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A method for the reconstruction of the dynamics of processes with discrete time, developed in our previous papers, has been applied for study the dynamics of concentration of sulfur dioxide in lower troposphere. For the analysis,... more
A method for the reconstruction of the dynamics of processes with discrete time, developed in our previous papers, has been applied for study the dynamics of concentration of sulfur dioxide in lower troposphere. For the analysis, recordings of sulfur dioxide concentration from four measurement stations located in Poland (two of them has been located in huge cities and two in rarely inhabited regions) were used. We managed to obtain the deterministic and stochastic component of this dynamics. In result, we estimate the lifetime of sulfur dioxide in troposphere and the increase of sulfur dioxide concentration influenced by anthropogenic sources.
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The influence of ion implantation on the structure and properties of polymers is a very complex issue. Many physical and chemical processes taking place during ion bombardment must be taken into consideration. The complexity of the... more
The influence of ion implantation on the structure and properties of polymers is a very complex issue. Many physical and chemical processes taking place during ion bombardment must be taken into consideration. The complexity of the process may exert both positive and negative influence on the structure of the material. The goal of this paper is to investigate the influence of H
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A numerical model, a variant of the large eddy lattice Boltzmann model, has been presented and applied to computation of the flow velocity distribution in open channels with rigid elements. A special property of the model is taking into... more
A numerical model, a variant of the large eddy lattice Boltzmann model, has been presented and applied to computation of the flow velocity distribution in open channels with rigid elements. A special property of the model is taking into account the influence of rigid stems on the velocity distribution in averaged manner instead of analysis of the influence of single stems. This approach allows us to use the model for computation of the velocity profiles in the area which is significantly greater than the typical size of a single stem.
The modelling of colloidal fouling and defouling of hollow fibre membranes in the presence of membrane oscillations is analysed by means of numerical simulations as an effect of complex coupling between hydrodynamic and surface forces. To... more
The modelling of colloidal fouling and defouling of hollow fibre membranes in the presence of membrane oscillations is analysed by means of numerical simulations as an effect of complex coupling between hydrodynamic and surface forces. To describe the latter the Derjaguin-Landau- Vervey-Overbeek (DLVO) model has been employed. We have investigated the influence of various parameters of the process like flow rate, mean particle diameter, amplitude and frequency of the oscillations, and others, on the efficiency of the defouling process. The investigated parameters is close to that of a silica suspension in , a typical system modelling used to investigate membrane separation. On the basis of numerical simulation results e have defined an optimal set of parameters preventing membrane fouling.
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A chaotic transition occurs when a continuous change of one of the parameters of the system causes a discontinuous change in the properties of the chaotic attractor of the system. Such phenomena are present in many dynamical systems, in... more
A chaotic transition occurs when a continuous change of one of the parameters of the system causes a discontinuous change in the properties of the chaotic attractor of the system. Such phenomena are present in many dynamical systems, in which a chaotic behavior occurs. The best known of these transitions are: the period-doubling bifurcation cascade, intermittency and crises. The effect of dichotomous Markov noise (DMN) on the properties of systems with chaotic transitions is discussed. DMN is a very simple two-valued stochastic process, with constant transition rates between the two states. In spite of its simplicity, this kind of noise is a very powerful tool to describe various phenomena present in many physical, chemical or biological systems. Many interesting phenomena induced by DMN are known. However, there is no research on the effect of this kind of noise on intermittency or crises. We present the change of the mean laminar phase length and of laminar phase length distributi...
We present the results of experimental investigations of liquid aerosols (mist) filtration on the monolayer and multilayer fibrous filters. We have observed the influence of the filter structure (fiber diameter distribution, the thickness... more
We present the results of experimental investigations of liquid aerosols (mist) filtration on the monolayer and multilayer fibrous filters. We have observed the influence of the filter structure (fiber diameter distribution, the thickness of the layers for multilayer filters) on the filtration efficiency and the pressure drop on the filter. We have also presented the changes of efficiency and pressure drop which appear as a result of the long work of the filter. Finally, the conditions at which the fiber drainage takes place have been shown.
