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For interface-tracking simulation of two-phase flows in micro-fluidics devices, Navier-Stokes phase-field method (NS-PFM) was examined, which is a combination of NS equations with phase-field model for interface based on the free-energy theory. A new version of NS-PFM which we have proposed was applied to flow problems of immiscible, incompressible, isothermal two-phase fluid on wetted solid surface at a high density ratio equivalent to that of an air-water system. Thermal non-ideal fluid flows with phase change around a critical point were simulated using another version of NS-PFM which solves a full set of NS equations and the van-der-Waals equation of state by the MacCormack finite difference scheme. The numerical results demonstrated the applicability of both NS-PFM.
パラメータγ S は界面と固体面との接触角θWを調整する(19),(20). 本研究では,高密度比二成分二相流の計算に以下で述べるNS,CH方程式の直接数値解法NS-PFM(7), (8),(11)-(13)を適用した.まず,3次元デカルト座標系(x, y, z)の下で幅Δx=Δy=Δz=1 の立方セルの
(a) ΔT=10-2T Fig.11: Density and velocity fields around 2D vapor bubble
nucleated on a flat heater with width 10Δx and temperature T0+ΔT in a van-der-Waals fluid at time t (T0=0.293, Δx=Δy=1, Δt=0.2, ρG=0.265, ρL=0.405)
t=10,000Δt
t=50,000Δt
t=100,000Δt (b) ΔT=5×10-2T
Lx
Ly
TH=T0+ΔTLH
TW=T0
T=T0,
Periodic boundaries
Non-slip wall Heater
Outflow boundaryP=P0,
x
y
/ 0v y∂ ∂ =
Fig.10: Two-dimensional computational domain
(b) Case2 (a=8Δx) t*=0.160 t*=0.319
Fig .7: Side view of two-phase fluid in channel at time t* = t |Uin|/Lz
Lz
x
zUin
Liquid Gas
InterfaceContact line
(a) Case1 (a=2Δx) t*=0.160 t*=0.319
Fig.6 : Computational domain
x
yz
Liquid
Gas
Lx= 70Δx Ly= 20Δy
Lz= 20Δz
Δx=Δy=Δz=1
Hydrophobic non-slip solid walls with θW =120deg.
Uniform inflow
Free outflow
Hydrophilic regionwith θW =60deg.
Uin=const.
0x
∂=
∂u
p=const.
0px
∂=
∂
Transition region
aΔx
Δx
ρ =ρL
ρL /ρG = 801.7
μL /μG = 73.76
Density ratio:
Viscosity ratio:
L inUCa μσ
=
L Z in
L
L URe ρμ
=
Capillary number:
ynolds number:Re
(a) (b)
(c) (d)
Fig.9 : Time series of snapshot of single hemispherical-shaped drop on a flat sold surface with heterogeneous wettability under no gravity in a stagnant gas
ρL /ρG =801.7, and μL /μG =73.76.
θW = 61.4°
Liquid(Water, 16mm)
Gas(Air)
64Δx
64Δy
32Δz
Δx=Δy=Δz=1
θW = 118.6°
32Δyx
y
z
Fig.8: Computational domain for simulation of motion of single hemispherical-shaped drop on a flat sold surface with heterogeneous wettability under no gravity in a stagnant gas
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Fig.12: Density field around the body at time t*= tUin/a for Re=2.025 (Uin=0.05,Δt=0.05,ρG=0.265, ρL=0.405)
(a) Ca =0, pout /p0=1 (b) Ca =0.7, pout /p0=1.1
t*=0.125
t*=1.250
t*=1.875
t*=2.50
t*=0.125
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