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Finding curvature; Methods, problems and solutions. Mmac meeting June 28th, 2012 Amin Ahmadi Joneidi. Finding curvature; Methods, problems and solutions. Energy and force terms. Ca, Capillary number. H, Mean curvature. K, Gaussian curvature. ζ , Lagrangian multiplier. - PowerPoint PPT Presentation

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Finding curvature;Methods, problems and solutionsMmac meetingJune 28th, 2012

Amin Ahmadi Joneidi/ Mechanical engineeringFinding curvature; Methods, problems and solutions1

/ Mechanical engineeringEnergy and force termsCa, Capillary numberH, Mean curvatureK, Gaussian curvature, Lagrangian multiplier PAGE 2

Stress jump across the membrane of the dropStress jump across the membrane of the RBC/ Mechanical engineering3

H = Physical meaning of curvature / Mechanical engineeringInterface definition

PAGE 4

H = 2 / Mechanical engineeringCurvature finding

PAGE 5

Contour integration method

Loewenberg and Hinch (1996)/ Mechanical engineering6n = 6El. Number = 720H =2.2838For 12 special nodes For remained nodes

Validation/ Mechanical engineering7n = 10El. Number = 2000H =2.2891For 12 special nodes For remained nodes

Validation/ Mechanical engineering8n = 12El. Number = 2880H =2.2899For 12 special nodes For remained nodes

Validation/ Mechanical engineering9

Drop in shear flow/ Mechanical engineering10

Switch from water to blood/ Mechanical engineeringCurvature findingParabola fitting method - Zinchenko et al. (1997)

PAGE 11/ Mechanical engineering12

Curvature in ellipsoid/ Mechanical engineering13Curvature finding using contour integration methodCurvature finding using Parabola fitting methodNode numberNumerical curvatureAnalytical curvatureNode 3001.6590481.659027Node 12002.3296542.324415Node 14241.6409741.636053************************Node 11.87231.6341Node 163.25472.8442Node 1361.94241.6954Node numberNumerical curvatureAnalytical curvatureNode 3001.6623571.659027Node 12002.3284832.324415Node 14241.6379661.636053************************Node 11.63571.6341Node 162.84752.8442Node 1361.69711.6954/ Mechanical engineering14

/ Mechanical engineeringMesh destructionPAGE 15

/ Mechanical engineeringSeek the problem

PAGE 16/ Mechanical engineering17

/ Mechanical engineering