Leonid Pekker

• Ph.D.
• Senior Researcher at FujiFilm Dimatix

The projection method is the standard approach for numerically integrating the incompressible Navier-Stokes equation initial-boundary-value problem. Typical boundary conditions specify either the velocity or the gradient velocity on the boundary. Here, we consider the pressure-tangential-velocity boundary condition in which the tangential component...

In this work, we extend the model of contact angles that we have previously developed for sessile drops on a wetted surface to the case of a meniscus in a capillary. The underlying physics of our model describe the intermolecular forces between the fluid and the surface of the capillary that result in the formation of a thin, non-removable fluid la...

In this article, we construct a novel one-dimensional model of drop ejection from a micro-size nozzle due to a short pressure pulse applied to the liquid in the nozzle. The pressure pulse supplies the kinetic energy to the perturbed liquid-bulge squeezed from the nozzle, which then ballistically lengthens forming a ligament. The Plateau-Rayleigh in...

We construct a novel model for the steady-state contact angles of liquid droplets at the wetted substrate. The non-removable, thin liquid film covering the substrate is governed by the intermolecular forces between molecules of liquid and solid, which we describe using the standard disjoining pressure approximation. Balancing the disjoining pressur...

We construct a novel model for the steady-state contact angles of liquid droplets at the wetted substrate. The non-removable, thin liquid film covering the substrate is governed by the intermolecular forces between molecules of liquid and solid, which we describe using the standard disjoining pressure approximation. Balancing the disjoining pressur...

In 1994, Eggers and Dupont suggested the slender jet model, a one-dimensional model that describes the motion of a thin axisymmetric column of viscous, incompressible fluid with a free surface. In their model, the momentum equation was derived in a manner that was not completely self-consistent. Consequently, the viscosity term was described with l...

In this article, we construct a novel one-dimensional model of microfluidic laminar flows in tapered circular and rectangular channels assuming the flow in channels fully developed. In the model, we take into account the inertance and dynamic pressure terms. The model can be used for a wide range of flows: from the pure capillary flow regime, where...

In this article, we construct a novel 1D-model of microfluidic laminar flows in tapered circular and rectangular channels assuming the flow in channels fully developed. In the model, we take into account the inertance and dynamic pressure terms. The model can be used for a wide range of flows: from the pure capillary flow regime, where the capillar...

In this article, the author describes a set of models of particle transport in microchannels that has been recently developed at FUJIFILM Dimatix for design and optimization inkjet print heads. The models are used to estimate the modes of particle transport in horizontal channels, the times for particles to settle at the bottom of a channel, and th...

In 1892, in his classical work, L. Rayleigh considered the instability of a cylinder of viscous liquid under capillary force, the so-called Plateau–Rayleigh instability. In this work, in linear approximation, he obtained a dispersion equation describing the increment of this instability as a function of wavelength, the radius of cylinder, the mass...

This paper proposes a model that expands Godyak's collisional sheath model to the case of hot electrodes (anode or cathode) with thermionic electron emission. In the model, the electrodes are assumed to be made from refractory metals and, consequently, the erosion of the electrodes is small and can be neglected. In the frame of two temperature ther...

In this paper, we propose a new set of boundary conditions at ablative hot walls with thermionic electron emission for two-temperature thermal arc models in which the temperature of electrons can deviate from the temperature of heavy particles, Te≠Th. The boundary conditions are for the electric potential, the two energy equations for electrons and...

In this paper we propose new boundary conditions at the hot walls with thermionic electron emission for two-temperature thermal arc models. In the derived boundary conditions the walls are assumed to be made from refractory metals and that the erosion of the wall is small and, therefore, is not taken into account in the model. In these boundary con...

In this paper we propose new boundary conditions at floating and biased walls for two-temperature thermal arc models. In the derived boundary conditions the walls are assumed to be cold and therefore there is no thermionic electron emission and erosion of the wall. The boundary conditions previously used in modeling high-pressure thermal arcs ignor...

The principle idea of using airbreathing electrical propulsion for a vehicle flying at orbital speed on the edge of Earth's atmosphere is examined. In this paper, a simple model of a Hall-effect thruster in which the propellant is an ambient air is presented. A new mode of the airbreathing thruster operation is presented in which incoming air is fu...

The principle idea of using air breathing electric propulsion for a vehicle flying at orbital speed on the edge of Earth's atmosphere is examined. In this paper, we present a simple model of a Hall Effect thruster in which the propellant is ambient air. The required lengths of the thruster chamber, the magnetic fields, the thrust, and other paramet...

