Thin layer approximation

Equations (4)-(6) hold for a bulk (non- or weakly absorbing) rare medium 2 (case (a) in Fig. 3). In the case of a thin film with thickness <7<<7p in contact with the IRE (case (b) in Fig. 3), the thin-layer approximation gives good results (5). Here it is assumed that the electric field is determined by the IRE and the bulk medium above the thin film. The thin film is then considered as a dielectric in this field, and equations similar to Eqs. (4)-(6) can be derived. 

A thin layer (approximately 10 mil thick) of RTV silicone was coated on the Micromet mini-dielectric sensor. The RTV silicone was first cured at room temperature, then in an oven at 120 C for a period of time, similar to certain RTV production cure schedules. The permittivity and loss factor of the RTV silicone were recorded during this cure cycle. 

Thin-Layer Approximation. Laminar analyses often make the further approximation that the boundary layer is so thin that when the simplified equations of motion are rewritten in terms of local surface coordinates, i.e., in terms of the x and y of Fig. 4.3a, several terms normally associated with curvature effects can be dropped. The Nusselt number equation, based on solutions to such laminar thin-layer equation sets, always takes the form... 

The thin-layer approximation fails because natural convective boundary layers are not thin. From the interferometric fringes in Fig. 4.2ft (which are essentially isotherms), the thermal boundary layer around a circular cylinder is seen to be nearly 30 percent of the cylinder diameter. For such thick boundary layers, curvature effects are important. Despite this failure, thin-layer solutions provide an important foundation for the development of correlation equations, as explained in the section on heat transfer correlation method. 

All three solder alloys dissolved the 1.0-pm Au layer to form the IMC AuSu4 throughout the solder ball bulk, and a second IMC, AgsSn. The AgsSn was distributed evenly in Sn-Pb-Ag alloy, but preferentially along the phase boundary of the Sn-rich grains in the Pb-free alloys. The microstructures are shown in Fig. 16. A very thin layer (approximately 0.5 pm) of Ni-Sn IMC was found to exist at the termination pad/solder interface of the Sn-Pb-Ag and Sn-Ag alloys. But the morphology of the Ni-Sn IMC was much different from CueSus at the interface which typically has a scalloped appearance [61,62]. A ternary compound existed at the termination pad/ Sn-Ag-Cu solder interface [60]. 

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