Surface stretch model

The first term on the right-hand side represents transfer to the elements of surface present over the entire time period t, while the second represents transfer to appearing or disappearing elements. The fresh surface model, Eq. (7-52), predicts larger coefficients than the surface stretch model, Eq. (7-51). 

The assumption of transfer by a purely turbulent mechanism in the Handlos-Baron model leads to the prediction that the internal resistance is independent of molecular diffusivity. However, such independence has not been found experimentally, even for transfer in well-stirred cells or submerged turbulent jets (D4). In view of this fact and the neglect of shape and area oscillations, models based upon the surface stretch or fresh surface mechanism appear more realistic. For rapid oscillations in systems with Sc 1, mass transfer rates are described by identical equations on either side of the drop surface, so that the mass transfer results embodied in Eqs. (7-54) and (7-55) are valid for the internal resistance if is replaced by p. Measurements of the internal resistance of oscillating drops show that the surface stretch model predicts the internal resistance with an average error of about 20% (B16, Yl). Agreement of the data for drops in liquids with Eq. (7-56) considerably improves if the constant is increased to 1.4, i.e.. 

Fig. 6. Schematic representation of the normal modes of an adsorbed diatomic molecule neglecting the surface structure, after Richardson and Bradshaw . In parentheses the experimentally measured values for CO in the ontop position on Pt(lll). (a) A frustrated translation (60 cm (b) A frustrated rotation (not yet detected), (c) The metal-molecule stretch (460cm ) . (d) The intramolecular stretch model (2100cm" ) . ...

Lamellar orientation in thin films of a model diblock copolymer with symmetric poly(styrene)- -PLLA (PS-PLLA) was investigated by Chen et al. [62] in the molten state on silicon wafer supported surfaces. Stretching and compression were apt to induce orientation of PLA. Pluta and Galeski [63] studied the plastic deformation of amorphous and thermally noncrystallizable 70/30 PLA/PDLLA induced by plane strain compression in a channel die. The results revealed that plastic deformation transformed an amorphous PLA or PDLLA (thermally noncrystallizable) into a crystalline fibrillar texture oriented in the flow direction. 

Solids and their surfaces were modeled by the Born model potential as discussed in the following paragraph. Adsorbed molecules were modeled by the molecular mechanics approach in which energy for a covalently bonded molecule is dependant mainly on bond stretching term (E ) along other contributing terms. 

The Alexander model is based on two assumptions that enable simple expressions for these two terms (1) The concentration profile of the layer is step-like. That is, the monomer volume fraction within the layer, (p Na3/d2L, is constant, independent of position (2) The chains are uniformly stretched. That is, all chain ends are positioned on a single plane at a distance L from the surface. [In this paper, we use the symbol to mean approximately equal to or equal to within a numerical factor of order one we use to mean proportional to .] The first assumption simplifies the calculation of Fin, while the second yields a simple expression for Fel. 

FUatyev, S.A., J.F. Driscoll, C.D. Carter, J.M. Donbar, Measured properties of turbulent premixed flames for model assessment, including burning velocities, stretch rates, and surface densities. Combust Flame, 2005. 141(1-2) 1-21. 

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