Determination of the Sizes of Particle Ejected from Shock-Loaded Surfaces during Their Deceleration in a Gaseous Medium
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AND LIQUIDS
Determination of the Sizes of Particle Ejected from Shock-Loaded Surfaces during Their Deceleration in a Gaseous Medium A. V. Fedorov*, I. S. Gnutov, and A. O. Yagovkin All-Russian Scientific Research Institute of Experimental Physics, Russian Federal Nuclear Center, Sarov, Nizhegorodskaya oblast, 607190 Russia *e-mail: [email protected] Received June 27, 2017
Abstract—Shock-wave sputtering of lead surface has been investigated. The dynamics of motion of particles has been determined by laser interferometric photon Doppler velocimetry (PDV) method, and their size has been calculated from the law of deceleration in a gaseous medium. DOI: 10.1134/S1063776118010156
1. INTRODUCTION
2. DETERMINATION OF PARTICLE SIZE DURING DECELERATION IN A GAS The law of deceleration of particles in a gas has the form [8]
In the case of shock-wave loading of metals, particles are ejected from the free surface; this process is known as shock sputtering. In analysis of shock sputtering, it is necessary to know the size of particles moving in a gaseous medium. Some methods make it possible to measure the particle size directly. For example, the pulse-holographic method developed in [1] makes it possible to register particles with a size larger than 1 μm. In investigating sputtering, shadow optical methods are also employed. The minimal size of particles determined by these methods is 3–5 μm [2]. According to the results obtained in [1, 2], a dust cloud contains particles of different sizes (from submicrometer to 100 μm).
(1) fD = ma = m dW = 1 Cd ρ1SmW (t )2, dt 2 where Cd is the drag coefficient for a particle in the gas, ρ1 is the gas density, Sm is the area of the midsection of the particle, and W(t) is the particle velocity. We assume that particles are spherical. Then the mass and the midsection of particles are given by
m = 1 ρ0πd , 6 3
(2)
2 (3) S m = πd , 4 where ρ0 is the density of the metal and d is the particle diameter. Denoting by W0 the initial velocity of particles at t = 0 (time of arrival of a shock wave at the free surface) and integrating Eq. (1), we reduce it to the form
This study aims at developing a new method for estimating the particle size (smaller than 0.3 μm) proceeding from the time dependence of the particle velocity. For this purpose, we used the modern high-sensitivity laser interferometric method known as photon Doppler velocimetry (PDV) [3– 7], which makes it possible to continuously register the tracks of individual particles as well as the velocity spectrum of a particle cloud. The sensitivity of other laser techniques (VISAR, ORVIS, and Fabry–Perot method) does not permit the recording of particle velocity and size. Using recorded velocity spectrograms, we estimated the sizes of particles ejected from the free surface during shock sputtering of lead from the known law of deceleration of particles in a gas [8, 9].
−1
⎡ ⎤ (4) W (t ) = ⎢k t + 1 ⎥ , W0 ⎦ ⎣d where k = 3Cdρ1/4ρ0. We define the Reynolds number, viz., the dimensionless quantity, which is one of the main characteri
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