MOTROL,2013,Vol 15, ʋ5, 91-97
ɗɇȿɊȽȿɌɂɑȿɋɄȺə ɆɈȾȿɅɖ ɉɊɈɐȿɋɋȺ ɍɅɖɌɊȺɁȼɍɄɈȼɈȽɈ ɊȺɋɉɕɅȿɇɂə ȼ
ɌɈɇɄɈɆ ɋɅɈȿ
Ⱥɥɢɧɚ Ʌɹɲɨɤ, Ɉɥɟɝ əɯɧɨ, Ⱥɥɟɤɫɚɧɞɪ Ʌɭɝɨɜɫɤɨɣ
ɇɚɰɢɨɧɚɥɶɧɵɣ ɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ ɍɤɪɚɢɧɵ «Ʉɢɟɜɫɤɢɣ ɩɨɥɢɬɟɯɧɢɱɟɫɤɢɣ ɢɧɫɬɢɬɭɬ»
Ⱥɞɪɟɫ: 03056, ɍɤɪɚɢɧɚ, ɝ. Ʉɢɟɜ, ɩɪɨɫ. ɉɨɛɟɞɵ, 37:
e-mail: atoll-sonic@rambler.ru
Ⱥɧɧɨɬɚɰɢɹ. ɉɪɟɞɥɨɠɟɧɚ ɫɯɟɦɚ ɡɚɬɪɚɬ ɷɧɟɪɝɢɢ ɩɪɢ ɨɫɭɳɟɫɬɜɥɟɧɢɢ ɩɪɨɰɟɫɫɚ ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ ɪɚɫɩɵɥɟɧɢɹ ɜ ɬɨɧɤɨɦ ɫɥɨɟ.
Ɉɛɨɫɧɨɜɚɧɵ ɢ ɪɚɫɩɢɫɚɧɵ ɷɧɟɪɝɢɢ, ɤɨɬɨɪɵɟ ɞɟɣɫɬɜɭɸɬ ɧɚ ɬɨɧɤɢɣ ɫɥɨɣ ɠɢɞɤɨɫɬɢ ɩɪɢ ɭɥɶɬɪɚɡɜɭɤɨɜɨɦ ɪɚɫɩɵɥɟɧɢɢ, ɚ
ɬɚɤɠɟ ɪɚɫɲɢɪɟɧɨ ɨɩɢɫɚɧɵ ɫɨɫɬɚɜɥɹɸɳɢɟ ɜɫɟɯ ɞɟɣɫɬɜɭɸɳɢɯ ɷɧɟɪɝɢɣ. ɉɪɢɜɟɞɟɧɵ ɚɧɚɥɢɬɢɱɟɫɤɢɟ ɜɵɪɚɠɟɧɢɹ ɞɥɹ
ɡɚɞɟɣɫɬɜɨɜɚɧɧɵɯ ɷɧɟɪɝɢɣ. ɉɪɟɞɫɬɚɜɥɟɧ ɛɚɥɚɧɫ ɷɧɟɪɝɢɣ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɪɨɰɟɫɫɚ ɭɥɶɬɪɚɡɜɭɤɨɜɨɣ ɪɚɫɩɵɥɟɧɢɹ ɜ
ɬɨɧɤɨɦ ɫɥɨɟ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɭɥɶɬɪɚɡɜɭɤɨɜɨɟ ɪɚɫɩɵɥɟɧɢɟ, ɷɧɟɪɝɟɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ, ɷɧɟɪɝɢɹ, ɬɨɧɤɢɣ ɫɥɨɣ, ɞɢɫɩɟɪɝɚɬɨɪ.
ȼȼȿȾȿɇɂȿ
ɍɥɶɬɪɚɡɜɭɤɨɜɵɟ ɤɚɜɢɬɚɰɢɨɧɧɵɟ ɬɟɯɧɨɥɨɝɢɢ
ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜ ɰɟɥɨɦ ɪɹɞɟ ɩɪɨɢɡɜɨɞɫɬɜ [38, 11, 21]. ɗɮɮɟɤɬɢɜɧɨɫɬɶ ɦɧɨɝɢɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ
ɩɪɨɰɟɫɫɨɜ ɭɞɚɟɬɫɹ ɩɨɜɵɫɢɬɶ ɡɚ ɫɱɟɬ ɩɪɢɦɟɧɟɧɢɹ
ɬɟɯɧɨɥɨɝɢɢ ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ ɪɚɫɩɵɥɟɧɢɹ ɜ ɬɨɧɤɨɦ
ɫɥɨɟ. ɗɬɚ ɬɟɯɧɨɥɨɝɢɹ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɢɬɶ
ɠɢɞɤɨɫɬɧɵɣ ɚɷɪɨɡɨɥɶ ɫ ɞɢɫɩɟɪɫɧɨɫɬɶɸ ɜ ɩɪɟɞɟɥɚɯ 5
... 30 ɦɤɦ ɢ ɨɛɟɫɩɟɱɢɬɶ ɮɨɪɦɢɪɨɜɚɧɢɟ ɡɚɞɚɧɧɨɣ
ɮɨɪɦɵ ɮɚɤɟɥɚ ɚɷɪɨɡɨɥɹ. ɉɨɥɭɱɟɧɵ ɪɟɡɭɥɶɬɚɬɵ
ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ
ɢɫɫɥɟɞɨɜɚɧɢɣ
ɩɪɨɰɟɫɫɚ
ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ ɪɚɫɩɵɥɟɧɢɹ [17, 19]. ɉɪɟɞɩɪɢɧɹɬɵ
ɩɨɩɵɬɤɢ ɚɧɚɥɢɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɭɤɚɡɚɧɧɨɝɨ
ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɪɨɰɟɫɫɚ [18]. Ɉɞɧɢɦ ɢɡ
ɜɚɪɢɚɧɬɨɜ ɚɧɚɥɢɬɢɱɟɫɤɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ ɹɜɥɹɟɬɫɹ
ɚɧɚɥɢɡ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɦɟɯɚɧɢɡɦɚ
ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ ɪɚɫɩɵɥɟɧɢɹ.
ɐɟɥɶɸ ɩɪɟɞɥɚɝɚɟɦɨɣ ɫɬɚɬɶɢ ɹɜɥɹɟɬɫɹ
ɪɚɡɪɚɛɨɬɤɚ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɩɪɨɰɟɫɫɚ
ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ ɪɚɫɩɵɥɟɧɢɹ ɜ ɬɨɧɤɨɦ ɫɥɨɟ.
ɜɫɥɟɞɫɬɜɢɟ ɨɛɪɚɬɧɨɝɨ ɩɶɟɡɨɷɮɮɟɤɬɚ, ɜɨɡɛɭɠɞɚɟɬ
ɫɬɨɹɱɢɟ ɩɪɨɞɨɥɶɧɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɤɨɥɟɛɚɧɢɹ ɜ
ɪɟɡɨɧɚɧɫɧɨɣ ɫɢɫɬɟɦɟ ɞɢɫɩɟɪɝɚɬɨɪɚ. ɉɪɢ ɷɬɨɦ
ɩɨɜɟɪɯɧɨɫɬɶ ɪɚɫɩɵɥɟɧɢɹ ɪɚɡɦɟɳɚɸɬ ɜ ɩɭɱɧɨɫɬɢ
ɜɨɥɧɵ
ɩɟɪɟɦɟɳɟɧɢɹ.
Ⱦɥɹ
ɞɨɫɬɢɠɟɧɢɹ,
ɧɟɨɛɯɨɞɢɦɨɣ ɞɥɹ ɧɚɱɚɥɚ ɩɪɨɰɟɫɫɚ ɪɚɫɩɵɥɟɧɢɹ,
ɚɦɩɥɢɬɭɞɵ ɤɨɥɟɛɚɧɢɣ ɩɪɢɦɟɧɹɸɬ ɚɤɭɫɬɢɱɟɫɤɢɟ
ɬɪɚɧɫɮɨɪɦɚɬɨɪɵ ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɢ. ɇɚ
ɪɚɫɩɵɥɢɬɟɥɶɧɭɸ ɩɨɜɟɪɯɧɨɫɬɶ ɩɨɞɚɸɬ ɠɢɞɤɨɫɬɶ,
ɤɨɬɨɪɚɹ ɩɨɤɪɵɜɚɟɬ ɟɟ ɫɥɨɟɦ ɬɨɥɳɢɧɨɣ 0,3 ...
1ɦɦ.
ɇɚ
ɩɨɜɟɪɯɧɨɫɬɢ
ɫɥɨɹ
ɠɢɞɤɨɫɬɢ
ɩɨɤɪɵɜɚɸɳɟɝɨ
ɧɨɪɦɚɥɶɧɨ
ɜɢɛɪɢɪɭɸɳɭɸ
ɩɨɜɟɪɯɧɨɫɬɶ, ɨɛɪɚɡɭɸɬɫɹ ɤɚɩɢɥɥɹɪɧɵɟ ɜɨɥɧɵ
(ɪɢɫ. 1).
