Viscous Dissipation Domain

One of the earliest analytical models for the calculation of flattening ratio of a droplet impinging on a solid surface was developed by Jones.1508] In this model, the effects of surface tension and solidification were ignored. Thus, the flattening ratio is only a function of the Reynolds number. Discrepancies between experimental results and the predictions by this model have been reported and discussed by Bennett and PoulikakosJ380] 

In case that the decay of impact kinetic energy due to viscous dissipation is the predominant mechanism in droplet flattening, Madejski s full model reduces to  

An analysis very similar to Madej ski s study 401] has been conducted by Fiedler and Naber[521] for normal liquids in combustion applications from which solidification phenomenon is absent. The derived results are almost identical to Madej ski s model. Markworth and Saunders1522 presented a substantial improvement upon the velocity field used by Madej ski, and demonstrated a correspondingly improved model prediction. 

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Viscous Dissipation Domain The decay of kinetic energy of an impacting droplet is due to viscous dissipation during flattening. 

If the dominating domain is selected correctly, the error induced by the simplification will be no more than about 20%. However, even well into the viscous dissipation domain, the effects of the surface tension are still significant, while in the surface tension domain, the effects of viscous dissipation disappear far more rapidly as one moves away from the borderline. In other words, the viscous energy dissipation contribution to the spread factor rapidly declines within the surface tension-dominated domain, while significant residual surface tension effects extend well into the viscous energy dissipation domain. 

Write a program to solve by means of RFM the equation of motion and using the velocity field, calculate viscous dissipation and solve for the energy equation. Neglect inertial and convective effects. Consider T0=200°C, Ti=150°C, /x=24000 Pa-s, k=0.267 W/mK, i o=0.1 m, i i=0.13 m, k=0.769, cc=0.496 rad/s. Compare the numerical results with the analytical solution. Hint The couette flow is constant along the angular direction, hence, it is no necessary to use the whole domain. 

The coalescence of polymers is driven by the work of surface tension, which counteracts the viscous dissipation associated with the molecular diffusion within the coalescing domain. This phenomenon is often referred to in the literature as polymer sintering. In the rotational molding process, coalescence occurs at temperatures above that of the material melting point when dealing with semicrystalline polymers, or above the glass transition temperature for amorphous resins. The first analytical model describing the coalescence process was proposed by Frenkel ... 

Here, p is the density k is the thermal conductivity /xf is the fluid dynamic viscosity p is the pressure T is the temperature u is the velocity vector Cp is the specific heat capacity, and O is the viscous dissipation the subscripts f and s represent fluid and solid, respectively. For nanofluids, the corresponding effective thermal conductivities and effective fluid dynamic viscosities will be introduced. When using CFX-10, the solid and fluid are treated as a unitary computational domain. The interface between the solid and fluid is automatically connected by equal temperature magnitudes and heat flux values thus, only the boundaries for the unit cell are needed. Specifically, for the hydraulic boundary conditions, a uniform velocity is applied at the channel inlet ... 

An operator of friction resistance, or viscous resistance, is used for linking these two state variables, because the relation is linear only in a validity domain restricted to low velocities (Newtonian fluid). In a gas, snch as air, the dependence of the force is most often expressed by a quadratic function of the velocity however, many different dependences are modeled in practice. The existence of friction signifies a dissipation of the kinetic energy into heat. 

At the formation of the structure of crosslinked polymers one can observe the formation of dissipative structures (DS) of two levels - micro- and macro-DS. Micro-DS are local order domains (clusters) and their formation is due to the high viscosity of the reactive medium in the gelation period. As it is known [47], this results in turbulence of viscous media and subsequent formation of ordered regions. 

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