Contact angle hysteresis: a review of fundamentals and applications

Contact angle hysteresis is an important physical phenomenon. It is omnipresent in nature and also plays a crucial role in various industrial processes. Despite its relevance, there is a lack of consensus on how to incorporate a description of contact angle hysteresis into physical models. To clarify this, starting from the basic definition of contact angle hysteresis, we introduce the formalism and models for implementing contact angle hysteresis into relevant physical phenomena. Furthermore, we explain the influence of the contact angle hysteresis in physical phenomena relevant for industrial applications such as sliding drops, coffee stain phenomenon (in general evaporative self-assembly), and curtain and wire coating techniques.

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

[2]  T. Senden,et al.  Wetting of Fibers , 2006 .

[3]  M. Shanahan,et al.  Influence of Evaporation on Contact Angle , 1995 .

[4]  P. Gennes,et al.  Shear-dependent slippage at a polymer/solid interface , 1992 .

[5]  J. Hyväluoma,et al.  Droplets on inclined rough surfaces , 2007, The European physical journal. E, Soft matter.

[6]  R. H. Dettre,et al.  Contact Angle Hysteresis. IV. Contact Angle Measurements on Heterogeneous Surfaces1 , 1965 .

[7]  Kenneth J. Ruschak,et al.  Hydrodynamic assist of dynamic wetting , 1994 .

[8]  Alidad Amirfazli,et al.  Understanding of sliding and contact angle results in tilted plate experiments , 2008 .

[9]  G. Grest,et al.  Atomistic Simulations of End-Linked Poly(dimethylsiloxane) Networks: Structure and Relaxation , 2004 .

[10]  L. Rayleigh On the Capillary Phenomena of Jets , 1879 .

[11]  D. Bonn,et al.  Wetting and Spreading , 2009 .

[12]  L. Scriven,et al.  Hydrodynamic Model of Steady Movement of a Solid / Liquid / Fluid Contact Line , 1971 .

[13]  L. Limat,et al.  Self-similar flow and contact line geometry at the rear of cornered drops , 2005 .

[14]  B. Carroll,et al.  Equilibrium conformations of liquid drops on thin cylinders under forces of capillarity. A theory for the roll-up process , 1986 .

[15]  Lan Dang,et al.  Drop retention force as a function of resting time. , 2008, Langmuir : the ACS journal of surfaces and colloids.

[16]  P. G. de Gennes,et al.  A model for contact angle hysteresis , 1984 .

[17]  Y. Shikhmurzaev Moving contact lines in liquid/liquid/solid systems , 1997, Journal of Fluid Mechanics.

[18]  P. Bahadur,et al.  Measurement of lateral adhesion forces at the interface between a liquid drop and a substrate. , 2009, Physical review letters.

[19]  Nagel,et al.  Contact line deposits in an evaporating drop , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  R. Chow,et al.  On the ability of drops or bubbles to stick to non-horizontal surfaces of solids , 1983, Journal of Fluid Mechanics.

[21]  H. B. Eral,et al.  Wetting of a drop on a sphere. , 2011, Langmuir : the ACS journal of surfaces and colloids.

[22]  Michael Müller,et al.  Comments on “An Essay on Contact Angle Measurements” by Strobel and Lyons , 2011 .

[23]  R. G. Cox The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow , 1986, Journal of Fluid Mechanics.

[24]  F. E. Bartell,et al.  Surface Roughness as Related to Hysteresis of Contact Angles. II. The Systems Paraffin–3 Molar Calcium Chloride Solution–Air and Paraffin–Glycerol–Air , 2002 .

[25]  S. Garoff,et al.  Using Vibrational Noise To Probe Energy Barriers Producing Contact Angle Hysteresis , 1996 .

[26]  A. Pisano,et al.  Coffee-ring effect-based three dimensional patterning of micro/nanoparticle assembly with a single droplet. , 2010, Langmuir : the ACS journal of surfaces and colloids.

[27]  Öpik Contact-Angle Hysteresis Caused by a Random Distribution of Weak Heterogeneities on a Solid Surface. , 2000, Journal of colloid and interface science.

[28]  F. E. Bartell,et al.  The Effect of Surface Roughness on Apparent Contact Angles and on Contact Angle Hysteresis. I. The system Paraffin–Water–Air , 1953 .

