Axisymmetric Drop Shape Analysis (ADSA): An Outline.

Drop shape techniques for the measurement of interfacial tension are powerful, versatile and flexible. The shape of the drop/bubble depends on the balance between surface tension and external forces, e.g. gravity. This balance is reflected mathematically in the Laplace equation of capillarity. Axisymmetric Drop Shape Analysis (ADSA) is a commonly used drop shape technique. A streamlined version of the development of ADSA over the past several decades is presented to illustrate its validity and range of utility. Several configurations of interest will be considered and presented systematically. Shape and surface tension will be linked to a shape parameter based on proper concepts of differential geometry. The resulting shape parameter will be shown to allow determination of the range of applicability of such a drop shape method.

[1]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Shi-Yow Lin,et al.  An examination on the accuracy of interfacial tension measurement from pendant drop profiles , 1995 .

[3]  D. Grigoriev,et al.  Stress relaxation behaviour of dipalmitoyl phosphatidylcholine monolayers spread on the surface of a pendant drop , 1999 .

[4]  Chun Huh,et al.  A method for estimating interfacial tensions and contact angles from sessile and pendant drop shapes , 1983 .

[5]  A. Amirfazli,et al.  Determination of line tension for systems near wetting. , 2003, Journal of colloid and interface science.

[6]  M. Hoorfar,et al.  Evaluation of the surface tension measurement of axisymmetric drop shape analysis (ADSA) using a shape parameter , 2005 .

[7]  Z. Policova,et al.  In vitro surface properties of the newly recognized gastric pathogen Helicobacter pylori , 1990, Infection and immunity.

[8]  Stephen M. Smith,et al.  SUSAN—A New Approach to Low Level Image Processing , 1997, International Journal of Computer Vision.

[9]  C. Elliott,et al.  Interfacial tension from height and diameter of a single sessile drop or captive bubble , 1980 .

[10]  O. S. Mills.  Tables for use in the measurement of interfacial tensions between liquids with small density differences , 1953 .

[11]  Stephen T. Hyde,et al.  The Language of Shape: The Role of Curvature in Condensed Matter: Physics, Chemistry and Biology , 1996 .

[12]  D. Vollhardt,et al.  Axisymmetric drop shape analysis as a film balance : Rate dependence of the collapse pressure and molecular area at close packing of 1-octadecanol monolayers , 1996 .

[13]  A Amirfazli,et al.  Development of a new methodology to study drop shape and surface tension in electric fields. , 2004, Langmuir : the ACS journal of surfaces and colloids.

[14]  José María Montanero,et al.  A new drop-shape methodology for surface tension measurement , 2004 .

[15]  A. Neumann,et al.  Current perspectives in pulmonary surfactant--inhibition, enhancement and evaluation. , 2008, Biochimica et biophysica acta.

[16]  J. Goerke,et al.  Surface activity of rabbit pulmonary surfactant subfractions at different concentrations in a captive bubble. , 1994, Journal of applied physiology.

[17]  A. Neumann,et al.  Simultaneous measurement of contact angle and surface tension using axisymmetric drop-shape analysis-no apex (ADSA-NA). , 2011, Langmuir : the ACS journal of surfaces and colloids.

[18]  A. Siegel,et al.  A robust comparison of biological shapes. , 1982, Biometrics.

[19]  E. Acosta,et al.  A double injection ADSA-CSD methodology for lung surfactant inhibition and reversal studies. , 2009, Colloids and surfaces. B, Biointerfaces.

[20]  Río,et al.  Axisymmetric Drop Shape Analysis: Computational Methods for the Measurement of Interfacial Properties from the Shape and Dimensions of Pendant and Sessile Drops. , 1997, Journal of colloid and interface science.

[21]  J. Montanero,et al.  Computational evaluation of the theoretical image fitting analysis—axisymmetric interfaces (TIFA-AI) method of measuring interfacial tension , 2007 .

