsible of the transmission of a large amount of shear stresses onto the elastin-proteoglycan matrix. The anomalous loading of the matrix could be correlated to the evolution of time-dependent shape modifications leading to ectasia.

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