Electroosmotic flow in a microchannel with pressure drop is considered as an incompressible liquid flow between...

Transcribed Image Text:

Electroosmotic flow in a microchannel with pressure drop is considered as an incompressible liquid flow between two large parallel plates, separated by a distance 2h, both moving at a constant velocity Uo in the negative x-direction as shown in the figure. The inlet and outlet pressures are: P(x=0)=P₁ and P(x=L)=P2 such that AP=P₁-P₂>0. [35%] L Uo Uo y ; v Xu 2h P₁ P₂ (a) Write down the boundary conditions for u and v at the top and bottom moving surfaces. (b) Write down the differential equations for the conservation of mass and x-momentum assuming steady, 2-D, and fully-developed flow. (c) Derive an expression to determine the velocity profile u-u(y; AP, L, h, μ, Uo). (d) Calculate the pressure drop, APo, required for the condition: u(y=0)=+Uo, and find all the y-location(s) at which u(y)=0. (e) For the same pressure drop, APo, calculate the shear stress profile Txy(y). Electroosmotic flow in a microchannel with pressure drop is considered as an incompressible liquid flow between two large parallel plates, separated by a distance 2h, both moving at a constant velocity Uo in the negative x-direction as shown in the figure. The inlet and outlet pressures are: P(x=0)=P₁ and P(x=L)=P2 such that AP=P₁-P₂>0. [35%] L Uo Uo y ; v Xu 2h P₁ P₂ (a) Write down the boundary conditions for u and v at the top and bottom moving surfaces. (b) Write down the differential equations for the conservation of mass and x-momentum assuming steady, 2-D, and fully-developed flow. (c) Derive an expression to determine the velocity profile u-u(y; AP, L, h, μ, Uo). (d) Calculate the pressure drop, APo, required for the condition: u(y=0)=+Uo, and find all the y-location(s) at which u(y)=0. (e) For the same pressure drop, APo, calculate the shear stress profile Txy(y).

Answer rating: 100% (QA)

a The boundary conditions at the top and bottom moving surfa... View the full answer