???????????? ?????. ??? ????? ???? ?????????? ????? ??? ????? ??????????? ????????? ???????? ??? ??????? ? ???????????? ????????. ?????????? ???????? ? ????????? ?????????. ??????????? ??????? ? ???????????? ????????. ?????????? ???????? ? ????????? ?????????. ??????????? ????????????? ????? ????????? ???????? ?????? ??? ????????? ??????????????? ???????? ?????????? ???? ? ?????? ????????. ??? ????????????? ??????? ???? ???? ???????? ?????? ? ???????????? ?????? ?????? ??????????? ????????? ????????????? [14]. ?.Ð?"?????? ?????? d ? ??? ?? ????????? ? ????????? ??????? ?? ????????????? ?????? ? ????????? â??": d ? << â??". ??? ????? ????????????? ?????? ??????? ????????? ????????, ????????? ? ???????? ???????? ?????. ??????????? ??????? ????????????? ??????? ????? ???????????? ?.?. ???????????????? (d ? <1 ???); ??????????????? (1< d ? <20 ???) ? ??????????????? (20< d ? <200 ???). ?. ??????? ????? ????? ??????? ? ???????????, ? ? ?????? ???????? ?????????? ?? ????? ???????? ??????????? ?????. ???????????????? ?????? ??????????????? ????????????. # ?. ????? ????? ??????? ? = + y v v (6) , 6 . 11 , ò ? ? R y y v v ? < = + +(7) ????? ?????????????? (3) ???????? ????????? ( ) , / ln 1 1 1 * R R R u ? ? ? + = (8) ??? R 1 = * u ? 1 /? -???????????? ??????? ??????? ???????, ? ?????? ???????? R 1 = 11.6; ? = 0.4 - ????????? ??????????????. ???????? ???????? ????????? (5) ? (8). Ð?"?? ????? ?? ?????? ????????????????? ???????? ??????? ????? ????? ?????????????? ???????? ???????? ? ??????????? [7,10] (9) ??? ?? ???????-????????? n = 0,66. ??????, ??? ????????, ??? ???????? ? ????? ???????????????? ??????????? n = 0,6-0,57. ?? ????????? (5), (8) ? * u ???????????? ???????? ? ?????? ? ????????, ñ / ì [13]. Ð?"?? ??????? ???????? ????? C f?? = ?/4, ??? ???????????? ?????? ? ??????? ?????????? ??????; ?=0.316/Re ? 0.25 ; Re ? =U ?? d ? /? (??? ?????????????? ?????? d=d ? ); ý d -????????????? ??????? ???????, ?; ? = ñâ v ñâ ; / 4 ? ? à d ý ???????? ????????? ?????, 3 3 ì / ì ; v à -???????? ??????????? ???????,= ? ?? /? ? . ?????? ?=0.25d ? ? ???????? R ? . 25 . 0 * v u d R ý = ?(14) ??????????? ???? ????????? ??? ????????????? ???????? ???????? ??????????? ??? ???????????? ?????????? ???? ??? ???????????? ????, ????? ????????? ??? ??????????? ?????????? (????????, ??? ??????????? ????????). # III. ??????????? ???????? ?????? Ð?"???????????????? ?????????????? ????????? ?????? ? ???????????? ????? ?????????? ??????? ??????? ?????????? ? ??????????????, ??? ? ??????????. ??????? ??????????, ??? ?????? ?????????? ??????? ??????? ? ????????? (????? 3-5 ??, ? ??????????? ?? ????????????????? ??????? ????? ? ?????????? ????????????????? ???) ?? ????????? ? ???????????? ?????????? ?????. Ð?"?? ????? ?????? ?????? ??? ????????????? ????????????????? ????????? ? ??????????? ???????? ???????????? ????????????? ???????? ?????? ?????????? ?????????. ? ???????????? ? ??????? ???????????? ???????? ????? ???????????????? ??????? ?? ??????? ?? ????????? ??????? ????????????? ? ? ? ? , ??? ? ???????? ??????? ???????????? ?????????????? ????????? ??????????? ??????, ? -1 , ? ?????? ??????????, ?. ?? ????????????????? ?????? ??? ???????? ? ? ? ? < 0.01, ??????? ????????? ?????? ????????????? ??????????? ????? ????????? 