In the paper we suggest a new closure for Grad's thirteen moment equations for medium rarefied gases by using a Hermite polynomial approximation for the monatomic gas velocity distribution function, and applying the Chapman-Enskog regularization method to Grad's velocity distribution function that corresponds to his thirteen moment equation. In our...

A zero-dimensional time-dependent high-pressure slab capillary discharge model with capillary wall thermal conduction and radiation absorption is presented. The model includes aesistor-inductor-capacitor circuit and a heat transfer radiation model based on a radiation database constructed using a commercially available radiation software, to calcul...

This paper derives transport equations for medium rarefied gases from the Bhatnagar-Gross-Krook (BGK) model kinetic equation using a Hermite polynomial approximation for the monoatomic gas distribution function. We apply the Chapman-Enskog regularization method to Grad's velocity distribution function that corresponds to his thirteen moment equatio...

We theoretically examine the idea of using the Electrohydrodynamic (EHD) ionic wind pump effect in thruster applications. This idea has been under discussion for many decades. However, there is still no commonly accepted view on EHD-thrusters, e.g., whether EHD-thruster is worthwhile or not, what level of thrust and thrust efficiency can be obtaine...

One-dimensional compressible flows of calorically perfect gases in which only a single driving potential is present are called simple flows. Because Mach number and property relations for simple flows can be expressed in closed form, such flows are usually treated individually. Most introductory compressible flow courses and most compressible flow...

This paper derives the transport equations for rarefied gases from the Bhatnagar-Gross-Krook (BGK) model kinetic equation using Hermite polynomial representation of the velocity distribution function. We apply the Champmen-Enskog method to Grad's thirteen moment equations to derive a closure of Grad's 13 moment equations, extending them to third or...

A zero-dimensional time-dependent high-pressure slab capillary discharge model with capillary wall thermal conduction and radiation absorption is presented. The model includes a resistor-inductor-capacitor circuit and a heat-transfer radiation model based on a radiation database constructed using PrismSPEC, a commercially available radiation softwa...

We develop an analytical Knudsen layer model at the ablative surface in gas flow; this model takes into account the temperature and velocity gradients in the bulk gas and the rebounding of gas molecules by the ablative wall back into the gas region. In addition, this model uses a bimodal velocity distribution function which preserves the laws of co...

A zero-dimensional time-dependent high-pressure slab capillary discharge model is presented. The model includes a heat-transfer radiation model based on a radiation database constructed using Prism SPECT, a commercially available radiation software, to calculate the radiation heat flux output from a uniform plasma slab. Thus, unlike earlier models,...

An analytical model of the Knudsen layer at ablative surfaces has been developed that takes into account the temperature gradient in the bulk gas and rebound of gas particles by the ablative wall back into the gas region. This model uses a bimodal velocity distribution function, which preserves the laws of conservation of mass, momentum, and energy...

A zero-dimensional time-dependent high-pressure slab capillary discharge model with capillary wall thermal conduction and wall radiation absorption is presented. The model includes a resistor-inductor-capacitor circuit and a heat-transfer radiation model based on radiation database constructed using PrismSPEC, a commercially available radiation sof...

A zero-dimensional time-dependent high-pressure slab capillary discharge model is presented. The model includes a heat transfer radiation model based on a radiation database. This database has been constructed using commercially available radiation software PrismSPEC to calculate the radiation heat flux output from an uniform plasma slab. Thus, unl...

One of the most important issues in CFD modeling of ablation process is the formulation of boundary conditions at the gas-surface interface. These boundary conditions cannot be obtained without analytical or parametric numerical modeling of the Knudsen layer formed near the evaporating surface. Analytical models are therefore of interest for numeri...

In this article we develop an analytical model of the Knudsen layer at the ablative wall taking into account the temperature gradient in the bulk gas. The analysis is based on the premise that the temperature gradient in the bulk gas can be taken into account in the velocity distribution function at the outer boundary of the Knudsen layer. The mode...

This work motivation is formulation of the boundary condition for numerical simulation of fluid dynamic with ablative boundaries. In this paper we develop an analytical model of the Knudsen layer by considering a kinetic formulation that takes into account the gas temperature gradient at a flat gas-wall interface. The main focus of this research is...

