ChemE_3230_PS1 - ChemE 3230 (Spring 2011) PROBLEM Set #1...

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ChemE 3230 (Spring 2011) PROBLEM Set #1 (Due by 02/11/2011) Read Denn Chapters 1-2 Problem 1.0 Using index notation, prove the following identities. (i) ( a × T ) b = a × ( T b ) (ii) T × ( a × b ) = a ( T b ) ( T a ) b (iii) ∇ × ∇ × v = ( v ) − ∇ 2 v Hint: you will find the following identity helpful: ε ijk ilm = δ jl km jm kl (25 Points) Problem 2.0 Spin coating is a widely used procedure for creating thin fluid films on surfaces. The figure below illustrates the procedure: A fluid containing the material to be coated is transported at a flow rate Q to the substrate through a rigid tube positioned in the center of the substrate; When a desired volume of material has accumulated on the substrate, the flow is stopped and the substrate rotated at a fixed angular speed Ω . This causes the fluid puddle (lower figure) to spread-out on the substrate, eventually producing a uniform film, thickness H ( r ) of the desired material. Figure 1:
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ChemE_3230_PS1 - ChemE 3230 (Spring 2011) PROBLEM Set #1...

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