Stability of inclined flow of a liquid film with soluble surfactants and variable mass density

2019 ◽  
Vol 4 (5) ◽  
Author(s):  
J. P. Pascal ◽  
S. J. D. D'Alessio ◽  
E. Ellaban
Keyword(s):  
Liquid Film ◽  
Mass Density ◽  
Variable Mass ◽  
Soluble Surfactants ◽  
Inclined Flow

Mass Determination by Direct Measurement of Electron Scattering

1975 ◽  
Vol 33 ◽  
pp. 240-241
Author(s):  
M. K. Lamvik ◽  
A. V. Crewe
Keyword(s):  
Cross Section ◽  
Electron Scattering ◽  
Mass Density ◽  
Variable Mass ◽  
Scattering Cross Section ◽  
Mass Determination ◽  
Number Density ◽  
Cross Sectional ◽  
Thin Slice ◽  
Scattering Cross

If a molecule or atom of material has molecular weight A, the number density of such units is given by n=Nρ/A, where N is Avogadro's number and ρ is the mass density of the material. The amount of scattering from each unit can be written by assigning an imaginary cross-sectional area σ to each unit. If the current I0 is incident on a thin slice of material of thickness z and the current I remains unscattered, then the scattering cross-section σ is defined by I=IOnσz. For a specimen that is not thin, the definition must be applied to each imaginary thin slice and the result I/I0 =exp(-nσz) is obtained by integrating over the whole thickness. It is useful to separate the variable mass-thickness w=ρz from the other factors to yield I/I0 =exp(-sw), where s=Nσ/A is the scattering cross-section per unit mass.

scholarly journals Anti-plane shear waves in periodic elastic composites: band structure and anomalous wave refraction

2015 ◽  
Vol 471 (2180) ◽  
pp. 20150152 ◽  
Author(s):  
Sia Nemat-Nasser
Keyword(s):  
Band Structure ◽  
Phase Velocity ◽  
Negative Refraction ◽  
Mass Density ◽  
Shear Waves ◽  
Variable Mass ◽  
Three Dimensional ◽  
Positive Energy ◽  
Plane Shear ◽  
Elastic Composites

For anti-plane shear waves in periodic elastic composites, it is shown that negative energy refraction can be accompanied by positive phase-velocity refraction and positive energy refraction can be accompanied by negative phase-velocity refraction , and that this can happen over a broad range of frequencies. Hence, in general, negative refraction does not necessarily require antiparallel group and phase-velocity vectors. Details are given for layered composites and the results are extended to, and illustrated for, two-dimensional periodic composites, revealing a wealth of information about the refractive characteristics of this class of composites. The composite's unit cell may consist of any number of constituents of any variable mass density and elastic modulus, admitting large discontinuities . A powerful variational-based solution method is used that applies to one-, two- and three-dimensional composites, irrespective of their constituents being homogeneous or heterogeneous. The calculations are direct, accurate and efficient, yielding the band structure, group-velocity, energy-flux and phase-velocity vectors as functions of the frequency and wavevector components, over an entire frequency band.

scholarly journals Effect of variable mass density on the kinematics of scalar gradient

2011 ◽  
Vol 23 (7) ◽  
pp. 075107 ◽  
Author(s):  
M. Gonzalez ◽  
P. Paranthoën
Keyword(s):  
Mass Density ◽  
Variable Mass

Effects of Surfactant on the Motion of a Large Bubble in a Capillary Tube

2011 ◽  
Author(s):  
Gokalp Gursel ◽  
Ufuk Olgac ◽  
Metin Muradoglu
Keyword(s):  
Film Thickness ◽  
Liquid Film ◽  
Evolution Equations ◽  
Stokes Equations ◽  
Capillary Tube ◽  
Navier Stokes ◽  
Large Bubble ◽  
Front Tracking Method ◽  
Wide Range ◽  
Soluble Surfactants

The finite-difference/front-tracking method is used to study the motion and deformation of a large bubble moving through a capillary tube in the presence of both insoluble and soluble surfactants. Emphasis is placed on the effects of surfactant on the liquid film thickness between the bubble and the tube wall. The numerical method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible Navier-Stokes equations. A non-linear equation of state is used to relate interfacial surface tension to surfactant concentration at the interface. The film thickness is first computed for the clean bubble case and the results are compared with the lubrication theory in the limit of small capillary numbers, i.e., Ca ≪ 1, and found to be in good agreement with the predictions of Bretherton [1]. Thereafter, the method is used to investigate the effects of insoluble and soluble surfactants on the film thickness for a wide range of governing non-dimensional numbers. It is found that both the insoluble and soluble surfactants have a thickening effect on the liquid film, which compares well with both the experimental results of Krechetnikov and Homsy [2] and analytical predictions of Daripa and Pasa [3].

scholarly journals The effect of soluble surfactants on liquid film flow

2012 ◽  
Vol 395 ◽  
pp. 012165 ◽  
Author(s):  
A Georgantaki ◽  
M Vlachogiannis ◽  
V Bontozoglou
Keyword(s):  
Liquid Film ◽  
Film Flow ◽  
Liquid Film Flow ◽  
Soluble Surfactants

Analysis of plug flow reactors with variable mass density

AIChE Journal ◽  
2014 ◽  
Vol 60 (12) ◽  
pp. 4185-4189 ◽  
Author(s):  
James S. Vrentas ◽  
Christine M. Vrentas
Keyword(s):  
Mass Density ◽  
Variable Mass ◽  
Plug Flow ◽  
Flow Reactors
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