The new distributed parameter model is formulated for the purpose of the investigation of a drying of suspended and sessile droplets of multi-component solutions. The main feature of this model is the division of a droplet/wet particle... more
The new distributed parameter model is formulated for the purpose of the investigation of a drying of suspended and sessile droplets of multi-component solutions. The main feature of this model is the division of a droplet/wet particle into the shells and formulating the mass and heat balances for each shell, which have a shape of spheres in a case of aerosol particles and a shape close to the cylinders in a case of sessile droplets. Presented model takes into account the crust formation during the second stage of drying. This effect is neglected in existing models of the phenomenon. The model predicts the dimension and a shape of particle or formed deposits. It also indicates the possibility of a segregation of components when their solubility and diffusion coefficients are different.
The modelling of colloidal fouling and defouling of hollow fibre membranes in the presence of membrane oscillations is analysed by means of numerical simulations as an effect of complex coupling between hydrodynamic and surface forces. To... more
The modelling of colloidal fouling and defouling of hollow fibre membranes in the presence of membrane oscillations is analysed by means of numerical simulations as an effect of complex coupling between hydrodynamic and surface forces. To describe the latter the Derjaguin-Landau- Vervey-Overbeek (DLVO) model has been employed. We have investigated the influence of various parameters of the process like flow rate, mean particle diameter, amplitude and frequency of the oscillations, and others, on the efficiency of the defouling process. The investigated parameters is close to that of a silica suspension in , a typical system modelling used to investigate membrane separation. On the basis of numerical simulation results e have defined an optimal set of parameters preventing membrane fouling.
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We have shown the results of numerical simulations of the droplet motion on the smooth and rough fibers, obtained by means of two-phase lattice Boltzmann method. We have observed two phenomena influencing on the velocity of the droplet:... more
We have shown the results of numerical simulations of the droplet motion on the smooth and rough fibers, obtained by means of two-phase lattice Boltzmann method. We have observed two phenomena influencing on the velocity of the droplet: the increasing of apparent contact angle on the surface of the rough fiber and the triple line pinning on the asperities. We have investigated the conditions of domination of both of these mechanisms.
We present a method for the reconstruction of the dynamics of processes with discrete time. The time series from such a system is described by a stochastic recurrence equation, the continuous form of which is known as the Langevin... more
We present a method for the reconstruction of the dynamics of processes with discrete time. The time series from such a system is described by a stochastic recurrence equation, the continuous form of which is known as the Langevin equation. The deterministic f and stochastic g components of the stochastic equation are directly extracted from the measurement data with the assumption that the noise has finite moments and has a zero mean and a unit variance. No other information about the noise distribution is needed. This is contrary to the usual Langevin description, in which the additional assumption that the noise is Gaussian (δ-correlated) distributed as necessary. We test the method using one dimensional deterministic systems (the tent and logistic maps) with Gaussian and with Gumbel noise. In addition, results for human heart rate variability are presented as an example of the application of our method to real data. The differences between cardiological cases can be observed in the properties of the deterministic part f and of the reconstructed noise distribution.
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Pomeau-Manneville intermittency in nonstationary systems is investigated. If one of the parameters characterizing a dynamical system is changed periodically, periodic orbits may appear even when the value of this parameter remains in a... more
Pomeau-Manneville intermittency in nonstationary systems is investigated. If one of the parameters characterizing a dynamical system is changed periodically, periodic orbits may appear even when the value of this parameter remains in a range which, in the stationary case, yields chaotic behavior. This property may be used for the control of systems exhibiting intermittency. If the parameter change is not large enough, a periodic orbit does not appear but the distribution of the laminar phases is modified. In the case of type I intermittency, this means a broadening of such a distribution or, alternatively, a splitting of its right peak. We present a theory of these phenomena. Numerical simulations both for one-dimensional maps and for flows support our predictions. Some of the phenomena discussed here were observed earlier in time series of heart rate variability.
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A simple model of behaviour of a single particle on the bulging membrane was presented. As a result of numerical solution of a motion equation the influence of the amplitude and frequency of bulging as well as the particle size on... more
A simple model of behaviour of a single particle on the bulging membrane was presented. As a result of numerical solution of a motion equation the influence of the amplitude and frequency of bulging as well as the particle size on particle behaviour, especially its downstream velocity was investigated. It was found that the bulging of a membrane may increase the mean velocity of a particle or reinforce its diffusive behaviour, dependeing on the permeation velocity. The obtained results may help to design new production methods of highly fouling-resistant membranes.