[29]  L. M. Hocking SLIDING AND SPREADING OF THIN TWO-DIMENSIONAL DROPS , 1981 .

[30]  B. Bhushan,et al.  Dynamic effects induced transition of droplets on biomimetic superhydrophobic surfaces. , 2009, Langmuir : the ACS journal of surfaces and colloids.

[31]  M. Cabrerizo-Vílchez,et al.  A new method for evaluating the most-stable contact angle using mechanical vibration , 2011 .

[32]  R. G. Cox The dynamics of the spreading of liquids on a solid surface. Part 2. Surfactants , 1986, Journal of Fluid Mechanics.

[33]  Chun Huh,et al.  Effects of surface roughness on wetting (theoretical) , 1977 .

[34]  D. Lohse,et al.  Rush-hour in evaporating coffee drops , 2011 .

[35]  Dieter 't Mannetje,et al.  Electrically assisted drop sliding on inclined planes , 2011 .

[36]  R. E. Ford,et al.  Studies at phase interfaces , 1966 .

[37]  R. Dullens,et al.  Surface effects on the demixing of colloid-polymer systems. , 2011, The journal of physical chemistry. B.

[38]  S. Siboni,et al.  The determination of a ‘stable-equilibrium’ contact angle on heterogeneous and rough surfaces , 2002 .

[39]  Abraham Marmur,et al.  When Wenzel and Cassie are right: reconciling local and global considerations. , 2009, Langmuir : the ACS journal of surfaces and colloids.

[40]  Rafael Tadmor,et al.  Line energy and the relation between advancing, receding, and young contact angles. , 2004, Langmuir : the ACS journal of surfaces and colloids.

[41]  T. Franosch,et al.  Glass transition in confined geometry. , 2010, Physical review letters.

[42]  J. Gardeniers,et al.  Charge Injection From Carbon Nanofibers Into Hexane Under Ambient Conditions , 2011, IEEE Transactions on Electron Devices.

[43]  J. Eggers,et al.  Film transitions of receding contact lines , 2007, 0706.2752.

[44]  H. Bodiguel,et al.  Stick-slip patterning at low capillary numbers for an evaporating colloidal suspension. , 2010, Langmuir : the ACS journal of surfaces and colloids.

[45]  G. D. Yarnold,et al.  A Theory of the Angle of Contact , 1949 .

[46]  R. Kofman,et al.  Ratchetlike motion of a shaken drop. , 2009, Physical review letters.

[47]  G. McHale,et al.  DETERMINATION OF THE RECEDING CONTACT ANGLE OF SESSILE DROPS ON POLYMER SURFACES BY EVAPORATION , 1999 .

[48]  Patrick M. Johnson,et al.  Directed self-assembly of colloidal dumbbells with an electric field. , 2010, Langmuir : the ACS journal of surfaces and colloids.

[49]  K. H. Kang,et al.  Analysis of electrowetting-driven spreading of a drop in air , 2010 .

[50]  H. Löwen,et al.  Crystalline multilayers of the confined Yukawa system , 2008, 0811.4763.

[51]  S. Vedantam,et al.  Phase field modeling of hysteresis in sessile drops. , 2007, Physical Review Letters.

[52]  B. Carroll The accurate measurement of contact angle, phase contact areas, drop volume, and Laplace excess pressure in drop-on-fiber systems , 1976 .

[53]  D. Lohse,et al.  Order-to-disorder transition in ring-shaped colloidal stains. , 2011, Physical review letters.

[54]  J. Eggers,et al.  Vibration-induced climbing of drops. , 2007, Physical review letters.

[55]  David Seveno,et al.  A molecular dynamics simulation of capillary imbibition , 2002 .

[56]  L. Schwartz,et al.  Contact angle hysteresis on heterogeneous surfaces , 1985 .

[57]  Robert A. Hayes,et al.  Dynamic Wetting and Dewetting of a Low-Energy Surface by Pure Liquids , 1998 .

[58]  Stephan Herminghaus,et al.  Interface profiles near three-phase contact lines in electric fields. , 2003, Physical review letters.

[59]  I. Saguy,et al.  Contact angle measurement on rough surfaces. , 2004, Journal of colloid and interface science.

[60]  R. Cerbino Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves , 2006 .

