Exact solutions to the interfacial surfactant transport equation on a droplet in a Stokes flow regime

2015 ◽  
Vol 27 (8) ◽  
pp. 082104 ◽  
Author(s):  
Christina Kallendorf ◽  
Anja Fath ◽  
Martin Oberlack ◽  
Yongqi Wang
Keyword(s):  
Exact Solutions ◽  
Transport Equation ◽  
Flow Regime ◽  
Stokes Flow ◽  
Surfactant Transport ◽  
Interfacial Surfactant

scholarly journals Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows

1975 ◽  
Vol 67 (4) ◽  
pp. 787-815 ◽  
Author(s):  
Allen T. Chwang ◽  
T. Yao-Tsu Wu
Keyword(s):  
Exact Solutions ◽  
Stokes Flow ◽  
Fundamental Solutions ◽  
The Body ◽  
Circular Cylinders ◽  
Geometrical Parameters ◽  
Flow Problems ◽  
Singularity Method ◽  
Wide Range ◽  
Body Shapes

The present study further explores the fundamental singular solutions for Stokes flow that can be useful for constructing solutions over a wide range of free-stream profiles and body shapes. The primary singularity is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives other fundamental singularities can be obtained, including rotlets, stresslets, potential doublets and higher-order poles derived from them. For treating interior Stokes-flow problems new fundamental solutions are introduced; they include the Stokeson and its derivatives, called the roton and stresson.These fundamental singularities are employed here to construct exact solutions to a number of exterior and interior Stokes-flow problems for several specific body shapes translating and rotating in a viscous fluid which may itself be providing a primary flow. The different primary flows considered here include the uniform stream, shear flows, parabolic profiles and extensional flows (hyper-bolic profiles), while the body shapes cover prolate spheroids, spheres and circular cylinders. The salient features of these exact solutions (all obtained in closed form) regarding the types of singularities required for the construction of a solution in each specific case, their distribution densities and the range of validity of the solution, which may depend on the characteristic Reynolds numbers and governing geometrical parameters, are discussed.

Nonlinear hydrodynamic phenomena in Stokes flow regime

2010 ◽  
Vol 239 (14) ◽  
pp. 1214-1224 ◽  
Author(s):  
J. Blawzdziewicz ◽  
R.H. Goodman ◽  
N. Khurana ◽  
E. Wajnryb ◽  
Y.-N. Young
Keyword(s):  
Flow Regime ◽  
Stokes Flow

Double-Layer Representation of Model Microorganisms by a Boundary Element Method

2012 ◽  
Author(s):  
Kohei Kyoya ◽  
Yohsuke Imai ◽  
Takami Yamaguchi ◽  
Takuji Ishikawa
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Flow Regime ◽  
Double Layer ◽  
Stokes Flow ◽  
Biomedical Engineering ◽  
Many Body ◽  
Body Interaction ◽  
Many Body Interactions ◽  
Element Method

Analysis of a suspension of microorganisms is important in environmental and biomedical engineering. Previous studies had problems of high computational load in simulating many-body interaction of non-spherical swimmers. In this study, we propose a boundary element method (BEM), based on the double-layer representation, for calculating interactions of two squirmers in Stokes flow regime. By comparing the trajectories of squirmers calculated by both single- and double-layer representations, we show the accuracy of the method. The developed method has potential to deal with many-body interactions of non-spherical microorganisms.

Hydrodynamics and Interfacial Surfactant Transport in Vascular Gas Embolism

2021 ◽  
Author(s):  
David Eckmann ◽  
Jie Zhang ◽  
Portonovo Ayyaswamy
Keyword(s):  
Stokes Equations ◽  
Tissue Injury ◽  
Review Literature ◽  
Liquid Interface ◽  
Navier Stokes ◽  
Gas Embolism ◽  
Cellular Mechanics ◽  
Transport Dynamics ◽  
Surfactant Transport ◽  
Interfacial Surfactant

Abstract Vascular gas embolism - bubble entry into the blood circulation - is pervasive in medicine, including over 340,000 cardiac surgery patients in the US annually. The gas-liquid interface interacts directly with constituents in blood, including cells and proteins, and with the endothelial cells lining blood vessels to provoke a variety of undesired biological reactions. Surfactant therapy, a potential preventative approach, is based in fluid dynamics and transport mechanics. Herein we review literature relevant to understanding of the key gas-liquid interface interactions inciting injury at the molecular, organelle, cellular and tissue levels, including clot formation, cellular activation, and adhesion events. We review the fluid physics and transport dynamics of surfactant-based interventions to reduce tissue injury from gas embolism. In particular, we focus on experimental research and computational and numerical approaches which demonstrate how surface-active chemical based intervention, based on competition with blood-borne or cell surface-borne macromolecules for surface occupancy of gas-liquid interfaces, alters cellular mechanics, mechanosensing and signaling coupled to fluid stress exposures occurring in gas embolism. We include a new analytical approach for which an asymptotic solution to the Navier-Stokes equations coupled to the convection-diffusion interaction for a soluble surfactant provides additional insight regarding surfactant transport with a bubble in a non-Newtonian fluid.

Sign in / Sign up

Export Citation Format

Share Document