Although pulsed plasma thrusters have significant experimental heritage over a range of power levels, more recently they are often described as attractive low-power thrusters due to their small dimensions, simplicity, and ability to provide high specific impulses at low power levels. This paper, however, discusses research into the potential applic...

An engineering model of a steady capillary plasma discharge is presented. Two regimes of operation are studied and compared, differing by the assumptions made in the treatment of the radiative fluxes. In the first case, the plasma density is high enough that the radiation Rosseland mean free path is smaller than the capillary radius; this case of b...

An important problem in optical multilayer thin film deposition is the adjusting of target uniformity masks to reach the desired film uniformity distribution over the substrate. Calibration tests, that is, special multilayer optical designs, are a widely used tool to determine deposition rates for deposited materials at different substrate points;...

In this paper, we present a method for determining the refractive index, extinction coefficient, and thickness of thin films using reflectance and transmittance measurements for one frequency of incident light. The measurement of reflectance is conducted from both sides of the sample and transmittance from either one of the two sides. All measureme...

An analytical model of a magnetron glow discharge is considered, assuming classical electron and ion transport across the magnetic field lines. The theoretical volt-ampere characteristic of the discharge is obtained. The shape of this characteristic is similar to that found in experiments. However, the experimental current densities exceed the theo...

A one-dimensional model for the low-pressure glow discharge in a transverse magnetic field is presented. Longitudinal confinement of electrons in the model is provided by a transverse magnetic field. The ion mean free path and ion gyro radius are assumed greater than the distance between the anode and the cathode, thus the influences of the magneti...

A simple model which allows one to calculate the rate coefficients of plasma-chemical reactions in low-pressure DC magnetron discharges is presented. In this model, the electron cyclotron frequency is assumed to be much greater than any electron collision frequency. We also assume that plasma-chemical reactions take place in the near-cathode bright...

A space averaged model of reactive sputtering which includes plasma chemistry for the first time in DC magnetron discharge has been developed by Ershov and Pekker [A. Ershov. L. Pekker, Thin Solid Films, 289 (1996) 140.]. Argon and oxygen have been chosen in this model as buffer and reactive gases, respectively, and silicon as the target material....

A model of reactive sputtering, which includes plasma chemistry for the first time in d.c. magnetron discharges, has been developed. Argon and oxygen have been chosen as buffer and reactive gases, respectively, and silicon as the target material. We have developed a space averaged model of the plasma chemistry in a d.c. magnetron reactive sputterin...

A model that describes the self-maintained glow discharge for a composite cathode in which cathode spots are formed on low work function material inclusions is presented. Based on this model, expressions are obtained for the radius of the spot, the cathode voltage, and the spot current as functions of Pd (where P is the gas pressure and d is the th...

A model is presented for the axial neutral particle pressure gradients and flow patterns in the positive column of a monatomic dc gas discharge. Taking into account both the charge imbalance volume force and charged-particle momentum divergence force components, an analytical expression is derived for the driving volume force acting on the neutral...

A model is presented which describes the radial distributions of the plasma density, electric potential, current density, and magnetic field in the positive column of a stationary glow discharge not in contact with the longitudinal walls of the discharge chamber. In this model, the compression of the positive column is provided by the azimuthal mag...

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The transverse loss of ''central'' ions trapped in the end sections of a tandem mirror system is studied for the case of infrequent collisions. This loss is associated with the pronounced elongation of the drift surfaces along one of the symmetry planes of the device, and it may substantially reduce the plasma confinement time in the system. Expres...

Transverse losses of central ions trapped in the end mirror cells of an ambipolar trap are considered. These losses are due to the pronounced elongation of the drift trajectories in the transverse direction and can significantly reduce the plasma confinement time tau sub con in the trap. A classification of the drift envelopes of the trapped ions i...

The paper examines an instability which arises in a peripheral ambipolar magnetic-mirror trap due to the anisotropic distribution of ions originating from the central mirror trap. The peripheral trap is filled with these 'central' ions, which can have a significant effect on the time of plasma containment. This instability limits the possibility of...

The instability that occurs in the end section of a tandem mirror because of an anisotropy of the distribution function of the ions entering the end section from the central section is investigated. The growth rate for this instability is found to be on the order of omega //p//i. This instability fills the end section with ″central″ ions, with poss...

The radiation from a localized Langmuir perturbation at the harmonics of the plasma frequency is shown to be quadrupole type. Corresponding quadrupole moments are found for the second and third harmonics.