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ABSTRACT A two-color lattice-Boltzmann method (LBM) was used for simulation of the behavior of droplets deposited on a fiber. The interaction of the droplet with the gas flowing around a fiber having smooth and rough surfaces was... more
ABSTRACT A two-color lattice-Boltzmann method (LBM) was used for simulation of the behavior of droplets deposited on a fiber. The interaction of the droplet with the gas flowing around a fiber having smooth and rough surfaces was analyzed. The equilibrium of conformation of droplets and their velocities were derived. The results of the calculation show the distinguished patterns of the interaction depending on the structure of the fiber roughness and the fiber and droplet dimensions.
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ABSTRACT The new distributed parameter model is formulated for the purpose of the investigation of spray drying of multi-component solutions. The main feature of this model is the division of a droplet/wet particle into shells and... more
ABSTRACT The new distributed parameter model is formulated for the purpose of the investigation of spray drying of multi-component solutions. The main feature of this model is the division of a droplet/wet particle into shells and formulating the mass and heat balances for each shell. In opposition to most similar numerical models, this one takes into account the crust formation during the second stage of drying. By means of this model, we investigate the conditions in which the segregation of the components in particle form takes place. We take into account the initial concentrations of the components in solution, its solubility and diffusion coefficients as model parameters for consideration of the different particle structures.
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We present a new numerical model of filtration of liquid aerosols on fibrous filters. The main goal of the model is to describe the dependence of pressure drop on time during the nonstationary filtration process. The main difference... more
We present a new numerical model of filtration of liquid aerosols on fibrous filters. The main goal of the model is to describe the dependence of pressure drop on time during the nonstationary filtration process. The main difference between the current model and another ones, present in the literature is that it contains very few parameters - in its minimal form only two - and still describes the results of experimental measurements with a very good accuracy. We also estimate the dependence of the parameters of the model on the process conditions (i.e. gas flow velocity and the geometrical parameters of the filter) what enables to use the presented model to predict filtration process evolution in any fibrous filters.
The large eddy simulation method, based on a lattice-Boltzmann algorithm, was used to compute the vertical velocity profile in an open channel flow with submerged and emerged vegetation. The numerical method is characterized by the... more
The large eddy simulation method, based on a lattice-Boltzmann algorithm, was used to compute the vertical velocity profile in an open channel flow with submerged and emerged vegetation. The numerical method is characterized by the relatively short time of computation and low complexity. On the other hand, it allows a more realistic description of the vegetation properties relative to the methods commonly used in 1-D numerical models. For the proper conditions, the method developed in this work gives results similar to other numerical methods. These results
are also in good agreement with the experimental data presented in other papers.
are also in good agreement with the experimental data presented in other papers.
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The dynamics of collisions between droplets and particles are investigated numerically by means of twocolor lattice-Boltzmann method (LBM). We observe three possible scenarios of a collision – one leading to a coalescence between a... more
The dynamics of collisions between droplets and particles are investigated numerically by means of twocolor
lattice-Boltzmann method (LBM). We observe three possible scenarios of a collision – one leading
to a coalescence between a droplet and particle and two leading to separation. We have investigated the
influence of nondimensional parameters, such as Weber and capillary number and droplet to particle
diameter ratio, on the kinetics of a collision. The influence of a shape of a particle on a collision with
droplet were also analyzed. The results have been compared with the experimental results presented in
works of other authors.
lattice-Boltzmann method (LBM). We observe three possible scenarios of a collision – one leading
to a coalescence between a droplet and particle and two leading to separation. We have investigated the
influence of nondimensional parameters, such as Weber and capillary number and droplet to particle
diameter ratio, on the kinetics of a collision. The influence of a shape of a particle on a collision with
droplet were also analyzed. The results have been compared with the experimental results presented in
works of other authors.