100% (µ 2 p =1), µ 2 p = (1-? E ? p ) -1 [14]. ??????? ??? ??????? ????????? ??? ?????? ??????????? ????????? ?????????? ????????????? ??????????? ????? ????? ???????? ???????: . 01 . 0 9 ae 2 < ? = µ ? ? ? ? f d ÷ p E (15) ?????? ???????? [1] ????????? ??? ?????? ???????? ?????? ? ??????, ??? ?? ????????? ? E ? u * /(0.1R) ? ? ? = ?|?Î?"??|?d ? 2 /(18µ ? ), ?|?Î?"??|? ? 0: , 134 . 0 3 . 0 * ae ae u R f d ÷ ? µ ? ? µ ? = ? < (16) ??? ? ? = 2?f -??????? ??????? ??????????? ?????????, ? -1 ; f -??????? ???????????? ????????? ?????, ? -1 ; R -?????? ??????, ? (??? ??????? R=d ? /2,u R d u R ÷ ? µ ? µ ? < < ? ) ????? ?????????? ?? ????????? [14] . 1 ò p ÷ Å v D ? ? + = (19) ??????????? ???????? ???????? ?????? ? ? (???????????? ????????) ?????? ????? ?????????????? ????????? (3) ? ???????? ? ? = ? / (1+ ? E ? p ). ??????????? ???????? ?????? ?? ???????????, ?.?. ?? ??????? ?? ??????? ? ???????????? ?????? ????? ?????????????. ??????? ( ) ( ) . / ln 1 1 1 1 * ? ? ? ? ? ? + + = R R R u p E ÷ ? ? ? ? ? (20) ? ?????????????? ????????? ??????????? ??? ?????????? ?????????? ??????, ??????? ????????????? ?????????????? ??????, ????????????? ????????????? ???????? ?????????? ?????? ? ?????? ?????? ??? ? ??????????? ????????? ??????? ????? ???. ????????????? ???????? ????? ?????????? ? ?????? ??????? ?? ????? ???????????? ? ???? [6,7]. ???????? R 1 ??? ??????? (23) ???????? ? ???? [6]. ae 1 exp , ÷ F V ? ? ? ? = ? ? ? ? ? ?( ( ) 2 1 1 * 1 ? ? ? ? ? ? ? = ? R arctg u u R ,(25) ? ??? ??????? (24) ( ) 2 / 3 1 2 1 * 1 3 6 ? ? ? ? ? ? + + ? = ? ? k k u u R , (26) ??? ? 1 = 3 ln ( ) ???????? ? ? ??????, ????????? ??????? ???????? ???????? ?????????? ???????, ?????????? ????? ??????? ???????? ? ?????? [2,6,11]. 1 ) 1 ( 1 2 + ? + Â Â Â ; ? 2 = 6 arctg 3 ) 2 ( Â Â ? ; ? = R 1 -0,3332 / 1 ae ae 2 / 1 ae ae ò 4 4 ? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? = H PW ñð ? ? ? ? ? ? ? ? , (30) ??? ???????? ???????? ?????????? ???????, ??/? 3 ; Î?"P??????? ????????, ??;W ????????? ???????? ???????? ? ??????, ?/?; H????? ??????, ?. ????????? Î?" P ?? ????????? Ð?"????-???????? ?? (30) ???????. 2 / 1 3 ae ò 2 4 ? ? ? ? ? ? ? ? = d W ñð ? ? ? ? , (312 0 ? u u u k + = , (32) ??? u k???????? ??????????????? ????????, ?/?; u ???????? ????????, ????????? ????????????? ??????????? ?????, ?/?. ???????? u ? ??????????????? ??? ???????? ????????? ??????? ????????????? ??????????? ??????? ???????? ???????, ?????????? ????? ???????? ?????????? ??????? ? ??????. ( ) ???????????? ????????? ????????????? ??????????? (? 2 ????) ???????????, ???? ? ????? ????????? ?????? ???????????? ???????, ???????? «???????» [4]. 3 / 1 3 3 / 1 2 ? ? ? ? ? ? ? ? = ? d W d d u ñð k k ? ? ?( ??????? ??????????? ?????????? ?? ??????????? ???????????? ?????????? ????????? ????????? ?? ????????? (Re ? >50) [11]. ( ) ( ) 5 , 0 5 , 1 2 ae ò 2 / Re / 4 ? ? ? ? ý ý d = , (34) ??? Re ? = W ?? d ? / ?????? ?????????? ??? ???????; d ? = 4? ?? /? ?????????????? ??????? ???????, ?; ? ?????????? ????????? ????? ???????, ? 3 /? 3 ; ? ????????? ???????????, ? 2 /? 