ɈɋɇɈȼɇɈɃ ɆȺɌȿɊɂȺɅ
Ɋɚɫɫɦɚɬɪɢɜɚɹ ɢɡɜɟɫɬɧɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ
ɦɨɞɟɥɢ [10, 20], ɤɨɬɨɪɵɟ ɨɩɢɫɵɜɚɸɬ ɩɪɨɰɟɫɫ
ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ ɪɚɫɩɵɥɟɧɢɹ ɜ ɬɨɧɤɨɦ ɫɥɨɟ, ɫɥɟɞɭɟɬ
ɨɬɦɟɬɢɬɶ, ɱɬɨ ɨɧɢ ɧɟ ɭɱɢɬɵɜɚɸɬ ɪɹɞ ɜɚɠɧɵɯ
ɮɚɤɬɨɪɨɜ, ɤɨɬɨɪɵɟ ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɸɬ ɧɚ
ɩɚɪɚɦɟɬɪɵ ɩɪɨɰɟɫɫɚ. Ɍɚɤ, ɧɚɩɪɢɦɟɪ, ɧɟ ɭɱɬɟɧɨ
ɜɥɢɹɧɢɟ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ ɢɥɢ ɨɬɞɟɥɶɧɵɟ ɡɚɬɪɚɬɵ
ɷɧɟɪɝɢɢ,
ɫɜɹɡɚɧɧɵɟ
ɫ
ɪɟɨɥɨɝɢɱɟɫɤɢɦɢ
ɨɫɨɛɟɧɧɨɫɬɹɦɢ ɪɚɫɩɵɥɹɟɦɨɣ ɠɢɞɤɨɫɬɢ. ɉɨɷɬɨɦɭ
ɞɥɹ ɭɝɥɭɛɥɟɧɧɨɝɨ ɚɧɚɥɢɡɚ ɛɚɥɚɧɫɚ ɷɧɟɪɝɢɣ ɜ
ɩɪɨɰɟɫɫɟ
ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ
ɪɚɫɩɵɥɟɧɢɹ
ɰɟɥɟɫɨɨɛɪɚɡɧɵɦ ɛɭɞɟɬ ɫɨɫɬɚɜɢɬɶ ɪɚɫɲɢɪɟɧɧɭɸ
ɷɧɟɪɝɟɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɩɪɨɰɟɫɫɚ.
Ɋɟɚɥɢɡɚɰɢɹ
ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ
ɪɚɫɩɵɥɟɧɢɹ
ɠɢɞɤɨɫɬɢ
ɩɪɨɢɫɯɨɞɢɬ
ɡɚ
ɫɱɟɬ
ɩɨɞɚɱɢ
ɫɢɧɭɫɨɢɞɚɥɶɧɨɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɫɢɝɧɚɥɚ ɧɚ
ɩɶɟɡɨɷɥɟɤɬɪɢɱɟɫɤɢɣ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ, ɤɨɬɨɪɵɣ,
Ɋɢɫ.1 ɋɯɟɦɚ ɨɛɪɚɡɨɜɚɧɢɹ ɤɚɩɢɥɥɹɪɧɵɯ ɜɨɥɧ ɢ
ɤɚɜɢɬɚɰɢɨɧɧɨɝɨ ɫɥɨɹ ɩɪɢ ɪɚɫɩɵɥɟɧɢɢ ɜ ɬɨɧɤɨɦ
ɫɥɨɟ (1 - ɤɚɩɢɥɥɹɪɧɵɟ ɜɨɥɧɵ; 2 - ɤɚɜɢɬɚɰɢɨɧɧɵɣ
ɫɥɨɣ; 3 - ɢɡɥɭɱɚɸɳɚɹ ɬɨɪɰɟɜɚɹ ɩɨɜɟɪɯɧɨɫɬɶ
ɞɢɫɩɟɪɝɚɬɨɪɚ)
Fig.1. A chart of formation of capillary waves and
cavitation layer when spraying in a thin layer (1 –
capillary waves; 2 – cavitation layer; 3 – radiating
butt-end surface dispersant)
Ⱥɥɢɧɚ Ʌɹɲɨɤ, Ɉɥɟɝ əɯɧɨ, Ⱥɥɟɤɫɚɧɞɪ Ʌɭɝɨɜɫɤɨɣ
ɉɪɢ ɪɚɡɪɭɲɟɧɢɢ ɤɚɩɢɥɥɹɪɧɵɯ ɜɨɥɧ, ɜɫɥɟɞɫɬɜɢɟ
ɩɨɬɟɪɢ ɢɦɢ ɭɫɬɨɣɱɢɜɨɫɬɢ, ɫ ɝɪɟɛɧɟɣ ɜɨɥɧ
ɫɪɵɜɚɸɬɫɹ ɢ ɭɥɟɬɚɸɬ ɜ ɩɪɨɫɬɪɚɧɫɬɜɨ ɛɥɢɡɤɢɟ ɤ
ɦɨɧɨɞɢɫɩɟɪɫɧɵɦ ɤɚɩɟɥɶɤɢ ɚɷɪɨɡɨɥɹ. ɉɪɢ ɷɬɨɦ
ɱɚɫɬɶ ɩɨɞɜɟɞɟɧɧɨɣ ɷɧɟɪɝɢɢ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ
ɨɛɪɚɡɨɜɚɧɢɟ ɤɚɩɥɢ ɚɷɪɨɡɨɥɹ, ɱɚɫɬɶ ɪɚɫɯɨɞɭɟɬɫɹ
ɧɚ ɨɛɟɫɩɟɱɟɧɢɟ ɩɨɥɟɬɚ ɤɚɩɥɢ ɢ ɭɞɟɪɠɚɧɢɟ ɟɟ
ɫɮɟɪɢɱɟɫɤɨɣ ɮɨɪɦɵ, ɚ ɱɚɫɬɶ ɢɡɥɭɱɚɟɬɫɹ ɫ
ɩɨɜɟɪɯɧɨɫɬɢ ɠɢɞɤɨɫɬɢ ɜ ɝɚɡɨɜɭɸ ɫɪɟɞɭ. ɉɨɷɬɨɦɭ
ɭɦɟɫɬɧɵɦ
ɛɭɞɟɬ
ɡɚɩɢɫɚɬɶ
ɭɪɚɜɧɟɧɢɟ
ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɛɚɥɚɧɫɚ ɜ ɨɛɳɟɦ ɜɢɞɟ ɤɚɤ:
Eɩɨɞɜ
ɝɞɟ
Eɨɛɪ Eɤɚɩɥɢ E ɝ .ɫ. ,
ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ ɜ ɫɥɨɟ ɠɢɞɤɨɫɬɢ;
Eɞɢɫɩ -
Eɤɚɩɥɢ - ɷɧɟɪɝɢɹ ɧɚ
ɤɚɩɥɢ
ɚɷɪɨɡɨɥɹ;
ɨɛɟɫɩɟɱɟɧɢɟ ɩɨɥɟɬɚ ɤɚɩɥɢ ɢ ɩɨɞɞɟɪɠɤɭ
ɫɮɟɪɢɱɧɨɫɬɢ ɟɟ ɮɨɪɦɵ; Eɝ .ɫ. - ɷɧɟɪɝɢɹ,
ɢɡɥɭɱɚɟɦɚɹ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɫɥɨɹ ɠɢɞɤɨɫɬɢ ɜ
ɝɚɡɨɜɭɸ ɫɪɟɞɭ.
ɋɨɫɬɚɜ ɷɧɟɪɝɢɣ, ɤɨɬɨɪɵɟ ɪɚɫɯɨɞɭɸɬɫɹ ɧɚ
ɨɛɪɚɡɨɜɚɧɢɟ
ɤɚɩɥɢ
ɚɷɪɨɡɨɥɹ,
ɦɨɠɟɬ
ɛɵɬɶ
ɩɪɟɞɫɬɚɜɥɟɧ ɫɨɝɥɚɫɧɨ ɫɯɟɦɟ (ɪɢɫ. 2).
ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɷɧɟɪɝɢɹ, ɤɨɬɨɪɚɹ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ
ɨɛɪɚɡɨɜɚɧɢɟ ɢ ɪɚɡɪɭɲɟɧɢɟ ɤɚɩɢɥɥɹɪɧɵɯ ɜɨɥɧ
ɦɨɠɟɬ ɜɤɥɸɱɚɬɶ ɞɜɟ ɫɨɫɬɚɜɥɹɸɳɢɟ – ɷɧɟɪɝɢɸ,
ɡɚɬɪɚɱɢɜɚɟɦɭɸ ɧɚ ɨɛɪɚɡɨɜɚɧɢɟ ɢ ɩɨɞɞɟɪɠɤɭ
ɤɚɜɢɬɚɰɢɢ ɜ ɫɥɨɟ ɠɢɞɤɨɫɬɢ ɧɚ ɜɢɛɪɢɪɭɸɳɟɣ
ɩɨɜɟɪɯɧɨɫɬɢ ( Eɤɚɜ ) ɢ ɷɧɟɪɝɢɸ, ɡɚɬɪɚɱɢɜɚɟɦɭɸ
ɡɚɬɪɚɱɢɜɚɟɦɚɹ
Et $ -
ɷɧɟɪɝɢɹ,
ɧɚ
ɤɨɬɨɪɚɹ
ɬɪɚɬɢɬɫɹ ɧɚ ɧɚɝɪɟɜ ɠɢɞɤɨɫɬɢ.
