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3. Liquid Surface Tension: Derive a mathematical equation that describes the shape, n(x), of the pediatric drug-tube microfluidics fluid interface in contact with the inner rigid wall of the tube. Assume that the slope is quite small such that R¹d²n/dx². The pressure difference across the interface is equally balanced by the specific weight (y) of the drug divided by the interface height, such that Ap~ pgny/R. Solve this differential equation using the following boundary conditions: n = h at x = 0 and a horizontal surface = 0 as x→ ∞o. See Figure below. Determine the maximum height, h, at the wall. y x=0 y = h η(x) X

3. Liquid Surface Tension: Derive a mathematical equation that describes the shape, n(x), of the pediatric drug-tube microfluidics fluid interface in contact with the inner rigid wall of the tube. Assume that the slope is quite small such that R¹d²n/dx². The pressure difference across the interface is equally balanced by the specific weight (y) of the drug divided by the interface height, such that Ap~ pgny/R. Solve this differential equation using the following boundary conditions: n = h at x = 0 and a horizontal surface = 0 as x→ ∞o. See Figure below. Determine the maximum height, h, at the wall. y x=0 y = h η(x) X

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Liquid Surface Tension: Derive a mathematical equation that describes the shape, n(x), of the pediatric drug-tube microfluidics fluid interface in contact with the inner rigid wall of the tube. Assume that the slope is quite small such that R¹d²n/dx². The pressure difference across the interface is equally balanced by the specific weight (y) of the drug divided by the interface height, such that Ap~ pgny/R. Solve this differential equation using the following boundary conditions: n = h at x = 0 and a horizontal surface = 0 as x→ ∞o. See Figure below. Determine the maximum height, h, at the wall. y x=0 y = h η(x) X
Transcribed Image Text:3. Liquid Surface Tension: Derive a mathematical equation that describes the shape, n(x), of the pediatric drug-tube microfluidics fluid interface in contact with the inner rigid wall of the tube. Assume that the slope is quite small such that R¹d²n/dx². The pressure difference across the interface is equally balanced by the specific weight (y) of the drug divided by the interface height, such that Ap~ pgny/R. Solve this differential equation using the following boundary conditions: n = h at x = 0 and a horizontal surface = 0 as x→ ∞o. See Figure below. Determine the maximum height, h, at the wall. y x=0 y = h η(x) X
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