[61]  Abraham Marmur,et al.  Drops down the hill: theoretical study of limiting contact angles and the hysteresis range on a tilted plate. , 2005, Langmuir : the ACS journal of surfaces and colloids.

[62]  J. Eggers,et al.  Motion of a drop driven by substrate vibrations , 2009 .

[63]  The motion of a viscous drop sliding down a Hele-shaw cell , 1986 .

[64]  Joel Koplik,et al.  Molecular dynamics of fluid flow at solid surfaces , 1989 .

[65]  A. W. Neumann,et al.  Generalization of the classical theory of capillarity , 1977 .

[66]  F. Yubero,et al.  Comments on “An Essay on Contact Angle Measurements”: Determination of Surface Roughness and Modeling of the Wetting Behavior , 2011 .

[67]  O. Voinov Hydrodynamics of wetting , 1976 .

[68]  A. Jacobi,et al.  Retention forces and contact angles for critical liquid drops on non-horizontal surfaces. , 2006, Journal of colloid and interface science.

[69]  F. Palumbo,et al.  Comments Regarding ‘An Essay on Contact Angle Measurements’ , 2011 .

[70]  A. Marmur Contact-angle hysteresis on heterogeneous smooth surfaces: theoretical comparison of the captive bubble and drop methods , 1998 .

[71]  J. Baret,et al.  Electrowetting: from basics to applications , 2005 .

[72]  Shawn W. Walker,et al.  Electrowetting with contact line pinning: Computational modeling and comparisons with experiments , 2009 .

[73]  B. Carroll The equilibrium of liquid drops on smooth and rough circular cylinders , 1984 .

[74]  J. Bikerman Sliding of drops from surfaces of different roughnesses , 1950 .

[75]  Srikanth Vedantam,et al.  Comment on How Wenzel and Cassie Were Wrong by Gao and McCarthy. , 2007, Langmuir : the ACS journal of surfaces and colloids.

[76]  L. Limat,et al.  Receding contact lines: From sliding drops to immersion lithography , 2011 .

[77]  J. Li,et al.  Numerical simulation of moving contact line problems using a volume-of-fluid method , 2001 .

[78]  J. Lewis,et al.  Patterning colloidal films via evaporative lithography. , 2007, Physical review letters.

[79]  Bharat Bhushan,et al.  Liquid microdroplet sliding on hydrophobic surfaces in the presence of an electric field. , 2010, Langmuir : the ACS journal of surfaces and colloids.

[80]  R. Tadmor Approaches in wetting phenomena , 2011 .

[81]  J. Ralston,et al.  Dynamics of Partial Wetting and Dewetting in Well-Defined Systems , 2003 .

[82]  L. W. Schwartz,et al.  Effective slip in numerical calculations of moving-contact-line problems , 1992 .

[83]  France.,et al.  Droplet Spreading: Partial Wetting Regime Revisited , 1998, cond-mat/9810040.

[84]  Spreading dynamics of polymer nanodroplets. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[85]  D. v. On the ability of drops or bubbles to stick to non-horizontal surfaces of solids. Part 2. Small drops or bubbles having contact angles of arbitrary size , 1985, Journal of Fluid Mechanics.

[86]  Banavar,et al.  Molecular dynamics of Poiseuille flow and moving contact lines. , 1988, Physical review letters.

[87]  Y. Pomeau,et al.  Contact angle on heterogeneous surfaces: Weak heterogeneities , 1985 .

[88]  M. Cabrerizo-Vílchez,et al.  Comparison of the relaxation of sessile drops driven by harmonic and stochastic mechanical excitations. , 2011, Langmuir : the ACS journal of surfaces and colloids.

[89]  A. Lukyanov,et al.  Effect of flow field and geometry on the dynamic contact angle. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[90]  Edward Bormashenko,et al.  The rigorous derivation of Young, Cassie–Baxter and Wenzel equations and the analysis of the contact angle hysteresis phenomenon , 2008 .

[91]  M. Strobel,et al.  An Essay on Contact Angle Measurements , 2011 .

[92]  Ho-Young Kim,et al.  Sliding of liquid drops down an inclined solid surface. , 2002, Journal of colloid and interface science.

[93]  P. Petrov,et al.  A combined molecular-hydrodynamic approach to wetting kinetics , 1992 .