Ɍɨɝɞɚ, ɨɛɳɢɣ ɛɚɥɚɧɫ ɷɧɟɪɝɢɣ, ɡɚɞɟɣɫɬɜɨɜɚɧɧɵɯ ɜ
ɩɪɨɰɟɫɫɟ ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ ɪɚɫɩɵɥɟɧɢɹ ɜ ɬɨɧɤɨɦ
ɫɥɨɟ, ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɤɚɤ
ȿɩɨɞɜ
E ɤɨɝ Eɜ.ɬ Eɞɢɫɩ Et $ ȿ ɤ.ɜ ȿɤɚɩɥɢ ȿ ɝ .ɫ.
.
(3)
ɉɪɢ
ɪɚɫɱɟɬɚɯ
ɢ
ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɢ
ɭɥɶɬɪɚɡɜɭɤɨɜɵɯ ɞɢɫɩɟɪɝɚɬɨɪɨɜ ɞɥɹ ɪɚɫɩɵɥɟɧɢɹ ɜ
ɬɨɧɤɨɦ ɫɥɨɟ ɜɵɛɨɪɨɦ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɪɚɡɦɟɪɨɜ
ɨɛɟɫɩɟɱɢɜɚɸɬ ɪɟɡɨɧɚɧɫɧɵɣ ɪɟɠɢɦ ɪɚɛɨɬɵ, ɬ.ɟ.
ɪɟɠɢɦ, ɩɪɢ ɤɨɬɨɪɨɦ ɩɨ ɞɥɢɧɟ ɞɢɫɩɟɪɝɚɬɨɪɚ ɜ
ɧɚɩɪɚɜɥɟɧɢɢ ɧɨɪɦɚɥɶɧɨɦ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɫɩɵɥɟɧɢɹ
ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ
ɫɬɨɹɱɚɹ
ɜɨɥɧɚ
ɭɩɪɭɝɨɣ
ɞɟɮɨɪɦɚɰɢɢ. ɉɪɢ ɷɬɨɦ ɜɵɛɨɪɨɦ ɞɢɚɦɟɬɪɚ
ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɫɩɵɥɟɧɢɹ ɢ ɩɨɩɟɪɟɱɧɵɯ ɪɚɡɦɟɪɨɜ
ɞɢɫɩɟɪɝɚɬɨɪɨɜ ɨɛɟɫɩɟɱɢɜɚɸɬ ɩɨɪɲɧɟɜɨɣ ɯɚɪɚɤɬɟɪ
ɤɨɥɟɛɚɧɢɣ. ɉɨɷɬɨɦɭ ɩɪɚɜɨɦɟɪɧɵɦ ɦɨɠɧɨ ɫɱɢɬɚɬɶ
ɪɚɫɫɦɨɬɪɟɧɢɟ ɩɥɨɫɤɢɯ ɫɬɨɹɱɢɯ ɜɨɥɧ ɝɚɪɦɨɧɢɱɟɫɤɢɯ
ɤɨɥɟɛɚɧɢɣ. Ɍɨɝɞɚ ɜ ɜɨɥɧɟ ɞɟɮɨɪɦɚɰɢɢ ɫɪɟɞɧɢɟ ɩɨ
ɜɪɟɦɟɧɢ ɡɧɚɱɟɧɢɹ ɩɥɨɬɧɨɫɬɟɣ ɩɨɬɟɧɰɢɚɥɶɧɨɣ
Eɩɨɬ
ɢ ɤɢɧɟɬɢɱɟɫɤɨɣ
ɡɚɩɢɫɚɬɶ ɤɚɤ [1, 2]:
( Eɤ .ɜ ).
Ⱦɥɹ ɚɧɚɥɢɡɚ ɷɧɟɪɝɢɢ Eɤɚɜ ɰɟɥɟɫɨɨɛɪɚɡɧɨ
ɩɪɢɧɢɦɚɬɶ
ɜɨ
ɜɧɢɦɚɧɢɟ
ɫɥɟɞɭɸɳɢɟ
ɫɨɫɬɚɜɥɹɸɳɢɟ:
ȿɤɚɜ
ɷɧɟɪɝɢɹ,
ɞɢɫɩɟɪɝɢɪɨɜɚɧɢɟ;
(1)
Eɩɨɞɜ. - ɩɨɞɜɟɞɟɧɧɚɹ ɚɤɭɫɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ;
Eɨɛɪ - ɷɧɟɪɝɢɹ, ɡɚɬɪɚɱɢɜɚɟɦɚɹ ɧɚ ɨɛɪɚɡɨɜɚɧɢɟ
ɧɚ ɨɛɪɚɡɨɜɚɧɢɟ ɤɚɩɢɥɥɹɪɧɵɯ ɜɨɥɧ
Eɜ.ɬ - ɷɧɟɪɝɢɹ, ɡɚɬɪɚɱɢɜɚɟɦɚɹ ɧɚ ɩɪɟɨɞɨɥɟɧɢɟ
Eɤɨɝ Eɜ.ɬ Eɞɢɫɩ Et $ , (2)
Eɤɢɧ
ɷɧɟɪɝɢɣ ɦɨɠɧɨ
Eɩɨɬ
1 1
ɪɤ2 (1 cos 2kx ) ;
2
8 U ɤ ɫɤ
Eɤɢɧ
1 1
ɪɤ2 (1 cos 2kx) ,
2
8 U ɤ ɫɤ
ɝɞɟ U ɤ ,
ɤ - ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɥɨɬɧɨɫɬɶ ɢ
ɫɤɨɪɨɫɬɶ ɡɜɭɤɚ ɜ ɦɚɬɟɪɢɚɥɟ, ɢɡ ɤɨɬɨɪɨɝɨ
c
ɝɞɟ Eɤɨɝ - ɷɧɟɪɝɢɹ, ɪɚɫɯɨɞɭɟɦɚɹ ɧɚ ɩɪɟɨɞɨɥɟɧɢɟ
ɤɨɝɟɡɢɢ;
Ɋɢɫ. 2 ɋɯɟɦɚ ɡɚɬɪɚɬ ɷɧɟɪɝɢɢ ɩɪɢ ɨɫɭɳɟɫɬɜɥɟɧɢɢ ɩɪɨɰɟɫɫɚ ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ ɪɚɫɩɵɥɟɧɢɹ ɜ
ɬɨɧɤɨɦ ɫɥɨɟ
Fig.2. A chart of charges of energy is during realization of process of ultrasonic spraying in a
thin
ɗɇȿɊȽȿɌɂɑȿɋɄȺə ɆɈȾȿɅɖ ɉɊɈɐȿɋɋȺ ɍɅɖɌɊȺɁȼɍɄɈȼɈȽɈ ɊȺɋɉɕɅȿɇɂə
ɢɡɝɨɬɨɜɥɟɧ
ɬɪɚɧɫɮɨɪɦɚɬɨɪ
ɤɨɥɟɛɚɬɟɥɶɧɨɣ
ɫɤɨɪɨɫɬɢ; k - ɜɨɥɧɨɜɨɟ ɱɢɫɥɨ; pɤ - ɚɦɩɥɢɬɭɞɚ
ɤɨɥɟɛɚɬɟɥɶɧɨɝɨ ɞɚɜɥɟɧɢɹ ɜ ɜɨɥɧɟ ɞɟɮɨɪɦɚɰɢɢ
ɫɬɭɩɟɧɢ ɦɚɥɨɝɨ ɞɢɚɦɟɬɪɚ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ; x ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɭɡɥɚ ɜ ɜɨɥɧɟ ɞɟɮɨɪɦɚɰɢɢ.
ɨɬɧɨɲɟɧɢɟ
ɜɨɥɧɨɜɵɯ
ɤɨɧɬɚɤɬɢɪɭɸɳɢɯ ɫɪɟɞ:
91
U ɤ cɤ
U ɪc ɪ ,
U ɪ ɬɚ
c ɪ - ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɥɨɬɧɨɫɬɶ ɢ
ȼ ɩɪɢɧɹɬɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ (ɪɢɫ.1) ɞɥɹ ɩɥɨɫɤɨɣ
ɫɬɨɹɱɟɣ ɝɚɪɦɨɧɢɱɟɫɤɨɣ ɜɨɥɧɵ ɞɚɜɥɟɧɢɟ ɦɨɠɧɨ
ɜɵɪɚɡɢɬɶ ɡɚɜɢɫɢɦɨɫɬɶɸ
ɝɞɟ
p
pɤ sin kx cos Zt ,
ɝɞɟ Z
ɫɨɩɪɨɬɢɜɥɟɧɢɣ
(6)
ɫɤɨɪɨɫɬɶ ɡɜɭɤɚ ɜ ɠɢɞɤɨɫɬɢ ɤɨɬɨɪɚɹ, ɪɚɫɩɵɥɹɟɬɫɹ.
ɍɱɢɬɵɜɚɹ ɭɪɚɜɧɟɧɢɹ (5) ɢ (6), ɡɜɭɤɨɜɚɹ ɷɧɟɪɝɢɹ
Eɩɨɞɜ , ɤɨɬɨɪɚɹ ɩɟɪɟɞɚɟɬɫɹ ɜ ɬɨɧɤɢɣ ɫɥɨɣ
2Sf - ɤɪɭɝɨɜɚɹ ɱɚɫɬɨɬɚ.
