scholarly journals Electric Transverse Emissivity of Sinusoidal Surfaces Determined by a Differential Method: Comparison with Approximation of Geometric Optics

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Taoufik Ghabara
Keyword(s):  
Transition Layer ◽  
Numerical Study ◽  
Rough Surfaces ◽  
Method Comparison ◽  
Electromagnetic Theory ◽  
Differential Method ◽  
Homogenization Theory ◽  
Geometric Optics ◽  
Optical Index ◽  
Validity Limit

We present in this paper a numerical study of the validity limit of the optics geometrical approximation in comparison with a differential method which is established according to rigorous formalisms based on the electromagnetic theory. The precedent studies show that this method is adopted to the study of diffraction by periodic rough surfaces. For periods much larger than the wavelength, the mechanism is analog to what happens in a cavity where a ray is trapped and undergoes a large number of reflections. For gratings with a period much smaller than the wavelength, the roughness essentially behaves as a transition layer with a gradient of the optical index. Such a layer reduces the reflection there by increasing the absorption. The code has been implemented for TE polarization. We determine by the two methods such as differential method and the optics geometrical approximation the emissivity of gold and tungsten cylindrical surfaces with a sinusoidal profile, for a wavelength equal to 0.55 microns. The obtained results for a fixed height of the grating allowed us to delimit the validity domain of the optic geometrical approximation for the treated cases. The emissivity calculated by the differential method and that given on the basis of the homogenization theory are satisfactory when the period is much smaller than the wavelength.

Wetting of rough surfaces: a homogenization approach

2005 ◽  
Vol 461 (2053) ◽  
pp. 79-97 ◽  
Author(s):  
Giovanni Alberti ◽  
Antonio DeSimone
Keyword(s):  
Contact Angle ◽  
Solid Surface ◽  
Transition Layer ◽  
Variational Formulation ◽  
Variational Approach ◽  
Rough Surfaces ◽  
Vapour Phase ◽  
Homogenization Theory ◽  
Minimal Energy ◽  
Homogenization Approach

The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness–induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapour phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational approach: the classical laws of Wenzel and Cassie–Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case.

Numerical Study of Microchamber Filling in Centrifugal Microfluidics

2011 ◽  
Author(s):  
Nick Niedbalski ◽  
Seok-Won Kang ◽  
Debjyoti Banerjee
Keyword(s):  
Surface Tension ◽  
Numerical Model ◽  
Physical Properties ◽  
Thermal Cycle ◽  
Numerical Study ◽  
Method Comparison ◽  
Thermal Conditions ◽  
Microfluidic System ◽  
Working Fluid ◽  
Driving Mechanism

Numerical investigation of the transient, coupled hydrodynamic and thermal behavior of a novel polymerase chain reaction (PCR) centrifugal microfluidic system is presented in this study. The driving mechanism for flow within these devices is modeled as a combination of the capillary forces and rotationally induced pressure gradient working in opposition to viscous forces, which are functions of rotation speed and fluid properties. The physical properties of the working fluid are in turn functions of temperature, some of which can have significant variations over the operating temperature ranges of a PCR thermal cycle. The complex balance of viscous, capillary, and rotationally induced inertial forces are crucial factors in optimizing the design of such devices. Hence, the effects of temperature variation on the filling performance cannot be neglected. A commercial CFD code is utilized to simulate the filling of a microchamber when subjected to thermal conditions typical of a PCR thermal cycle. The numerical model accounts for the temperature dependence of the working fluid’s viscosity and surface tension by simultaneously solving the Navier-Stokes and energy equations. The free surface morphology (position, shape) and total chamber fill fraction as a function of time is predicted by using the volume of fluids (VOF) method. Comparison of the predictions from the temperature dependent numerical model to that which assume said physical properties to be constant, demonstrates the strong effect of the fluid’s viscosity and surface tension on the filling rate for various rotation speeds.

scholarly journals Wetting of doubly periodic rough surfaces in Wenzel’s regime

2018 ◽  
Vol 145 ◽  
pp. 03006
Author(s):  
Stanimir Iliev ◽  
Nina Pesheva ◽  
Pavel Iliev
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Numerical Study ◽  
Rough Surfaces ◽  
Contact Angle Hysteresis ◽  
Stick Slip ◽  
Liquid Meniscus ◽  
Three Phase ◽  
Mutual Disposition ◽  
Physical Defects

In this work we present preliminary results from our numerical study of the shapes of a liquid meniscus in contact with doubly sinusoidal rough surfaces in Wenzel’s wetting regime. Using the full capillary model we obtain the advancing and the receding equilibrium meniscus shapes for a broad interval of surface roughness factors. The contact angle hysteresis is obtained when the three-phase contact line is located on one row (block case) or several rows (kink case) of physical defects. We find that depending on the mutual disposition of the contact line and the lattice of periodic defects, different stick-slip behaviors of the contact line depinning mechanism appear, leading to different values of the contact angle hysteresis.

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