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A model of bacterial filtration on fibrous filter media is developed. The single fibre efficiency as well as the efficiency of the whole filter – at the onset of the process and the evolution of those quantities - are analysed. The... more
A model of bacterial filtration on fibrous filter media is developed. The single fibre efficiency as
well as the efficiency of the whole filter – at the onset of the process and the evolution of those
quantities - are analysed. The differences between the numerical modelling of colloidal particles and
bacteria are stressed in detail. The main differences are the active motion ability of bacteria and
biofilm formation. The parameters of the model were identified based on the literature data.
well as the efficiency of the whole filter – at the onset of the process and the evolution of those
quantities - are analysed. The differences between the numerical modelling of colloidal particles and
bacteria are stressed in detail. The main differences are the active motion ability of bacteria and
biofilm formation. The parameters of the model were identified based on the literature data.
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The lattice Boltzmann method is presented as an efficient tool for computation the velocity profiles in open channel flow with rigid stems. The results obtained for regular distribution of stems are compared with the results obtained by... more
The lattice Boltzmann method is presented as an efficient tool for computation the velocity profiles in open channel flow with rigid stems. The results obtained for regular distribution of stems are compared with the results obtained by means of other methods giving good quantitative agreement. The lattice Boltzmann method is also applied for the cases of nonuniform distribution of stems or stems with nonequal height and the velocity profiles for these cases are also computed.
The phenomenon of giant suppression of activation, when two or more correlated noise signals act on the system, was found a few years ago in dynamical bistable or metastable systems. When the correlation between these noise signals is... more
The phenomenon of giant suppression of activation, when two or more correlated noise signals act on the system, was found a few years ago in dynamical bistable or metastable systems. When the correlation between these noise signals is strong enough and the amplitudes of the noise are chosen correctly - the life time of the metastable state may be longer than in the case of the application of only a single noise even by many orders of magnitude. In this paper, we investigate similar phenomena in systems exhibiting several chaotic transitions: Pomeau-Manneville intermittency, boundary crisis and interior crisis induced intermittency. Our goal is to show that, in these systems the application of two noise components with the proper choice of the parameters in the case of intermittency can also lengthen the mean laminar phase length or, in the case of boundary crisis, lengthen the time the trajectory spends on the pre-crisis attractor. In systems with crisis induced intermittency, we introduce a new phenomenon we called quasi-deterministic giant suppression of activation in which the lengthening of the laminar phase lengths is caused not by the action of two correlated noise signals but by a single noise term which is correlated with one of the chaotic variables of the system.
Properties of dynamical systems with dichotomous Markov noise which exhibit crises are investigated. We find numerically the dependence of the mean residence time on the precrisis attractor on the transition rate (or transition... more
Properties of dynamical systems with dichotomous Markov noise which exhibit crises are investigated. We find numerically the dependence of the mean residence time on the precrisis attractor on the transition rate (or transition probability in the discrete-time case) of dichotomous Markov noise. To explain this dependence, we construct a simple Markov chain model, which allows us to find the mean residence time for the given transition rate with a good accuracy. Next, we find the distribution of residence times for a system driven by dichotomous Markov noise and also build a simple model to explain its properties.
Alattice-Boltzmannmethod (LBM) was used for simulation of the 2D binarycoalescence of droplets. The main subject of our interests is the influence of the droplet size and the interfacial tension on binarycoalescencetime (BCT). The BCT of... more
Alattice-Boltzmannmethod (LBM) was used for simulation of the 2D binarycoalescence of droplets. The main subject of our interests is the influence of the droplet size and the interfacial tension on binarycoalescencetime (BCT). The BCT of two free particles as well as the case when one of the particles is deposited on the surface is considered. The results of calculations are in good agreement with experimental data presented in other papers.
The kinetics of the collisions between droplet and the fiber is being studied in both theoretical and numerical way. During theoretical investigations the balances between the various components of total energy of the droplet have been... more
The kinetics of the collisions between droplet and the fiber is being studied in both theoretical and numerical way. During theoretical investigations the balances between the various components of total energy of the droplet have been used. As a result, we have obtained the conditions (expressed in terms of
non-dimensional parameters characterizing the system) at which the deposition of the droplet on the fiber or the separation of the droplet from the fiber occurs. The results of theoretical computation have been compared with the results of the numerical simulations using the two-color lattice-Boltzmann
method.
non-dimensional parameters characterizing the system) at which the deposition of the droplet on the fiber or the separation of the droplet from the fiber occurs. The results of theoretical computation have been compared with the results of the numerical simulations using the two-color lattice-Boltzmann
method.