Ɍɨɝɞɚ,
ɩɨɥɧɵɟ
ɡɧɚɱɟɧɢɹ
ɩɥɨɬɧɨɫɬɟɣ
ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɢ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɣ ɛɭɞɭɬ
ɢɦɟɬɶ ɜɢɞ:
ɠɢɞɤɨɫɬɢ, ɧɚɯɨɞɹɳɢɣɫɹ ɧɚ ɜɢɛɪɢɪɭɸɳɟɣ
ɩɨɜɟɪɯɧɨɫɬɢ ɞɢɫɩɟɪɝɚɬɨɪɚ, ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧɚ
ɤɚɤ
~
Eɩɨɞɜ 9 1Sɞ h ɪ Eɞɢɫɩ
~
Eɩɨɬ
~
Eɤɢɧ
1 1
pɤ2 sin 2 kx cos 2 Zt ;
2
2 U ɤ cɤ
ɢɥɢ
1 1
pɤ2 cos 2 kx cos 2 Zt . (4)
2
2 U ɤ cɤ
Eɩɨɞɜ
Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɜ ɜɨɥɧɟ ɞɟɮɨɪɦɚɰɢɢ ɩɨ
ɞɥɢɧɟ ɞɢɫɩɟɪɝɚɬɨɪɚ ɡɧɚɱɟɧɢɟ ɩɥɨɬɧɨɫɬɢ ɩɨɥɧɨɣ
~
~
~
Eɤɢɧ Eɩɨɬ ɫ
ɡɜɭɤɨɜɨɣ ɷɧɟɪɝɢɢ Eɞɢɫɩ
ɭɱɟɬɨɦ ɭɪɚɜɧɟɧɢɣ (4) ɢɦɟɟɬ ɜɢɞ:
~
Eɞɢɫɩ
1 1
pɤ2 cos 2 Zt .
2
2 U ɤ cɤ
1 Sɞ hɪ 2
pɤ cos2 Zt ,
2 U ɪ c ɪ cɤ
(7)
S ɞ - ɩɥɨɳɚɞɶ ɢɡɥɭɱɚɸɳɟɣ ɩɨɜɟɪɯɧɨɫɬɢ
ɞɢɫɩɟɪɝɚɬɨɪɚ; h ɪ - ɬɨɥɳɢɧɚ ɫɥɨɹ ɠɢɞɤɨɫɬɢ.
ɝɞɟ
ɋɥɟɞɭɟɬ
ɨɬɦɟɬɢɬɶ,
ɱɬɨ
ɬɨɥɳɢɧɚ
ɫɥɨɹ,
ɩɨɤɪɵɜɚɸɳɟɝɨ
ɢɡɥɭɱɚɸɳɭɸ
ɬɨɪɰɟɜɭɸ
ɩɨɜɟɪɯɧɨɫɬɶ ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ ɞɢɫɩɟɪɝɚɬɨɪɚ,
ɞɨɜɨɥɶɧɨ ɦɚɥɟɧɶɤɚɹ, ɚ ɫɚɦɚ ɩɨɜɟɪɯɧɨɫɬɶ ɩɥɨɫɤɚɹ.
ɉɨɷɬɨɦɭ ɛɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɜ ɠɢɞɤɨɫɬɶ
(5)
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɧɚ ɬɨɪɰɟɜɨɣ ɪɚɛɨɱɟɣ
ɩɨɜɟɪɯɧɨɫɬɢ ɞɢɫɩɟɪɝɚɬɨɪɚ ɨɛɪɚɡɭɟɬɫɹ ɭɡɟɥ
ɞɚɜɥɟɧɢɹ, ɜ ɤɨɬɨɪɨɦ ɧɚɛɥɸɞɚɟɬɫɹ ɦɚɤɫɢɦɭɦ
ɤɢɧɟɬɢɱɟɫɤɨɣ ɢ ɦɢɧɢɦɭɦ ɩɨɬɟɧɰɢɚɥɶɧɨɣ
ɷɧɟɪɝɢɣ.
ɉɨɫɤɨɥɶɤɭ
ɬɨɪɰɟɜɚɹ
ɪɚɫɩɵɥɢɬɟɥɶɧɚɹ
ɩɨɜɟɪɯɧɨɫɬɶ ɞɢɫɩɟɪɝɚɬɨɪɚ ɩɨɤɪɵɬɚ ɬɨɧɤɢɦ ɫɥɨɟɦ
ɠɢɞɤɨɫɬɢ, ɱɚɫɬɶ ɭɥɶɬɪɚɡɜɭɤɨɜɨɣ ɷɧɟɪɝɢɢ
ɩɟɪɟɞɚɟɬɫɹ ɟɣ.
ɍɱɢɬɵɜɚɹ ɧɨɪɦɚɥɶɧɨɟ ɩɚɞɟɧɢɟ ɩɥɨɫɤɨɣ ɜɨɥɧɵ ɧɚ
ɩɥɨɫɤɭɸ
ɝɪɚɧɢɰɭ
ɪɚɡɞɟɥɚ
ɞɜɭɯ
ɫɪɟɞ,
9 1 ɩɟɪɟɞɚɱɢ ɷɧɟɪɝɢɢ ɨɬ
ɤɨɷɮɮɢɰɢɟɧɬ
ɞɢɫɩɟɪɝɚɬɨɪɚ ɜ ɠɢɞɤɨɫɬɶ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɤɚɤ
ɢɡɥɭɱɚɸɬɫɹ ɩɥɨɫɤɢɟ ɜɨɥɧɵ ɞɥɢɧɨɣ O . ȼ ɷɬɨɦ
ɫɥɭɱɚɟ ɪɚɡɦɟɪɵ ɢɡɥɭɱɚɸɳɟɣ ɩɨɜɟɪɯɧɨɫɬɢ
ɨɛɟɫɩɟɱɢɜɚɸɬ ɫɩɪɚɜɟɞɥɢɜɨɫɬɶ ɫɨɨɬɧɨɲɟɧɢɹ
hɪ Sɞ
O
.
(8)
ȼɵɩɨɥɧɟɧɢɟ ɷɬɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ ɩɨɞɬɜɟɪɠɞɚɟɬ,
ɱɬɨ ɜɨɥɧɚ, ɤɨɬɨɪɚɹ ɢɡɥɭɱɚɟɬɫɹ, ɩɥɨɫɤɚɹ ɩɨ ɜɫɟɣ
ɬɨɥɳɢɧɟ ɫɥɨɹ ɠɢɞɤɨɫɬɢ.
ɉɪɢ ɪɟɚɥɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ
ɪɚɫɩɵɥɟɧɢɹ
ɢɫɩɨɥɶɡɭɸɬɫɹ
ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ
ɨɩɪɟɞɟɥɟɧɧɵɟ
Ⱥɥɢɧɚ Ʌɹɲɨɤ, Ɉɥɟɝ əɯɧɨ, Ⱥɥɟɤɫɚɧɞɪ Ʌɭɝɨɜɫɤɨɣ
ɞɢɚɩɚɡɨɧɵ ɩɚɪɚɦɟɬɪɨɜ: ɬɨɥɳɢɧɚ ɫɥɨɹ ɠɢɞɤɨɫɬɢ
ɢɡɦɟɧɹɟɬɫɹ ɨɬ 0,3 ɞɨ 0,8 ɦɦ, ɚ ɱɚɫɬɨɬɚ
ɜɨɡɛɭɠɞɟɧɢɹ ɢɡɦɟɧɹɟɬɫɹ ɨɬ 20 ɞɨ 100 ɤȽɰ.
ɍɤɚɡɚɧɧɵɟ ɡɧɚɱɟɧɢɹ ɧɟ ɩɨɡɜɨɥɹɸɬ ɨɛɪɚɡɨɜɚɬɶɫɹ
ɫɬɨɹɱɟɣ ɜɨɥɧɟ ɞɟɮɨɪɦɚɰɢɢ ɩɨ ɬɨɥɳɢɧɟ ɫɥɨɹ
ɠɢɞɤɨɫɬɢ. ɉɨɷɬɨɦɭ ɡɜɭɤɨɜɚɹ ɷɧɟɪɝɢɹ ɛɭɞɟɬ
ɩɟɪɟɧɨɫɢɬɶɫɹ
ɩɥɨɫɤɨɣ
ɛɟɝɭɳɟɣ
ɜɨɥɧɨɣ
ɞɟɮɨɪɦɚɰɢɢ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɞɢɫɩɟɪɝɚɬɨɪɚ, ɤ
ɫɜɨɛɨɞɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɫɥɨɹ ɠɢɞɤɨɫɬɢ, ɫ
ɤɨɬɨɪɨɣ ɩɪɨɢɫɯɨɞɢɬ ɩɪɨɰɟɫɫ ɪɚɫɩɵɥɟɧɢɹ.
