Chem-To-Math的博客

泊松-玻尔兹曼Poisson–Boltzmann方程的提出1.简要历史回顾1.1 基本原理1.2 方程推导1.简要历史回顾泊松-玻尔兹曼方程是用来计算电解质溶液中离子浓度和电荷密度分布的一个微分方程，其基本形式为∇2ϕ(r)=−4πϵ∑ici0ziqe−βziqϕ(r)(1)\nabla^2\phi(\textbf r)=-\frac{4\pi}{\epsilon}\sum_{i} c_i^0z_iqe^{-\beta z_iq\phi(\textbf r)} \tag{1}∇2ϕ(r)=−ϵ4π​i

传质方程Equation of Continuity for Species A with Constant ρDABρDAB\rho \mathscr{D}_{AB} in terms of wAwAw_A控制方程表达通式： ρDwADt=ρDAB∇2wA+rAρDwADt=ρDAB∇2wA+rA\rho \dfrac {Dw_A}{Dt}=\rho \mathscr{D}_{AB}\...

流体传质方程Equation of Continuity for Species αα \alpha in terms of jjαjjα \pmb j_\alpha控制方程表达通式： ρDwαDt=−∇⋅jjα+rαρDwαDt=−∇⋅jjα+rα\rho \dfrac {D w_\alpha}{Dt}=-\nabla \cdot \pmb j_\alpha + r_\alpha...

牛顿流体传热方程Equation of Energy for Newtonian Fluids with Constant ρρ\rho and kkk控制方程表达通式： ρC^pDTDt=k∇2T+μΦΦvρC^pDTDt=k∇2T+μΦΦv\rho \hat {C}_p \dfrac {DT}{Dt}=k\nabla^2T+\mu \pmb \Phi_v1.直角坐标系(x,y...

流体传热方程Equation of Energy in terms of qqqq\pmb q控制方程表达通式： ρC^pDTDt=−∇⋅qq−∂lnρ∂lnTDpDt−ττ:∇vvρC^pDTDt=−∇⋅qq−∂lnρ∂lnTDpDt−ττ:∇vv\rho \hat {C}_p \dfrac {DT}{Dt}=-\nabla \cdot \pmb q-\dfrac {\partial ...

牛顿流体耗散方程Dissipation Function for Newtonian Fluids1.直角坐标系(x,y,zx,y,z x, y, z ) 直角坐标系Cartesian coordinates ( x,y,z  x,y,z \textit { x,y,z }): NO. ΦΦv=2[(∂vx∂x)2+(∂...

流体动量控制方程Equation of Motion for a Newton’s Fluid with Constant ρρ\rho and μμ\mu控制方程通式： ρDvvDt=−∇p+μ∇2vv+ρggρDvvDt=−∇p+μ∇2vv+ρgg\rho \dfrac {D \pmb v}{D t}=- \nabla p + \mu \nabla^2 \pmb v+\rho \...

流体动量控制方程The Equation of Motion in terms of ττ\tau控制方程通式： ρDvvDt=−∇p−∇⋅ττ+ρgρDvvDt=−∇p−∇⋅ττ+ρg\rho \dfrac {D \pmb v}{D t}=- \nabla p-\nabla \cdot \pmb \tau+\rho g1.直角坐标系(x,y,zx,y,z x, y, z )...

Newton’s Law of Viscosity先定义 ττ\mathbf{\tau } τ=−μ(∇vv+(∇vv)†)+(23μ−κ)(∇⋅vv)δτ=−μ(∇vv+(∇vv)†)+(23μ−κ)(∇⋅vv)δ \tau=-\mu(\nabla \pmb v+(\nabla \pmb v)^{\dagger} ) +(\frac{2}{3}\mu-\kappa)(\nabla\cd...

流体连续性方程TheEquationofContinuityTheEquationofContinuity\color{Blue} {The\quad Equation \quad of \quad Continuity} 流体连续性方程表达通式 ∂ρ∂t+∇⋅ρvv=0∂ρ∂t+∇⋅ρvv=0\dfrac {\partial \rho}{\partial t}+ {\nabla } \...