[22]  Dongqing Li,et al.  Automation of axisymmetric drop shape analysis for measurements of interfacial tensions and contact angles , 1990 .

[23]  D. Mack,et al.  Surface hydrophobicity of the intestinal tract. , 1992, The American journal of physiology.

[24]  Patrik Hoffmann,et al.  A Snake-Based Approach to Accurate Determination of Both Contact Points and Contact Angles , 2006 .

[25]  N. Wüstneck,et al.  Surface dilatational behavior of pulmonary surfactant components spread on the surface of a pendant drop. 2. Dipalmitoyl phosphatidylcholine and surfactant protein B , 2002 .

[26]  A. Neumann,et al.  Methodology for high accuracy contact angle measurement. , 2009, Langmuir : the ACS journal of surfaces and colloids.

[27]  S. Hartland.  Axisymmetric fluid-liquid interfaces , 1976 .

[28]  E. J. Vega,et al.  Exploring the precision of backlight optical imaging in microfluidics close to the diffraction limit , 2011 .

[29]  D. Kwok,et al.  Measurement of contact angles from the maximum diameter of non-wetting drops by means of a modified axisymmetric drop shape analysis , 1991 .

[30]  S. Fordham.  On the calculation of surface tension from measurements of pendant drops , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[31]  W. Schoel,et al.  The captive bubble method for the evaluation of pulmonary surfactant: surface tension, area, and volume calculations. , 1994, Biochimica et biophysica acta.

[32]  E. Acosta,et al.  Mixed DPPC/DPPG monolayers at very high film compression. , 2009, Langmuir : the ACS journal of surfaces and colloids.

[33]  R. M. Prokop,et al.  An investigation of the compression rate dependence on the surface pressure-surface area isotherm for a dipalmitoyl phosphatidylcholine monolayer at the air/water interface , 1996 .

[34]  A. Neumann,et al.  Further development of Axisymmetric Drop Shape Analysis-captive bubble for pulmonary surfactant related studies. , 2004, Biochimica et biophysica acta.

[35]  L. Walker,et al.  A non-gradient based algorithm for the determination of surface tension from a pendant drop: application to low Bond number drop shapes. , 2009, Journal of colloid and interface science.

[36]  B. Blaisdell.  The Physical Properties of Fluid Interfaces of Large Radius of Curvature. I. Integration of LaPlace's Equation for the Equilibrium Meridian of a Fluid Drop of Axial Symmetry in a Gravitational Field. Numerical Integration and Tables for Sessile Drops of M , 1940 .

[37]  James W. Jennings,et al.  An efficient method for the determination of interfacial tensions from drop profiles , 1988 .

[38]  E. Acosta,et al.  Effect of humidity on lung surfactant films subjected to dynamic compression/expansion cycles , 2007, Respiratory Physiology & Neurobiology.

[39]  P. Laplace,et al.  Traité de mécanique céleste , 1967 .

[40]  E. Acosta,et al.  Effect of surfactant concentration, compression ratio and compression rate on the surface activity and dynamic properties of a lung surfactant. , 2012, Biochimica et biophysica acta.

[41]  Ali Kalantarian,et al.  Accuracy of surface tension measurement from drop shapes: the role of image analysis. , 2013, Advances in Colloid and Interface Science.

[42]  C. Teitelboim.  RADIATION REACTION AS A RETARDED SELF-INTERACTION. , 1971 .

[43]  S. S. Susnar,et al.  Effect of electric fields on contact angle and surface tension of drops. , 2005, Journal of colloid and interface science.

[44]  A Wilhelm Neumann,et al.  Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces without use of apex coordinates. , 1983, Langmuir : the ACS journal of surfaces and colloids.

[45]  Alidad Amirfazli,et al.  A high-accuracy polynomial fitting approach to determine contact angles , 2003 .

[46]  C. E. Weatherburn,et al.  Differential Geometry of Three Dimensions , 2016 .

[47]  Chau Do,et al.  Automatic measurement of surface tension from noisy images using a component labeling method , 2007 .

