High-order lubrication theory in channels and tubes with variable geometry

Lubrication theory is used widely due to its simplicity and accuracy in many circumstances such as for the modeling of thin fluid films, the motion of particles near surfaces, and the flow in narrow geometries and configurations. Here, we present an extension to the classical lubrication theory to s...

Full description

Saved in:
Bibliographic Details
Published in:Acta mechanica 2022-10, Vol.233 (10), p.4063-4081
Main Authors: Housiadas, Kostas D., Tsangaris, Christos
Format: Article
Language:English
Subjects:
Accuracy
Analysis
Aspect ratio
Channels
Classical and Continuum Physics
Control
Domains
Dynamical Systems
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Fluid films
Fluid flow
Heat and Mass Transfer
Incompressible flow
Laminar flow
Lubrication
Mathematical analysis
Microfluidics
Newtonian fluids
Original Paper
Perturbation methods
Pressure drop
Solid Mechanics
Theoretical and Applied Mechanics
Thin films
Tubes
Vibration
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Lubrication theory is used widely due to its simplicity and accuracy in many circumstances such as for the modeling of thin fluid films, the motion of particles near surfaces, and the flow in narrow geometries and configurations. Here, we present an extension to the classical lubrication theory to study the laminar flow of an incompressible and highly viscous simple Newtonian fluid in microfluidic channels and tubes with variable geometry using a formal perturbation expansion in terms of the aspect ratio. The analysis generalizes and extends the work of Tavakol et al., Proc. R. Soc. A, 473 (2017) by considering (a) different shapes for the upper and lower walls of the channel, and (b) axisymmetric tubes with variable circular cross section. Analytical expressions in series form for the average pressure drop, required to maintain the constant flowrate through the channel or tube, are derived, where the formulas are provided in terms of the function(s) that describe the shape of the wall(s). Furthermore, the formulas are processed with techniques that increase the accuracy and extend the domain of convergence of series. For symmetric and periodic undulating channels and tubes, the comparison of the analytical results derived here with numerical results from the literature reveals the great accuracy and efficiency of the high-order lubrication theory, as well as its superiority against the well-known domain perturbation method.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-022-03313-4