3 ; ???????????? ??????????????? ????????????? ??????????? ???? [4]. ??? ??????? ???????????? ??????????? ?? ?????? ? ???????????? ????????? ? ?????? ? ????????? ???????? ??????????????, ??? ?????????? ???? ?? ????????? ??????????? ???????. ???? ?? ?????????? ???? ?????? ????????? ??????????? ????????? ???????, ?? ?????????? ????????? ?????????????? ??????????? ?? ?????? ???????? ? ?????????, ??? ??????? ????????????? ??????????. # V. ??????????? ??? ????????????? Ð?"???? ?????????? ?????????? ???? ?????????????? ????????? ??? ??????? ?????????? ?? ?????? ? ??????? ?????? ? ???????? ? ???????? ??? ???????????? ??????. ??????????? ??????? ???????? ?????????????? ???????? ?????????? ?????? ? ?????????????? ????? ???????? ??????? ???????, ??????? ???? ?? ????? ??????? ?????????????? ???????. ? ?????? [15] ???????????? ??????? ???????? ???????? ?????? ???????????? ??? ?????????????? ????????? (?????????? (32)): 2 îáò 2 2 0 u u u u k + + = ? ,(35) ??? u ??????????? ???????????????: ì ê ì d d u u ae ê îáò 6 ? ? ? ? ? = , (36)??? u ? -???????? ???????? ????? ??????? ???????, ?/?: u ? = ? n d ? , n -??????? ????????, ? -1 ; d ? - ??????? ???????, ?; ? -??????????? ????????????? ??? ???????? ?????, ? k = f(Re ? ). ??????? ???????????? ???????? ?? ????????? ??????????? ????? ?????? ?? ????????? [6,7] ?????? ?????? ??????? ??????????? ? ???????? ???? ??? ??????????? ??????? ??????. ?? ??????? 2 ???????? ?????????? ????????? ? ????????????????? ?????? [15] ??? ??????????? ?????????????? ????? ? ???????? ??????? ???????. Ð?"?????? ?????? ?????????????? ????? -30, 8?10 -6 ; 593?10 -6 , ?. 3![??? ?, ? ? (y)???????????? ?????????????? ???????????? ? ???????????? ????????, ? 2 /?; U ????????, ì/ñ . ?? ??????????? ??????, ?.?. ??? ? = 0, ???? ?? ????? ????? ???????? ? ????[12]: ???????? ????????, ?/?; ? ?U ???????? ???? ????????, ?/?.?????? ????????????? ????? ???????? ? * = ?(y)/? ?? . ????? ??????? ??????????????? ?????? ? ????????? (1), ???????? ??????????, ? ????????? ???????? ?? ??????? ???????????? ????, ???????[7,12]:????????? (3)???????? ?????????? ????? ? ????????? ?????????? ??????????? ?????????????? ?? ?????? ????????????? ???????????? ? ? ???????????? ???????? ? ? (y), ? ????? ?????????????? ???????????? ?????????? ? * (?????????????? ?????? ????????) ? ?????????? ????. ? ????? ???? ??????????? ???????? ???????? ????? ???????? ????? ?????????????? ????????? (3) ? ?????????? ????????? ????????????? ????????????? ?????? ? ? (y), ????????? ???????????????? ??????. ? ?????? ?????? ? ??????, ?????????????? Ð?"???????? ? ???????? ??????????????, ??? ????????? ???????????? ???????? ? ?????? ??????? ??????????????? D ? ~ y 4 . ?? ????????? ????? ???????????? ??????? ? ? (y) ? ?????(4) ??? y + = u * y/????????????? ??????????; ?=0.4 ?????????;](image-2.png "3 ?") ![??? C f????????????? ?????? ??? ???????? ?????? ?? ????????? ? U ????? ??????? ????????;](image-3.png "") ![??? ???????????? ??????????? ?? ????? (? ?????) ? ???????? ????, ?/?;? 1??????? ??????? ??????? ?? ?????, ?; y?????????? ?????????? ? ??????????? ????, ?.????? ?????????????? (22) ? ???????? ????????????? ?????? ?????? D ? = u * ? 1 (y/? 1 ) 2 , ??? ?????? ? ????????? ???????????? ??????? ??? (? * ? 1), ??????????? ??????????? ??????? ???