摩擦係数 × 速度<latexit sha1_base64="cYR9oZVwxvn80AMMYa0ldmakXEs=">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</latexit>

ξvf

摩擦力力f
<latexit sha1_base64="ww9ZmKLmZ9ixxBTgLfXY/XSLPBg=">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</latexit>

dv⇠v = mdt


fv=1⇠<latexit sha1_base64="w3n5GvT7RmEMdcGJ6saIShKxIgs=">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</latexit>

t=1

f = ⇠v1exp✓流速fc
J ⌘ vc, J =⇠<latexit sha1_base64="QCSe/OsvxbqI4mfiG7QCsAH/Cs0=">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</latexit>dµd ln c
RT dc
F == RT=dxdxc dx
Ff⌘
NAfc
RT dc
dc
J=== D⇠NA ⇠ dx 拡散係数 dx<latexit sha1_base64="i6y2zA/BfJ8ojCCbQCG3LpemA0o=">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</latexit>

⇠tm◆

拡散c

J(x, t) =xc(x, t)
Dx

Fickの第一法則

J : 流速(flux) [mol m-2 s-1]
D : 拡散定数(diffusion constant) [mol m-2 s-1 mol-1 m3 m]= [ m2 s-1]

拡散c

J(x, t) =xc(x, t)
Dx

Fickの第一法則

J : 流速(flux) [mol m-2 s-1]
D : 拡散定数(diffusion constant) [mol m-2 s-1 mol-1 m3 m]= [ m2 s-1]

拡散c

J(x, t) =xc(x, t)
Dx

Fickの第一法則

J : 流速(flux) [mol m-2 s-1]
D : 拡散定数(diffusion constant) [mol m-2 s-1 mol-1 m3 m]= [ m2 s-1]

拡散c

J(x, t) =xc(x, t)
Dx

Fickの第一法則

J : 流速(flux) [mol m-2 s-1]
D : 拡散定数(diffusion constant) [mol m-2 s-1 mol-1 m3 m]= [ m2 s-1]

拡散c

J(x, t) =xc(x, t)
Dx

Fickの第一法則

J : 流速(flux) [mol m-2 s-1]
D : 拡散定数(diffusion constant) [mol m-2 s-1 mol-1 m3 m]= [ m2 s-1]

J(x + dx, t)J(x, t)c(x, t)(Sdx) = [J(x, t)⇧ ⌅⇤ ⌃t ⇧ ⌅⇤ ⌃=dV

flux inJ(x + dx, t)]S⇧⌅⇤⌃
flux outJ
J(x + dx, t) = J(x, t) +dx
xc(x, t)J(x, t) = Dx ⇥2c(x, t)
1
Jc=dx = D 2tdxxx2c(x, t)c(x, t)=Dtx2

J(x + dx, t)J(x, t)c(x, t)(Sdx) = [J(x, t)⇧ ⌅⇤ ⌃t ⇧ ⌅⇤ ⌃=dV

flux inJ(x + dx, t)]S⇧⌅⇤⌃
flux outJ
J(x + dx, t) = J(x, t) +dx
xc(x, t)J(x, t) = Dx ⇥2c(x, t)1Jc
=dx = D 2tdxxx
2c(x, t)c(x, t)=Dt
x2

J(x + dx, t)J(x, t)c(x, t)(Sdx) = [J(x, t)⇧ ⌅⇤ ⌃t ⇧ ⌅⇤ ⌃=dV

flux inJ(x + dx, t)]S⇧⌅⇤⌃
flux out

JJ(x + dx, t) = J(x, t) +dx
xc(x, t)J(x, t) = Dx ⇥2c(x, t)
1Jc=dx = D 2tdxxx2c(x, t)c(x, t)=Dt
x2

J(x + dx, t)J(x, t)c(x, t)(Sdx) = [J(x, t)⇧ ⌅⇤ ⌃t ⇧ ⌅⇤ ⌃=dV

flux inJ(x + dx, t)]S⇧⌅⇤⌃
flux outJ
J(x + dx, t) = J(x, t) +dx
xc(x, t)J(x, t) = Dx ⇥2c(x, t)
1Jc=dx = D 2tdxxx2c(x, t)c(x, t)=Dtx2拡散方程式のFTによる解法