ɍɱɢɬɵɜɚɹ, ɱɬɨ ɞɚɜɥɟɧɢɟ ɜ ɛɟɝɭɳɟɣ ɩɥɨɫɤɨɣ
ɝɚɪɦɨɧɢɱɟɫɤɨɣ
ɜɨɥɧɟ
ɨɩɪɟɞɟɥɹɟɬɫɹ
ɡɚɜɢɫɢɦɨɫɬɶɸ
p
Ⱦɥɹ ɫɬɨɹɱɟɣ ɜɨɥɧɵ ɜ ɩɪɢɧɹɬɨɣ ɪɚɧɟɟ ɫɢɫɬɟɦɟ
ɨɬɫɱɟɬɚ (ɪɢɫ.1) ɫɩɪɚɜɟɞɥɢɜɚ ɡɚɜɢɫɢɦɨɫɬɶ
Sɞ hɪ
Uɪ
ɢɡɥɭɱɚɸɳɟɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɩɨɥɭɱɢɦ
X H ɤZ cos Zt .
pm2 cos 2 (Zt kx)
Ɋɟɲɚɹ ɫɨɜɦɟɫɬɧɨ ɜɵɪɚɠɟɧɢɹ (12) ɢ (13) ɩɪɢ
ɝɞɟ X m - ɚɦɩɥɢɬɭɞɚ ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɜ
ɪɚɫɩɵɥɢɜɚɟɦɨɣ ɠɢɞɤɨɫɬɢ.
0 ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ
pɤ
H ɤZUɤ cɤ ctgZt .
(14)
1 S ɞ h ɪ (H ɤ ZU ɤ ) cɤ
u
2
U ɪc ɪ
2
Eɩɨɞɜ
.
(15)
u ctg Zt cos (Zt kx)
2
2
(10)
ɉɪɢ
ɭɜɟɥɢɱɟɧɢɢ
ɚɦɩɥɢɬɭɞɵ
ɤɨɥɟɛɚɧɢɣ
ɜɢɛɪɢɪɭɸɳɟɝɨ
ɬɨɪɰɚ
ɞɢɫɩɟɪɝɚɬɨɪɚ
ɧɚ
ɩɨɜɟɪɯɧɨɫɬɢ ɠɢɞɤɨɫɬɢ ɨɛɪɚɡɭɸɬɫɹ ɫɬɨɹɱɢɟ
ɤɚɩɢɥɥɹɪɧɵɟ ɜɨɥɧɵ. Ʉɨɝɞɚ ɫɢɥɵ ɩɨɜɟɪɯɧɨɫɬɧɨɝɨ
ɧɚɬɹɠɟɧɢɹ ɧɟ ɜ ɫɨɫɬɨɹɧɢɢ ɭɞɟɪɠɢɜɚɬɶ
ɰɟɥɨɫɬɧɨɫɬɶ ɜɵɬɹɧɭɬɨɣ ɤɚɩɢɥɥɹɪɧɨɣ ɜɨɥɧɵ, ɟɟ
ɝɪɟɛɟɧɶ ɪɚɡɪɭɲɚɟɬɫɹ ɢ ɫ ɧɟɝɨ ɫɪɵɜɚɟɬɫɹ ɤɚɩɥɹ
ɚɷɪɨɡɨɥɹ.
Ɍɨɝɞɚ, ɩɨɞɫɬɚɜɥɹɹ ɜɵɪɚɠɟɧɢɟ (10) ɜ (9),
ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɩɨɞɜɟɞɟɧɧɨɣ ɤ ɫɥɨɸ ɠɢɞɤɨɫɬɢ
ɷɧɟɪɝɢɢ ɛɭɞɟɬ ɢɦɟɬɶ ɜɢɞ
Eɩɨɞɜ
ɭɫɥɨɜɢɢ x
ɉɨɞɫɬɚɜɢɜ ɜɵɪɚɠɟɧɢɟ (14) ɜ (11), ɭɪɚɜɧɟɧɢɟ ɞɥɹ
ɷɧɟɪɝɢɢ, ɤɨɬɨɪɚɹ ɩɟɪɟɞɚɟɬɫɹ ɫ ɢɡɥɭɱɚɸɳɟɣ
ɩɨɜɟɪɯɧɨɫɬɢ ɜ ɫɥɨɣ ɠɢɞɤɨɫɬɢ, ɨɤɨɧɱɚɬɟɥɶɧɨ
ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ
ɋɨɩɨɫɬɚɜɢɜ ɡɚɜɢɫɢɦɨɫɬɢ (7) ɢ (9) ɩɪɢ x 0 ,
ɬ.ɟ. ɞɥɹ ɬɨɱɤɢ, ɫɨɜɩɚɞɚɸɳɟɣ ɫ ɩɨɜɟɪɯɧɨɫɬɶɸ
ɞɢɫɩɟɪɝɚɬɨɪɚ, ɩɨɥɭɱɢɦ
1 cɪ 2
pɤ .
2 cɤ
(13)
(9)
X m2 cos 2 (Zt kx),
pm2
H - ɜɟɥɢɱɢɧɚ
x 0
ɫɩɪɚɜɟɞɥɢɜɚ
ɡɚɜɢɫɢɦɨɫɬɶ
H H ɤ sin Zt , ɝɞɟ H ɤ - ɚɦɩɥɢɬɭɞɚ ɤɨɥɟɛɚɧɢɣ
ɩɨɥɧɚɹ ɷɧɟɪɝɢɹ, ɩɟɪɟɧɨɫɢɦɚɹ ɜɨɥɧɨɣ ɩɨ ɜɫɟɦɭ
ɫɥɨɸ ɠɢɞɤɨɫɬɢ, ɛɭɞɟɬ ɢɦɟɬɶ ɜɢɞ
U ɪc ɪ
ɝɞɟ
ɜ
ɞɟɮɨɪɦɚɰɢɢ ɦɚɬɟɪɢɚɥɚ ɤɨɧɰɟɧɬɪɚɬɨɪɚ, ɚ ɧɚ
ɬɨɪɰɟɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɤɨɬɨɪɚɹ ɢɡɥɭɱɚɟɬ, ɜ ɬɨɱɤɟ
pm - ɚɦɩɥɢɬɭɞɚ ɤɨɥɟɛɚɬɟɥɶɧɨɝɨ ɞɚɜɥɟɧɢɹ ɜ
Eɩɨɬ ,
ɪɚɫɩɵɥɢɜɚɟɦɨɣ ɠɢɞɤɨɫɬɢ, ɚ ȿ ɤɢɧ
2
dH
,
dt
ɍɱɢɬɵɜɚɹ, ɱɬɨ X
pm cos(Zt kx) ,
Sɞ hɪ
(12)
X - ɤɨɥɟɛɚɬɟɥɶɧɚɹ ɫɤɨɪɨɫɬɶ
ɝɞɟ
ɭɥɶɬɪɚɡɜɭɤɨɜɨɦ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ.
ɝɞɟ
Eɛɟɝ.ɜ
pɤ
cos kx sin Zt ,
U ɤ cɤ
X
1 Sɞ h ɪ
pɤ2 cos 2 (Zt kx) (11)
2 U ɪ c ɪ cɤ
ɗɇȿɊȽȿɌɂɑȿɋɄȺə ɆɈȾȿɅɖ ɉɊɈɐȿɋɋȺ ɍɅɖɌɊȺɁȼɍɄɈȼɈȽɈ ɊȺɋɉɕɅȿɇɂə
ɇɚ ɨɬɪɵɜ ɤɚɩɥɢ ɡɚɬɪɚɱɢɜɚɟɬɫɹ ɨɩɪɟɞɟɥɟɧɧɚɹ
Eɤɚɩɥɢ ,
ɷɧɟɪɝɢɹ
ɡɚɜɢɫɢɦɨɫɬɶɸ [18]
Eɤɚɩɥɢ
ɝɞɟ
ɤɨɬɨɪɚɹ
ɨɩɪɟɞɟɥɹɟɬɫɹ
9 2 - ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ ɷɧɟɪɝɢɢ ɨɬ
U ɝ ɢ ɫɝ ɠɢɞɤɨɫɬɢ ɤ ɝɚɡɨɜɨɣ ɫɪɟɞɟ;
ɝɞɟ
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɥɨɬɧɨɫɬɶ ɢ ɫɤɨɪɨɫɬɶ ɡɜɭɤɚ ɜ
ɝɚɡɨɜɨɣ ɫɪɟɞɟ.
4Sd ɤ2V ,
ȼ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɷɧɟɪɝɢɸ ɤɨɝɟɡɢɢ Eɤɨɝ ,
ɡɚɬɪɚɱɢɜɚɟɦɭɸ ɧɚ ɩɨɞɞɟɪɠɚɧɢɟ ɫɜɹɡɢ ɦɟɠɞɭ
ɦɨɥɟɤɭɥɚɦɢ ɠɢɞɤɨɫɬɢ, ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ
ɡɚɜɢɫɢɦɨɫɬɶɸ [16]
(16)
d ɤ - ɫɪɟɞɧɢɣ ɞɢɚɦɟɬɪ ɤɚɩɥɢ ɚɷɪɨɡɨɥɹ.