[6]. ? ? * > 1, ? ????? ??????? ?????? ??? D ? = u * ? 1 (y/? 1 ) 3 ?????[6].](image-4.png "") ![??? R 1 = u * ? 1 /????????????? ??????? ??????? ???????; * u???????????? ???????? ?? ????????? ??????????? ?????, ?/?; ? ??????????? ?????????????? ???????? ???????? ????, ? 2 /?; z = (R 1 Sc) -0,333 ; Sc = ?/D????? ??????; ? * = ? d /? c????????? ????????????? ???????????? ???????? ?????????? ? ???????? ???.](image-5.png "") ??????????????????????????????????????? ? ? ? ? > 100 ??????? ????????? ???????????? ? ???? (µ 2 p ? 0). ?? ???????? ? (15) ? (16)???????? ????????? ??? ??????, ?? ??????????????????????? ????????????E?p=?9 ae ? µ ? d ÷ 2f>, 100(17)?????? ?????d ÷>30?ae ? ? µf=13.4* ae u µ R ? ?.(18)?? ????????? (16) ? (18) ???????, ??? ???????,I?????????? ? ???????????? ??????, ??? ?????? ??????? ?? ??????????? ?????, ??? ?????? ?? ?????? ? ???????? ?????????? ???, ??? ?????? ???????? ????? ? ???? ??????? ?? ?????????. ??????????? ???????????? ???????? ?????? * * (??? ??????? ae ae 4 . 13 134 . 0( ) C Volume XIV Issue II VersionGlobal Journal of Researches in Engineering?); © 2014 Global Journals Inc. (US) ?????? ?????????????? ???????????????????????????//????????????? ????????????????? ??????????????? ????????????, ?????? ?????????????? ???????????????????????????????? ?????????. -?.: ???????????,2011. -?.336.11. ??????? ?.?., ??????? ?.?. ?????????????????????????????????????????????????????????? ?????????. © 2014 Global Journals Inc. (US) * Integrated treatment of sewer systems at industrial enterprises using the jet flotation method DVAlekseev NANikolaev ALaptev 2005 Kazan State Technological University press 156 Kazan * Mixing in liquid media: physical fundamentals and engineering calculation methods LNBraginskii VIBegachev VMBarabash 1984 Khimiya Leningrad * Investigation of diffusion boundary layers by the holographic interferometry method. Doklady AN SSSR SGDyakonov NBSosnovskaya LPKlinova 1982 264 * Contact packings of industrial heat and mass transfer apparatuses. Kazan: Otechestvo AMKagan AGLaptev ASPushnov MIFarakhov 2013 454 * Mathematical modeling of the process of dissolution of solid particles in apparatuses containing mixing devices LPKlinova NBSosnovskaya SGDyakonov Massoobmennye protsessy i apparaty khimicheskoi tekhnologii: mezhvuz. sb. nauch. tr. Kazan, KSTU 1987 * Transport models and liquid extraction efficiency AGLaptev 2005 229 Kazan Kazan State Power Engineering University press * Models of boundary layer and calculations of heat and mass transfer processes AGLaptev 2007 Kazan University press 500 Kazan * Mathematical modeling of mass transfer during mixing of two-phase media AGLaptev VIElizarov SDyakonov Zhurnal prikladnoi khimii 3 1993 * A model of turbulence in the liquid phase of a bubble layer // Mezhdunarodnyi zhurnal prikladnykh i fundamental'nykh issledovanii AGLaptev EALapteva 2013 * Methods of intensification and modeling of heat and mass transfer processes AGLaptev NANikolaev MMBasharov 2011 288 Moscow: Teplotekhnik * Mathematical models and calculation of heat and mass transfer characteristics of apparatuses. 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