18 P 05 Aerosol as system with hierarchical structure

J. Aerosol ~ i . , Vol. 24, Su~I. 1, ~ . S129-S1~, 1~3 ~ n ~ in G r i t Britain.

~21-85~/93 $6.~ + 0.~ Pergamon Press Ltd

18 P 05

AEROSOLAS SYSTEM WITH HIERARCHICAL sTRUCTuRE V. Ryazanov

I n s t i t u t e for Nuclear Research, pr. Nauki,47,252028,Kiev,Ukraine

KEYWORDS hierarchical structure, aerosol dynamics, oontroled process, generating function, thermodynamical forces, currents.

Aerosol clusters may increase on account of coagulation, sources phase transitions and divide into pa~ts, too. We will describe such aerosol system as complex formation out particles-monomers (molecules), which move inside of aerosol clusters on the whole but they may be in free state in monomers form also. Phase merging algorithms of random evolutions (Korolyuk, Swishchuk, 1992) is applicable for description of such molecul cluster dynamics. We consider aerosol volume element as system and apply nonequ iI ibr ium stochast ic thermodynamics torte iat ions (Ryazanov,lggS). We describe the molecul entrance in system by subordinate process (Feller, lg71) A(n~(t)), where A is entranced molecular current distributed in clusters n ~ (t), n~(t) is controled process (Feller, lg71). While this

('S)

is generating functional where E ( ' " } is averaging, F n (or generating funct ion in homogeneous case) for clusters number in aerosol volume element, ~ ( S ) : 7fe-s'zf(x}d26 is Laplace transform of density distribution function b(x) of a value jumps of molecular current entranced in system in k th system part (in k th cluster), m K is avereQe time of" molecul stay in k th cluster. The dependence b(x) in (I) on thermodynamical forces is expressed in form AS 24, Suppl. I--K

S129

SI30

\,' R : :ZANOV

Output f u n c t i o n

is w r i t t e n as f u n c t i o n of" c l u s t e r s number ~(~e#}.

K i n e t i c p o t e n t i a l f o r moleculs number in form of complex f u n c t i o n

system is

written

in

¢(-s,m=-&F.[ e ~" e'v~(s'] , &~l~(e-5 Zone,) ~ where~[(~ -5) is generating function for the number of moleouls in one aerosol cluster. Averaging (3) by distribution of" cluster number with acting thermodynamioal forces we have (4)

-- i

cm

FCi

in approximation mK , ~YK , g~, dependence may=~beaccounted) t h a t

);

0

not depend on n

~---

~c-s,-~; ~) ol~e.s,n~_,,cm ~

(these

~~÷(

~

(e"

~

We have from (5) f o r c u r r e n t s values in aerosol system

(6)

where ~ % is avera~[e number,of moleculs in k th cluster, 9C~(~)= =~ ~ 8-X~/~W~T~'~~The approximation may be used of type where

°

a

~

(e -~ ~ =

a

m ~ en W~K(s

is p r o p o r t i o n a l i t y c o e f f i c i e n t . In s t a t i o n a r y c a s e [<('~[,-~/'/ ~)=0 .The connection between thermodynamioal foroes~

and If

in stationary regimes is obtained from this.

REFERENCES

Feller, W. (1971),

An I n t r o d u c t i o n t o P r o b a b i l i t y Theory and i t s A p p l i c a t i o n s , Wiley, New York.

Swishohuk (1992), Semi-Mapkov random e v o l u t i o n s , Naukova dumka, Kiev. Kh/azanov V.V. ( 1993), W~rainski i f'izioheski i zhurnal, V. 38, p, 617. Korolyuk,V.S., A.V.