ɉɪɢ ɷɬɨɦ ɫɪɟɞɧɢɣ ɞɢɚɦɟɬɪ ɤɚɩɥɢ ɚɷɪɨɡɨɥɹ
ɧɚɯɨɞɢɬɫɹ ɩɨ ɮɨɪɦɭɥɟ [18]
§ 8SV ·
¸
a ¨3
¨ Uɪ f 2 ¸,
¹
©
dɤ
ɝɞɟ
Eɤɚɩɥɢ ɨɤɨɧɱɚɬɟɥɶɧɨ ɩɪɢɦɟɬ ɜɢɞ
Eɜ.ɬ ,
ɗɧɟɪɝɢɹ
ɜɹɡɤɨɝɨ
ɬɪɟɧɢɹ
ɨɛɭɫɥɨɜɥɟɧɧɚɹ ɞɟɣɫɬɜɢɟɦ ɫɢɥ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ,
ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ
ɫɤɨɪɨɫɬɢ
ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ
ɞɜɢɠɟɧɢɹ ɢ ɦɨɠɟɬ ɛɵɬɶ ɜɵɪɚɠɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶɸ
[13]
16a 2 3 (SV ) 5
(3 U ɪ f 2 ) 2
.
E ɜ . ɬ.
ɍɥɶɬɪɚɡɜɭɤɨɜɚɹ ɷɧɟɪɝɢɹ, ɤɨɬɨɪɚɹ ɞɨɲɥɚ ɞɨ
ɩɨɜɟɪɯɧɨɫɬɢ ɫɥɨɹ ɠɢɞɤɨɫɬɢ, ɱɚɫɬɢɱɧɨ ɢɡɥɭɱɚɟɬɫɹ
ɜ ɝɚɡɨɜɭɸ ɫɪɟɞɭ.
ɉɪɢ ɦɚɥɨɣ ɬɨɥɳɢɧɟ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɫɥɨɹ
ɠɢɞɤɨɫɬɢ ɩɪɢɧɹɬɨɟ ɪɚɧɟɟ ɩɪɟɞɩɨɥɨɠɟɧɢɟ ɨ
ɧɨɪɦɚɥɶɧɨɦ ɩɚɞɟɧɢɢ ɩɥɨɫɤɨɣ ɜɨɥɧɵ ɧɚ ɩɥɨɫɤɭɸ
ɝɪɚɧɢɰɭ ɪɚɡɞɟɥɚ ɛɭɞɟɬ ɫɩɪɚɜɟɞɥɢɜɵɦ ɢ ɞɥɹ
ɝɪɚɧɢɰɵ ɪɚɡɞɟɥɚ ɠɢɞɤɨɫɬɶ-ɝɚɡɨɜɚɹ ɫɪɟɞɚ.
Ɍɨɝɞɚ ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɷɧɟɪɝɢɹ, ɢɡɥɭɱɚɟɦɚɹ ɫ
ɩɨɜɟɪɯɧɨɫɬɢ ɠɢɞɤɨɫɬɢ ɜ ɝɚɡɨɜɭɸ ɫɪɟɞɭ,
ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɚɜɢɫɢɦɨɫɬɶɸ
Eɝ.ɫ.
'U ɪ.ɿ ɜɢɩ - ɦɨɥɹɪɧɚɹ ɷɧɟɪɝɢɹ ɢɫɩɚɪɟɧɢɹ
ɱɢɫɬɨɣ ɠɢɞɤɨɫɬɢ ɿ; V p.i - ɟɟ ɦɨɥɹɪɧɵɣ ɨɛɴɟɦ.
ɋ ɭɱɟɬɨɦ ɡɚɜɢɫɢɦɨɫɬɟɣ (16) ɢ (17) ɜɵɪɚɠɟɧɢɟ
Eɤɚɩɥɢ
Eɤɨɝ
(17)
ɝɞɟ a | 0,3 .
ɞɥɹ ɷɧɟɪɝɢɢ
1
§ 'U ɪ.ɿ ɜɢɩ · 2
¨
¸
¨ V ɪ.ɿ ¸ ,
©
¹
9 2 Eɩɨɞɜ Eɨɛɪ Eɤɚɩɥɢ
2 U ɝ cɝ
Eɩɨɞɜ Eɨɛɪ Eɤɚɩɥɢ ,
U ɝ ɫɝ U ɪ ɫ ɪ
ɝɞɟ
S
Q S
h
l ,
Q
– ɩɥɨɳɚɞɶ;
ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ;
– ɫɤɨɪɨɫɬɶ
h – ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ
ɩɨɜɟɪɯɧɨɫɬɹɦɢ; l – ɞɥɢɧɚ.
ɑɬɨ ɤɚɫɚɟɬɫɹ ɷɧɟɪɝɢɢ, ɤɨɬɨɪɚɹ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ
ɧɚɝɪɟɜ
ɠɢɞɤɨɫɬɢ
( Et $ ),ɬɨ
ɩɪɟɧɟɛɪɟɱɶ, ɩɨɫɤɨɥɶɤɭ ɨɧɚ
ɟɸ
ɦɨɠɧɨ
lim ( Et $ )
E $ o0
0.
t
ɗɬɨ ɨɛɴɹɫɧɹɟɬɫɹ ɬɟɦ, ɱɬɨ ɠɢɞɤɨɫɬɶ ɧɚ
ɪɚɫɩɵɥɢɜɚɟɦɨɣ
ɩɨɜɟɪɯɧɨɫɬɢ
ɧɟɩɪɟɪɵɜɧɨ
ɜɨɡɨɛɧɨɜɥɹɟɬɫɹ ɛɥɚɝɨɞɚɪɹ ɩɨɫɬɨɹɧɧɨɣ ɩɨɞɚɱɢ
ɠɢɞɤɨɫɬɢ. ɉɨɷɬɨɦɭ ɫɥɨɣ ɠɢɞɤɨɫɬɢ ɧɟ ɭɫɩɟɜɚɟɬ
ɩɪɨɝɪɟɜɚɬɶɫɹ ɞɨ ɬɚɤɨɣ ɬɟɦɩɟɪɚɬɭɪɵ, ɤɨɬɨɪɚɹ
ɜɥɢɹɥɚ ɛɵ ɧɚ ɩɪɨɰɟɫɫ ɪɚɫɩɵɥɟɧɢɹ.
ɇɚ ɞɢɫɩɟɪɝɢɪɨɜɚɧɢɟ [15], ɬɨ ɟɫɬɶ ɪɚɫɩɵɥɟɧɢɟ
ɠɢɞɤɨɣ ɮɚɡɵ ɧɭɠɧɨ ɩɨɬɪɚɬɢɬɶ ɨɩɪɟɞɟɥɟɧɧɨɟ
ɤɨɥɢɱɟɫɬɜɨ ɷɧɟɪɝɢɢ. ɗɬɚ ɷɧɟɪɝɢɹ ɫɨɫɬɨɢɬ ɢɡ
ɩɨɜɟɪɯɧɨɫɬɧɨɣ ɷɧɟɪɝɢɢ ɦɟɥɤɨɞɢɫɩɟɪɫɧɨɣ ɮɚɡɵ,
ɤɨɬɨɪɚɹ
ɬɨɥɶɤɨ
ɱɬɨ
ɨɛɪɚɡɨɜɚɥɚɫɶ,
ɢ
ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ [9]:
Ⱥɥɢɧɚ Ʌɹɲɨɤ, Ɉɥɟɝ əɯɧɨ, Ⱥɥɟɤɫɚɧɞɪ Ʌɭɝɨɜɫɤɨɣ
Eɞɢɫɩ
Eɩɨɜɟɪ ȿ ɦɟɯɚɧ .
ɉɪɢ ɷɬɨɦ
Eɩɨɜɟɪ
U u AVA u BVB ,
ɝɞɟ U – ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɫɢɫɬɟɦɵ;
ɤɨɧɟɱɧɨɝɨ
ɩɪɨɞɭɤɬɚ
ɠɢɞɤɨɫɬɧɨɝɨ
ɦɟɥɤɨɞɢɫɩɟɪɫɧɨɝɨ ɚɷɪɨɡɨɥɹ. ɗɬɨɬ ɚɧɚɥɢɡ ɩɨɡɜɨɥɢɬ
ɩɪɟɞɥɨɠɢɬɶ ɩɭɬɢ ɩɨɜɵɲɟɧɢɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ
ɬɟɯɧɨɥɨɝɢɢ ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ ɪɚɫɩɵɥɟɧɢɹ ɜ ɬɨɧɤɨɦ
ɫɥɨɟ ɢ ɜɵɹɫɧɢɬɶ ɩɪɟɞɟɥɵ ɞɨɩɭɫɬɢɦɨɝɨ ɢɡɦɟɧɟɧɢɹ
ɪɟɨɥɨɝɢɱɟɫɤɢɯ
ɯɚɪɚɤɬɟɪɢɫɬɢɤ
ɪɚɫɩɵɥɢɜɚɟɦɵɯ
ɠɢɞɤɨɫɬɟɣ.
u A ,u B –
ɅɂɌȿɊȺɌɍɊȺ
ɩɥɨɬɧɨɫɬɢ ɷɧɟɪɝɢɢ ɮɚɡ Ⱥ ɢ ȼ; V A , VB – ɨɛɴɟɦɵ
ɮɚɡ Ⱥ ɢ ȼ.
ȿ ɦɟɯɚɧ
Eɤ
1. Ƚɨɥɶɞɛɟɪɝ Ɂ.Ⱥ. , 1968. Ⱦɚɜɥɟɧɢɟ ɡɜɭɤɚ.
ɑɚɫɬɶ II. - ȼ ɤɧ.: Ɇɨɳɧɵɟ ɭɥɶɬɪɚɡɜɭɤɨɜɵɟ ɩɨɥɹ.Ɇ.: ɇɚɭɤɚ – ɋ.49-87.