2⇥c(x, t)⇥ c(x, t)
=D2⇥t
⇥x
1
F[c(x, t)] ⇥ c(k, t) =22⇥⇥c(x, t)e⇥c(x, t)⇥ c(x, t)
F[] = DF[]⇥t⇥x2⇥c(k, t)2= Dk c(k, t)⇥t
2c(k, t) = c(k, 0) exp( Dk t)

ikx

dx

2

⇥c(x, t)⇥ c(x, t)
=D2⇥t
⇥x
1
F[c(x, t)] ⇥ c(k, t) =22⇥⇥c(x, t)e⇥c(x, t)⇥ c(x, t)
F[] = DF[]⇥t⇥x2⇥c(k, t)2
= Dk c(k, t)⇥t
2c(k, t) = c(k, 0) exp( Dk t)

ikx

dx

2

⇥c(x, t)⇥ c(x, t)
=D2
⇥t
⇥x
1
F[c(x, t)] ⇥ c(k, t) =22⇥⇥c(x, t)e⇥c(x, t)⇥ c(x, t)
F[] = DF[]⇥t⇥x2⇥c(k, t)2
= Dk c(k, t)⇥t
2c(k, t) = c(k, 0) exp( Dk t)

ikx

dx

2

⇥c(x, t)⇥ c(x, t)
=D2
⇥t
⇥x
1
F[c(x, t)] ⇥ c(k, t) =22⇥⇥c(x, t)e⇥c(x, t)⇥ c(x, t)
F[] = DF[]⇥t⇥x2⇥c(k, t)2
= Dk c(k, t)⇥t
2c(k, t) = c(k, 0) exp( Dk t)

ikx

dx

2⇥c(x, t)⇥ c(x, t)
=D2
⇥t
⇥x
1
F[c(x, t)] ⇥ c(k, t) =22⇥⇥c(x, t)e⇥c(x, t)⇥ c(x, t)
F[] = DF[]⇥t⇥x2⇥c(k, t)2
= Dk c(k, t)⇥t
2c(k, t) = c(k, 0) exp( Dk t)

ikx

dx

1c(k, 0) =2⇥c(x, 0)eikx

dx⇥c(x, 0) = c0 (x)⇥c0 ik0c0c0ikx
c(k, 0) =(x)edx =
e=
2⇥
2⇥
2⇥
⇥c0
2c(k, t) =exp( Dk t)
2⇥

1c(k, 0) =2⇥c(x, 0)eikx

dx⇥c(x, 0) = c0 (x)⇥c0 ik0c0
c0
ikx
c(k, 0) =(x)edx =
e=
2⇥
2⇥
2⇥
⇥
c0
2c(k, t) =exp( Dk t)
2⇥

1c(k, 0) =2⇥c(x, 0)eikx

dx⇥c(x, 0) = c0 (x)⇥c0 ik0
c0c0
ikx
c(k, 0) =(x)edx =
e=
2⇥
2⇥
2⇥
⇥c0
2c(k, t) =exp( Dk t)
2⇥

1c(k, 0) =2⇥c(x, 0)eikx

dx⇥c(x, 0) = c0 (x)⇥c0 ik0c0c0ikxc(k, 0) =(x)edx =
e=
2⇥
2⇥
2⇥
⇥
c0
2c(k, t) =exp( Dk t)
2⇥

1c(k, 0) =2⇥c(x, 0)eikx

dx

⇥c(x, 0) = c0 (x)⇥c0 ik0c0c0
ikx
c(k, 0) =(x)edx =
e=
2⇥
2⇥
2⇥
⇥c0
2c(k, t) =exp( Dk t)2⇥

c(x, t) = F [c(k, t)]c012=F [exp( Dtk )]2⇥c02 ikx=exp( Dtk )e dk
2
⇥12

⇥c0x
2=exp()
exp{ Dt[k + ix/(2Dt)] }dk
24Dt
⇥
⇥
2c0x
=exp()
24Dt
Dtc0x2=⇥exp()
4Dt
4 Dt

c(x, t) = F [c(k, t)]c012=
F [exp( Dtk )]2⇥c02 ikx=exp( Dtk )e dk
2
⇥
12

⇥c0x
2=exp()
exp{ Dt[k + ix/(2Dt)] }dk
24Dt
⇥⇥
2c0x
=exp()
24Dt
Dtc0x2=⇥exp()
4Dt
4 Dt

時間
空間