Numerical analysis of ion temperature effects to the plasma wall transition using a one-dimensional two-fluid model. I. Finite Debye to ionization length ratio

Abstract

A one-dimensional, two-fluid, steady state model is used for the analysis of ion temperature effects to the plasma-wall transition. In this paper, the model is solved for a finite ratio between the Debye and the ionization length, while in Part II [T. Gyergyek and J. Kovačič, Phys Plasmas 24, 063506 (2017)], the solutions for [Formula: see text] are presented. Ion temperature is treated as a given, independent parameter and it is included in the model as a boundary condition. It is shown that when the ion temperature larger than zero is selected, the ion flow velocity and the electric field at the boundary must be consistent with the selected ion temperature. A numerical procedure, how to determine such "consistent boundary conditions," is proposed, and a simple relation between the ion temperature and ion velocity at the boundary of the system is found. The effects of the ion temperature to the pre-sheath length, potential, ion temperature, and ion density drops in the pre-sheath and in the sheath are investigated. It is concluded that larger ion temperature results in a better shielding of the plasma from the wall. An attempt is made to include the ion heat flux into the model in its simplest form [Formula: see text], where [Formula: see text] is a constant heat conduction coefficient. It is shown that inclusion of such a term into the energy transfer equation introduces an additional ion heating mechanism into the system and the ion flow then becomes isothermal instead of adiabatic even in the sheath.

Stabilization and Coagulation of Colloidal Suspensions during Crystallization

“…Then, the zeta potentials at different concentrations of additional ions were measured to understand the ions’ effect on motion and interaction of colloidal particles. It was found that the added Na + or Cl – would also align around the charged cefradine nanocrystals by ion diffusion and electrostatic attraction, which will push the previous ions out of the diffusion layer by electrostatic repulsion, and the diffusion layer will become thinner (Figure c). , Besides, the large amounts of ions could promote the formation of ionic groups, which will lead to the net shielding effect and weaken the charge of particles . Therefore, the effective zeta potential will decrease with the addition of NaCl, and the shielding effect is maximized for 0 mV at 28 mM (Figure d).…”

Full structure of the thermal plasma including the ion isothermal drag

“…Also the plasma is symmetrical around the central plane z = 0 ; therefore, it is studied in the half-space 0 ≤ z ≤ L . Then, the two-fluid model of plasma is represented by [16,21,30,32,34,36];…”

“…We have done the computations with = 108.0832 calculated for the electropositive gas Argon. Relation (34) is known as the floating condition and f is called the floating potential.…”

“…The mathematical examination of plasmas near walls and electrodes has attracted considerable interest and has been turned to the main issue of many explorations [8][9][10][11][12][13][14][15][16][17][18][19]. Among the several parameters that their effects have been studied on the plasma variables and structure, the ion temperature effects in thermal plasmas are significant and have been examined by many authors [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Analisis Molekular dan Transpor Ion Natrium Silikat

“…Fluks partikel berhubungan dengan kecepatan hanyut (198; 200; 201; 203; 204), dengan: J = sc (14) Hubungan ini merupakan kelanjutan dari argument yang sudah kita gunakan beberapa kali sebelumnya. Jadi, semua partikel dalam jarak s∆ t A, dapat melewati jendela dengan luas A dalam selang waktu ∆ t (205)(206)(207)(208)(209). Dengan demikian, jumlah mol dapat lewat dalam selang waktu itu adalah: s∆ t x c, sehingga: Sc = -D (15) Jika sekarang kita menyatakan ⁄ dalam ᵮ, menggunakan persamaan 15, maka kita memperoleh: S = -= × ᵮ (16) Terdapat satu kasus ketika kita sudah mengetahui kecepatan hanyut dan gaya efektif yang bekerja pada partikel: ion dalam larutan mempunyai kecepatan hanyut s = µE jika ion itu mengalami gaya еɀE, dan ɀFE per mol, dari medan listrik dengan kuat medan E (210)(211)(212).…”