2. ɂɫɚɤɨɜɢɱ Ɇ.Ⱥ., 1973. Ɉɛɳɚɹ ɚɤɭɫɬɢɤɚ.
- Ɇ., ɇɚɭɤɚ. – 495 ɫ.
3. Ʌɭɝɨɜɫɶɤɢɣ, Ɉ. Ɏ., Ʌɹɲɨɤ Ⱥ. ȼ.,
ɉɢɠɢɤɨɜ ɘ. Ɉ., 2011. ɋɩɨɫɿɛ ɬɚ ɩɪɢɫɬɪɨʀ ɞɥɹ
ɨɬɪɢɦɚɧɧɹ ɪɿɞɢɧɧɨɝɨ ɚɟɪɨɡɨɥɸ // ȼɿɫɧɢɤ
ɇɚɰɿɨɧɚɥɶɧɨɝɨ ɬɟɯɧɿɱɧɨɝɨ ɭɧɿɜɟɪɫɢɬɟɬɭ ɍɤɪɚʀɧɢ
«Ʉɢʀɜɫɶɤɢɣ ɩɨɥɿɬɟɯɧɿɱɧɢɣ ɿɧɫɬɢɬɭɬ». ɋɟɪɿɹ
ɦɚɲɢɧɨɛɭɞɭɜɚɧɧɹ. – ʋ 61, ɬɨɦ 1 . – ɋ. 107 – 113.
4. Ʌɭɝɨɜɫɤɨɣ, Ⱥ.Ɏ., 2000 ɍɥɶɬɪɚɡɜɭɤɨɜɨɟ
ɪɚɫɩɵɥɟɧɢɟ ɜ ɫɢɫɬɟɦɚɯ ɩɨɞɝɨɬɨɜɤɢ ɬɨɩɥɢɜɧɨɜɨɡɞɭɲɧɨɣ
ɫɦɟɫɢ
//
Ɍɟɯɧɿɤɚ
ɜ
ɫɿɥɶɫɶɤɨɝɨɫɩɨɞɚɪɫɶɤɨɦɭ ɜɢɪɨɛɧɢɰɬɜɿ, ɝɚɥɭɡɟɜɟ
ɦɚɲɢɧɨɛɭɞɭɜɚɧɧɹ, ɚɜɬɨɦɚɬɢɡɚɰɿɹ. Ɂɛ. ɇɚɭɤ. ɉɪ..
Ʉɿɪɨɜɨɝɪɚɞɫɶɤɨɝɨ ɞɟɪɠ. Ɍɟɯɧ.. ɭɧɿ-ɬɭ. – ȼɢɩ. 7. –
ɋ. 30-33.
5. Ʌɭɝɨɜɫɶɤɢɣ, Ɉ.Ɏ., 1999. Ɉɬɪɢɦɚɧɧɹ
ɞɪɿɛɧɨɞɢɫɩɟɪɫɧɨɝɨ
ɚɟɪɨɡɨɥɸ
ɲɥɹɯɨɦ
ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ ɞɢɫɩɟɪɝɭɜɚɧɧɹ // ȼɟɫɬɧ. ɇɚɰ.
ɬɟɯɧ. ɭɧ-ɬɚ ɍɤɪɚɢɧɵ «Ʉɉɂ». Ɇɚɲɢɧɨɫɬɪɨɟɧɢɟ. –
ȼɢɩ. 34. - ɋ. 193– 202.
6. Ʌɭɝɨɜɫɶɤɢɣ, Ⱥ.Ɏ., ɑɭɯɪɚɟɜ ɇ.ȼ., 2007.
ɍɥɶɬɪɚɡɜɭɤɨɜɚɹ
ɤɚɜɬɚɰɢɹ
ɜ
ɫɨɜɪɟɦɟɧɧɵɯ
ɬɟɯɧɨɥɨɝɢɹɯ: ɦɨɧɨɝɪɚɮ. – Ʉ. 2007. – 244 ɫ. – ISBN
966-594-927-6.
7. Ʌɭɝɨɜɫɶɤɢɣ, Ɉ. Ɏ., əɯɧɨ Ɉ. Ɇ. , 2004.
ɍɥɶɬɪɚɡɜɭɤɨɜɟ ɪɨɡɩɢɥɟɧɧɹ ɪɿɞɢɧɢ ɬɚ ɦɨɠɥɢɜɨɫɬɿ
ɣɨɝɨ ɡɚɫɬɨɫɭɜɚɧɧɹ ɜ ɬɟɯɧɨɥɨɝɿɱɧɢɯ ɩɪɨɰɟɫɚɯ //
Ƚɿɪɧɢɱɿ, ɛɭɞɿɜɟɥɶɧɿ, ɞɨɪɨɠɧɿ ɬɚ ɦɟɥɿɨɪɚɬɢɜɧɿ
ɦɚɲɢɧɢ. ȼɫɟɭɤɪɚʀɧɫɶɤɢɣ ɡɛɿɪɧɢɤ ɧɚɭɤɨɜɢɯ ɩɪɚɰɶ.
– 2004. – ȼɢɩ. 64. - ɋ. 49-55.
8. Ʌɹɲɨɤ
Ⱥ.ȼ.
ɍɥɶɬɪɚɡɜɭɤɨɜɟ
ɪɨɡɩɢɥɟɧɧɹ ɪɿɞɢɧɢ ɭ ɦɟɯɚɬɪɨɧɧɢɯ ɫɢɫɬɟɦɚɯ
ɲɬɭɱɧɨɝɨ ɦɿɤɪɨɤɥɿɦɚɬɭ / Ⱥ.ȼ. Ʌɹɲɨɤ, Ɉ.Ɏ.
Ʌɭɝɨɜɫɶɤɢɣ // ȼɫɟɭɤɪɚʀɧɫɶɤɢɣ ɧɚɭɤɨɜɨ-ɬɟɯɧɿɱɧɢɣ
ɠɭɪɧɚɥ «ɉɪɨɦɢɫɥɨɜɚ ɝɿɞɪɚɜɥɿɤɚ ɿ ɩɧɟɜɦɚɬɢɤɚ» –
ʋ4 (34)’2011. – ɋ. 20– 25.
9.
Ɇɨɥɟɤɭɥɹɪɧɚɹ ɮɢɡɢɤɚ. , 1973 ɂɡɞ.
2-ɟ, ɞɨɩ. ɍɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ ɭɧɢɜɟɪɫɢɬɟɬɨɜ. – Ɇ.:
«ȼɵɫɲɚɹ ɲɤɨɥɚ». - ɋ. 322-323.
10. ɇɨɜɢɰɤɢɣ Ȼ.Ƚ., 1983. ɉɪɢɦɟɧɟɧɢɟ
ɚɤɭɫɬɢɱɟɫɤɢɯ
ɤɨɥɟɛɚɧɢɣ
ɜ
ɏɢɦɢɤɨɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɚɯ (ɉɪɨɰɟɫɫɵ ɢ ɚɩɩɚɪɚɬɵ
ɯɢɦɢɱɟɫɤɨɣ ɢ ɧɟɮɬɹɧɨɣ ɬɟɯɧɨɥɨɝɢɢ). – Ɇ.: ɏɢɦɢɹ.
– 192 ɫ.
11. Ɉɫɚɞɱɭɤ
ɉ.,
2010.:
ȼɩɥɢɜ
ɭɥɶɬɪɚɡɜɭɤɨɜɨɝɨ ɩɨɥɹ ɧɚ ɩɪɨɰɟɫ ɨɱɢɳɟɧɧɹ
mQ 2
.
2
Ɍɨ ɟɫɬɶ
Eɞɢɫɩ
U u AV A u BVB mQ 2
.
2
ɉɪɢ ɧɟɡɧɚɱɢɬɟɥɶɧɨɣ ɚɦɩɥɢɬɭɞɟ ɤɨɥɟɛɚɧɢɣ
ɜɢɛɪɢɪɭɸɳɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɞɢɫɩɟɪɝɚɬɨɪɚ ɫɥɨɣ
ɠɢɞɤɨɫɬɢ ɞɜɢɠɟɬɫɹ ɤɚɤ ɨɞɧɨ ɰɟɥɨɟ ɫ
ɜɢɛɪɢɪɭɸɳɟɣ ɩɨɜɟɪɯɧɨɫɬɶɸ. Ɉɞɧɚɤɨ ɩɪɢ
ɭɜɟɥɢɱɟɧɢɢ ɚɦɩɥɢɬɭɞɵ ɤɨɥɟɛɚɧɢɣ ɜɫɥɟɞɫɬɜɢɟ
ɢɧɟɪɰɢɨɧɧɵɯ
ɫɜɨɣɫɬɜ
ɠɢɞɤɨɫɬɢ
ɧɚ
ɟɟ
ɩɨɜɟɪɯɧɨɫɬɢ ɨɛɪɚɡɭɸɬɫɹ ɫɬɨɹɱɢɟ ɤɚɩɢɥɥɹɪɧɵɟ
ɜɨɥɧɵ (ɪɢɫ. 1).