[48]  H. Callen.  Thermodynamics and an Introduction to Thermostatistics , 1988 .

[49]  Z. Policova,et al.  Bacterial cell surface hydrophobicity properties in the mediation of in vitro adhesion by the rabbit enteric pathogen Escherichia coli strain RDEC-1. , 1989, The Journal of clinical investigation.

[50]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[51]  A. Neumann,et al.  Laplacian drop shapes and effect of random perturbations on accuracy of surface tension measurement for different drop constellations. , 2015, Advances in colloid and interface science.

[52]  Z. Policova,et al.  Design and accuracy of pendant drop methods for surface tension measurement , 2011 .

[53]  Yi Y. Zuo,et al.  Applied Surface Thermodynamics , 2010 .

[54]  Olivier Renaud,et al.  Robust analysis of the central tendency, simple and multiple regression and ANOVA: a step by step tutorial. , 2010 .

[55]  H. Girault,et al.  The measurement of interfacial tension of pendant drops using a video image profile digitizer , 1984 .

[56]  A. Olshan,et al.  Robust and least-squares orthogonal mapping: methods for the study of cephalofacial form and growth. , 1982, American journal of physical anthropology.

[57]  J. Montanero,et al.  A new method of image processing in the analysis of axisymmetric drop shapes , 2005 .

[58]  M Hoorfar,et al.  Recent progress in axisymmetric drop shape analysis (ADSA). , 2006, Advances in colloid and interface science.

[59]  F. Skinner,et al.  Contact angle measurements from the contact diameter of sessile drops by means of a modified axisymmetric drop shape analysis , 1989 .

[60]  A. Wilhelm Neumann,et al.  Determination of Surface Tension and Contact Angle from the Shapes of Axisymmetric Fluid Interfaces without Use of Apex Coordinates , 2006 .

[61]  J. A. Holgado-Terriza,et al.  Development of a new Langmuir-type pendant-drop film balance , 1999 .

[62]  S. Schürch,et al.  Torpor-associated fluctuations in surfactant activity in Gould's wattled bat. , 2002, Biochimica et biophysica acta.

[63]  C. Maze,et al.  Modifications of a non-linear regression technique used to calculate surface tension from sessile drops , 1971 .

[64]  Daniel Y. Kwok,et al.  Contact angle measurement and contact angle interpretation , 1999 .

[65]  Peter Gehr,et al.  Pulmonary surfactant: Surface properties and function of alveolar and airway surfactant , 1992 .

[66]  H. Haagsman,et al.  A spreading technique for forming film in a captive bubble. , 1998, Biophysical journal.

[67]  J. Goerke,et al.  Comparison of captive and pulsating bubble surfactometers with use of lung surfactants. , 1994, Journal of applied physiology.

[68]  M. Hoorfar,et al.  Constrained sessile drop as a new configuration to measure low surface tension in lung surfactant systems. , 2004, Journal of applied physiology.

[69]  A. W. Neumann,et al.  Computational evaluation of axisymmetric drop shape analysis-profile (ADSA-P) , 1992 .

[70]  A. Morita,et al.  Influence of drop volume on surface tension evaluated using the pendant drop method , 2002 .

[71]  A. Neumann,et al.  Drop size dependence of contact angles on two fluoropolymers , 2009 .

[72]  M. Hoorfar,et al.  Improvement of interfacial tension measurement using a captive bubble in conjunction with axisymmetric drop shape analysis (ADSA) , 2004 .

[73]  A. Neumann,et al.  Recent progress in the determination of solid surface tensions from contact angles. , 2007, Advances in colloid and interface science.

[74]  E. Buckingham.  On Physically Similar Systems; Illustrations of the Use of Dimensional Equations , 1914 .

[75]  J. E. Sohn,et al.  The Determination of Interfacial Tension by Video Image Processing of Pendant Fluid Drops. , 1987 .

