Transcript esercizi diffusione con reazione risolti

 ! + !"" !+ ( !$ !"" # # !""-
3" ! ! # #) $$ & →
→ "
$ ! !"" " =54.; !.5- !#"' #$!=4-70" +!##!$"'#(=54.960!-+
& !"& + " & + + # !"& =9 !# !-
"&& " & # !"& " !# !!!!! #-
#&
" ""# #! &. $#" " ! #, $ !" # !! % $ " !#
!# ! ""$ !4".-
d 2 cA
D 2 − kcA = 0
(6.1)
dx
2:.63$ !"!#"&" -
cA = s per x = 0
cA → 0 per x → ∞
!$ 2:.63!$! 4#& "" !"-
Dλ 2 − k = 0
# !-
k
λ=±
D
!#&(##-
 k 

k 
cA = C1 exp 
x  + C2 exp  −
x
D 
 D 

!&" "
C1 = 0
(6.2)
(6.3)
(6.4)
(6.5)
(6.6)
2:.73!$-
C2 = s
!#&2:.63(#-

k 
cA = s exp  −
x
D 

" -

k 
cAH = s exp  −
H
D 

!!# !-
 10 −7 

k 
cAH = s exp  −
H  = 0.3⋅ exp  −
⋅ 5  = 0.182 moli/lt
−5
D 

 10

(6.7)
(6.8)
(6.9)
(6.10)
""" $ !#!" !"#!
""$ =7%54.7 60!- # !!" !" + !!! δ =6 + " &$+4=5-70-!# !" !" + +
(""+!#!!$$ &!# $ !→
+ !"" " !# =54.7 0!- &
!"& !,
." &!#!# ""++δ -
.#!! ++" !" #&
4" !" ! 4( & , # " &!"& (-
d 2 cA
=0
(7.1)
dx 2
2;.63$""&" .#!" ("
" &,!##!!" #!!#!$ $"!" $# #""' " #"'!# "-
x = 0 → cA = cA,0
x = δ → −D
dcA
= kcA
dx
(7.2)
La soluzione della (7.2) è:
cA ( x ) = Ax + B
2;.73! $!#"-
cA = cA,0
!!$-
−DA = k ( Aδ + cA,0 )
(7.3)
(7.4)
(7.5)
#-
A=−
cA,0
D
+δ
k
(7.6)
"$ " &("-


x 

cA = cA,0  1−
(7.7)

D
+
δ


k
)!" &!#""$-


δ 

cA,δ = cA,0  1−
(7.8)

D
+
δ


k
#!!"" $ !!" $-
DcA,0
dc
nA = −D A =
(7.9)
D
dx
+δ
k
!!# !-






δ 
2

cA,δ = cA,0  1−
 = 0.78 moli/l (7.10)
 = 1.3  1− 3⋅10 −3
D
+
δ



+ 2


k
10 −3
DcA,0 3⋅10 −3 ⋅1.3⋅10 −3
nA =
=
= 7.8 ⋅10 −7 moli/cm 2s (7.11)
D
3+ 2
+δ
k
$#=54(""# ""$#" =4-50
""!" & c0A = 0.3moli/L -!
! !!" "&&" !!! 6δδ =:44µ#$$
&"" !&+ "" &&"#
!"""=54.6!.5-!" "&&" ## &ε=54<
$#!!$ "( "" &&"#"
#!""$/" "&&" D =54.960!-
$ ! "" &!"& -
$" !# !-
(8.1)
Qc0A − Qc A − η kc AεV = 0
2<.63" &(! "" ""$"' & #"'$#""&&" η kc A "" $#""$
"&&" εV ." #" " τ = V / Q = 100 2<.63
!" &#!"-
c0A
cA =
(8.2)
(1+ ηkετ )
# $ !-
x=
η k ετ
(1+ ηkετ )
(8.3)
$ !!! "" &.
#!"!#-
0.01⋅ ( 0.03)
kδ 2
Λ=
=
= 0.95
Deff
10−5
2
(8.4)
"" &#&# !" 2# tanh Λ
& η =
$ η = 0.79 .! "#""$ # 2<.83
Λ
-
η k ετ
0.79 ⋅0.01⋅0.1⋅100
=
= 0.073 = 7.3% (8.5)
x=
(1+ ηkετ ) (1+ 0.79 ⋅0.01⋅0.1⋅100)