ȼɵɜɟɞɟɧɧɚɹ ɢɡ ɫɨɫɬɨɹɧɢɹ ɪɚɜɧɨɜɟɫɢɹ, ɠɢɞɤɨɫɬɶ
ɩɪɢɨɛɪɟɬɚɟɬ ɜ ɩɨɥɟ ɬɹɝɨɬɟɧɢɹ ɢ ɜ ɩɨɥɟ ɫɢɥɵ
ɩɨɜɟɪɯɧɨɫɬɧɨɝɨ
ɧɚɬɹɠɟɧɢɹ
ɧɟɤɨɬɨɪɭɸ
ɩɨɬɟɧɰɢɚɥɶɧɭɸ ɷɧɟɪɝɢɸ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ
ɭɱɢɬɵɜɚɟɬɫɹ ɫɜɨɛɨɞɧɚɹ ɷɧɟɪɝɢɹ ɜ ɬɨɦ ɫɦɵɫɥɟ,
ɤɚɤ ɨɧɚ ɩɨɧɢɦɚɟɬɫɹ ɜ ɬɟɪɦɨɞɢɧɚɦɢɤɟ, ɬɨ ɟɫɬɶ
ɫɜɨɛɨɞɧɚɹ ɷɧɟɪɝɢɹ Ƚɟɥɶɦɝɨɥɶɰɚ. Ⱦɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ
ɷɬɚ ɷɧɟɪɝɢɹ ɧɟ ɩɟɪɟɣɞɟɬ ɜ ɬɟɩɥɨ, ɠɢɞɤɨɫɬɶ ɧɟ
ɦɨɠɟɬ ɭɫɩɨɤɨɢɬɶɫɹ. ȼ ɧɟɣ ɜɨɡɛɭɠɞɚɟɬɫɹ
ɤɨɥɟɛɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ, ɤɨɬɨɪɨɟ ɫɩɨɫɨɛɫɬɜɭɟɬ
ɜɨɡɧɢɤɧɨɜɟɧɢɸ
ɤɚɩɢɥɥɹɪɧɨ-ɝɪɚɜɢɬɚɰɢɨɧɧɵɯ
ɜɨɥɧ [12, 14].
Eɤ.ɜ
Eɫɜɨɛ
U TSɟɧɬ
U – ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɫɢɫɬɟɦɵ, T –
ɬɟɦɩɟɪɚɬɭɪɚ; S ɟɧɬ – ɷɧɬɪɨɩɢɹ.
ɝɞɟ
ȼɕȼɈȾɕ
ɉɨɥɭɱɟɧɧɵɣ ɛɚɥɚɧɫ ɷɧɟɪɝɢɣ ɩɨɡɜɨɥɹɟɬ ɨɰɟɧɢɬɶ
ɡɧɚɱɢɦɨɫɬɶ
ɜɥɢɹɧɢɹ
ɨɬɞɟɥɶɧɵɯ
ɩɚɪɚɦɟɬɪɨɜ
ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɪɨɰɟɫɫɚ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɗɇȿɊȽȿɌɂɑȿɋɄȺə ɆɈȾȿɅɖ ɉɊɈɐȿɋɋȺ ɍɅɖɌɊȺɁȼɍɄɈȼɈȽɈ ɊȺɋɉɕɅȿɇɂə
ɫɨɧɹɲɧɢɤɨɜɨʀ ɨɥɿʀ.// MOTROL. - ʋ12 ɋ, ɋ. 309 –
314.
12.
Ɋɭɤɨɜɨɞɫɬɜɨ
ɤ
ɥɚɛɨɪɚɬɨɪɧɵɦ
ɡɚɧɹɬɢɹɦ ɩɨ ɮɢɡɢɤɟ. 1973. ɉɨɞ ɪɟɞ. Ʌ.Ʌ. Ƚɨɥɶɞɢɧɚ,
ɢɡɞ. 2-ɟ, Ƚɥɚɜɧɚɹ ɪɟɞɚɤɰɢɹ ɮɢɡɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ
ɥɢɬɟɪɚɬɭɪɵ ɢɡɞ-ɜɚ «ɇɚɭɤɚ», – ɋ. 209-213
13.
ɋɚɜɟɥɶɟɜ ɂ.ȼ., 1970. Ʉɭɪɫ ɨɛɳɟɣ
ɮɢɡɢɤɢ.
Ɇɟɯɚɧɢɤɚ,
ɤɨɥɟɛɚɧɢɹ
ɢ
ɜɨɥɧɵ,
ɦɨɥɟɤɭɥɹɪɧɚɹ ɮɢɡɢɤɚ – Ɇ.: ɂɡɞ. «ɇɚɭɤɚ», Ƚɥɚɜɧɚɹ
ɪɟɞ. ɮɢɡɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɥɢɬ-ɵ. Ɍɨɦ 1. – 512ɫ.
14. ɋɢɜɭɯɢɧ Ⱦ.ȼ., 2005.
Ɉɛɳɢɣ ɤɭɪɫ
ɮɢɡɢɤɢ: ɍɱɟɛ. ɩɨɫɨɛɢɟ: Ⱦɥɹ ɜɭɡɨɜ. ȼ 5 ɬ. Ɍ.II.
Ɍɟɪɦɨɞɢɧɚɦɢɤɚ ɢ ɦɨɥɟɤɭɥɹɪɧɚɹ ɮɢɡɢɤɚ. – 5-ɟ ɢɡɞ.,
ɢɫɩɪ. – Ɇ.: ɎɂɁɆȺɌɅɂɌ. – 544 ɫ. ISBN 5-92210601-5.
15. ɍɦɢɧɫɶɤɢɣ ɋ., əɤɨɜɟɧɤɨ Ⱥ. 2012.:
Ƚɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɟ ɞɢɫɩɟɪɝɢɪɨɜɚɧɢɟ ɞɢɡɟɥɶɧɵɯ
ɬɨɩɥɢɜ ɞɥɹ ɫɧɢɠɟɧɢɹ ɧɚɝɚɪɨɨɛɪɚɡɨɜɚɧɢɹ.//
MOTROL. - ʋ 14-1, ɋ. 34 – 37.
16.
Ɏɢɡɢɱɟɫɤɚɹ ɯɢɦɢɹ. Ɍɟɨɪɟɬɢɱɟɫɤɨɟ
ɢ ɩɪɢɤɬɢɱɟɫɤɨɟ ɪɭɤɨɜɨɞɫɬɜɨ. ɍɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ
ɜɭɡɨɜ. 1987. ɉɨɞ ɪɟɞɚɤɰɢɟɣ ɚɤɚɞɟɦɢɤɚ Ȼ.ɉ.
ɇɢɤɨɥɶɫɶɤɨɝɨ. 2-ɟ ɭɡɞ., ɩɟɪɟɪɚɛ. ɢ ɞɨɩ. – Ʌ.:
ɏɢɦɢɹ, - ɋ. 249-250.
17.
ɏɦɟɥɟɜ ȼ .ɇ., ɒɚɥɭɧɨɜ Ⱥ. ȼ.,
ɒɚɥɭɧɨɜɚ Ⱥ. ȼ., 2010. ɍɥɶɬɪɚɡɜɭɤɨɜɨɟ ɪɚɫɩɵɥɟɧɢɟ
ɠɢɞɤɨɫɬɟɣ: ɦɨɧɨɝɪɚɮɿɹ – Ȼɢɣɫɤ: ɂɡɞ-ɜɨ Ⱥɥɬ. ɝɨɫ.
ɬɟɯɧ. ɭɧ-ɬɚ. – 250 ɫ.
18.
ɗɤɧɚɞɢɨɫɹɧɰ
Ɉ.Ʉ.,
1970.
ɉɨɥɭɱɟɧɢɟ ɚɷɪɨɡɨɥɟɣ. - ȼ ɤɧ.: Ɏɢɡɢɱɟɫɤɢɟ ɨɫɧɨɜɵ
ɭɥɶɬɪɚɡɜɭɤɨɜɨɣ ɬɟɯɧɨɥɨɝɢɢ.
ɉɨɞ ɪɟɞ. Ʌ.Ⱦ.
Ɋɨɡɟɧɛɟɪɝɚ. - Ɇ.: ɇɚɭɤɚ. – ɋ. 339-392.
19.
Bisa K., Dirnagl K., Esche R. Siemens
Z.,
1954. Zerstaubung von Flussigkeiton mit
Ultraschall. – 28, 8, 314.
20.
Peskin R.L., Raco R.J., 1963.
Ultrasonic Atomization of Liquids. – JASA. – 35. - N
9. - 1378.
21.
Shushlyakov A., Ovcharenko V.,
Shushlyakov D., Krivonosov G., 2009.: Energy and
environmental efficiency promotion of thermal power
generators// MOTROL. - ʋ11A, ɋ. 54 – 59.
ENERGY MODEL PROCESS OF ULTRASOUND
SPRAYING IN A THIN LAYER
Summary. The offered chart of charges of energy is
during realization of process of ultrasonic spraying in a
thin. Well-grounded and described energies which
acting on thin layer of liquid at ultrasonic spraying, and
extended described components of existing energy.
Analytical expressions are resulted for the involved
energies. The presented balance of energies in the
process of ultrasonic spraying.
Key words: ultrasonic spraying, energy model, energy, thin
layer, dispergator