[76]  Neumann,et al.  Simultaneous Determination of Surface Tension and Density of Polymer Melts Using Axisymmetric Drop Shape Analysis. , 1999, Journal of colloid and interface science.

[77]  Jinlong Yang,et al.  Automated Droplet Manipulation Using Closed-Loop Axisymmetric Drop Shape Analysis. , 2016, Langmuir : the ACS journal of surfaces and colloids.

[78]  A. Garg,et al.  A study of captive bubbles with axisymmetric drop shape analysis , 1998 .

[79]  Song,et al.  Determination of Interfacial Tension from the Profile of a Pendant Drop Using Computer-Aided Image Processing , 1996, Journal of colloid and interface science.

[80]  C. Maze,et al.  A non-linear regression method for calculating surface tension and contact angle from the shape of a sessile drop , 1969 .

[81]  S. Czinn,et al.  Surface properties of Helicobacter mustelae and ferret gastrointestinal mucosa. , 1996, Clinical and investigative medicine. Medecine clinique et experimentale.

[82]  R. M. Prokop,et al.  Manifestation of the liquid-expanded/liquid-condensed phase transition of a dipalmitoylphosphatidylcholine monolayer at the air-water interface , 1997 .

[83]  A Wilhelm Neumann,et al.  Total Gaussian curvature, drop shapes and the range of applicability of drop shape techniques. , 2014, Advances in colloid and interface science.

[84]  Y. Rotenberg,et al.  Free energy formulation of the theory of capillarity , 1985 .

[85]  J. Montanero,et al.  An analysis of the sensitivity of pendant drops and liquid bridges to measure the interfacial tension , 2007 .

[86]  Shi-Yow Lin,et al.  Systematic effects of bubble volume on the surface tension measured by pendant bubble profiles , 1996 .

[87]  T. Young.  III. An essay on the cohesion of fluids , 1805, Philosophical Transactions of the Royal Society of London.

[88]  H. M. Paynter,et al.  Simultaneous determination of contact angle and interfacial tension from sessile drop measurements , 1981 .

[89]  Song,et al.  Determination of Interfacial Tension from the Profile of a Pendant Drop Using Computer-Aided Image Processing , 1996, Journal of colloid and interface science.

[90]  J. A. Holgado-Terriza,et al.  Axisymmetric drop shape analysis as penetration Langmuir balance , 1999 .

[91]  S. Schürch,et al.  A captive bubble method reproduces the in situ behavior of lung surfactant monolayers. , 1989, Journal of applied physiology.

[92]  Z. Policova,et al.  Phase Transitions in Dipalmitoylphosphatidylcholine Monolayers. , 2016, Langmuir : the ACS journal of surfaces and colloids.

[93]  A. Wilhelm Neumann,et al.  Characterization of Virulence Factors of Mouse-Adapted Helicobacter pylori Strain SS1 and Effects on Gastric Hydrophobicity , 2001, Digestive Diseases and Sciences.

[94]  Y. Zuo,et al.  Biophysical influence of airborne carbon nanomaterials on natural pulmonary surfactant. , 2015, ACS nano.

[95]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[96]  E. Acosta,et al.  A dynamic compression–relaxation model for lung surfactants , 2010 .

[97]  A. Amirfazli,et al.  AUTOMATION OF THE AXISYMMETRIC DROP SHAPE ANALYSIS-DIAMETER FOR CONTACT ANGLE MEASUREMENTS , 1999 .

[98]  A. Shafiei,et al.  Chitosan Enhances the In Vitro Surface Activity of Dilute Lung Surfactant Preparations and Resists Albumin-Induced Inactivation , 2006, Pediatric Research.

[99]  J. F. Padday,et al.  The stability of axisymmetric menisci , 1973, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[100]  D. Kwok,et al.  Contact angle interpretation: re-evaluation of existing contact angle data , 2000 .

[101]  Dongqing Li,et al.  Axisymmetric drop shape analysis as a film balance , 1994 .