By Vladimir S. Ajaev
Interfacial Fluid Mechanics: A Mathematical Modeling Approach presents an creation to mathematical types of viscous move utilized in quickly constructing fields of microfluidics and microscale warmth move. the elemental actual results are first brought within the context of easy configurations and their relative significance in regular microscale functions is mentioned. Then, numerous configurations of significance to microfluidics, so much significantly skinny films/droplets on substrates and constrained bubbles, are mentioned intimately. subject matters from present learn on electrokinetic phenomena, liquid circulation close to established sturdy surfaces,evaporation/condensation, and surfactant phenomena are mentioned within the later chapters.
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Extra info for Interfacial Fluid Mechanics: A Mathematical Modeling Approach
Studies of this configuration are important for a number of applications involving coating of a solid surface with a layer of liquid (which is often solidified after the coating is complete). Even though in practical applications on the microscale, such as manufacturing computer hard drives, centrifugal force rather than gravity drives the flow, the key issues in mathematical modeling are essentially the same; we focus on the gravity-driven film flow in the present section. Consider a film of viscous liquid of density ρ and viscosity μ flowing down a plane inclined at an angle α , as illustrated in Fig.
21) has to be solved on the domain [0, xˆCL ] with the contact line coordinate xˆCL chosen large enough to ensure that the liquid film is flat near xˆ = 0. We choose xˆCL = 10 and use the boundary conditions h0 (0) = 0, h0 (xˆCL ) = 0, h0 (xˆCL ) = −Θ . 22). , using the bvp4c solver from MATLAB. 21) for values of xˆ approaching xˆCL . 21) requires that h0 → ∞ near the contact line. Clearly, a solution with this property cannot be accurately described by the standard numerical methods which rely on the assumption that all derivatives of the solution are bounded.
13 shows that points corresponding to different grid sizes lie on a straight line. The slope of this line is equal to 2, meaning that the error norm decays as (Δ x) ˜ 2 in accordance with our theoretical prediction. Comparison between the numerical results for the error and its expected theoretical behavior is a useful tool for validation of numerical codes. Numerical solution of evolution equations is easy to implement not only in MATLAB but also in Fortran or C/C++ since several efficient solvers for systems of ordinary differential equations are available online.
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