[94]  Matthias Wessling,et al.  Carbon nanofibers in catalytic membrane microreactors , 2011 .

[95]  Richard G. Weiss,et al.  Molecular Gels: Materials with Self-Assembled Fibrillar Networks , 2005 .

[96]  A. Marmur,et al.  Comparison of sessile drop and captive bubble methods on rough homogeneous surfaces: a numerical study. , 2011, Langmuir : the ACS journal of surfaces and colloids.

[97]  P. Gennes Wetting: statics and dynamics , 1985 .

[98]  Martin Brinkmann,et al.  Drops on functional fibers: from barrels to clamshells and back , 2011 .

[99]  X. F. Yang Equilibrium contact angle and intrinsic wetting hysteresis , 1995 .

[100]  T. Blake,et al.  The possibility of different time scales in the dynamics of pore imbibition. , 2004, Journal of colloid and interface science.

[101]  T. J. McCarthy,et al.  How Wenzel and cassie were wrong. , 2007, Langmuir : the ACS journal of surfaces and colloids.

[102]  C. Furmidge,et al.  Studies at phase interfaces. I. The sliding of liquid drops on solid surfaces and a theory for spray retention , 1962 .

[103]  Robbins,et al.  Simulations of contact-line motion: Slip and the dynamic contact angle. , 1989, Physical review letters.

[104]  Lc Gao,et al.  Reply to "Comment on How Wenzel and Cassie Were Wrong by Gao and McCarthy" , 2007 .

[105]  C. Sykes,et al.  Average spreading parameter on heterogeneous surfaces , 1994 .

[106]  B. Bhushan,et al.  Improved nanobubble immobility induced by surface structures on hydrophobic surfaces. , 2009, Langmuir : the ACS journal of surfaces and colloids.

[107]  P. Hänggi,et al.  Depinning of three-dimensional drops from wettability defects , 2008, 0811.2918.

[108]  Extrand A Thermodynamic Model for Contact Angle Hysteresis. , 1998, Journal of colloid and interface science.

[109]  T. Blake,et al.  Experimental evidence of nonlocal hydrodynamic influence on the dynamic contact angle , 1999 .

[110]  T. Dupont,et al.  Capillary flow as the cause of ring stains from dried liquid drops , 1997, Nature.

[111]  David Quéré,et al.  FLUID COATING ON A FIBER , 1999 .

[112]  H. Löwen,et al.  Multilayered crystals of macroions under slit confinement , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[113]  H. Hölscher,et al.  Friction at atomic-scale surface steps: experiment and theory. , 2008, Physical review letters.

[114]  W. Nelson,et al.  Dynamic contact angles and hysteresis under electrowetting-on-dielectric. , 2011, Langmuir : the ACS journal of surfaces and colloids.

[115]  M. Cabrerizo-Vílchez,et al.  A new model to estimate the Young contact angle from contact angle hysteresis measurements , 2010 .

[116]  Robert N. Wenzel,et al.  Surface Roughness and Contact Angle. , 1949 .

[117]  G. McKinley,et al.  Assessing the accuracy of contact angle measurements for sessile drops on liquid-repellent surfaces. , 2011, Langmuir : the ACS journal of surfaces and colloids.

[118]  C. Extrand,et al.  Liquid Drops on an Inclined Plane: The Relation between Contact Angles, Drop Shape, and Retentive Force , 1995 .

[119]  R. Ganapathy,et al.  Confined glassy dynamics at grain boundaries in colloidal crystals , 2011, Proceedings of the National Academy of Sciences.

[120]  Michael H.G. Duits,et al.  Suppressing the coffee stain effect: how to control colloidal self-assembly in evaporating drops using electrowetting , 2011 .

[121]  R. N. Wenzel RESISTANCE OF SOLID SURFACES TO WETTING BY WATER , 1936 .

[122]  T. Blake,et al.  An Investigation of Electrostatic Assist in Dynamic Wetting , 2000 .

[123]  M. Dijkstra,et al.  Phase behavior and structure of a new colloidal model system of bowl-shaped particles. , 2010, Nano letters.

[124]  R. H. Dettre,et al.  Contact Angle Hysteresis: I. Study of an Idealized Rough Surface , 1964 .

[125]  T. Blake,et al.  Wetting at high capillary numbers. , 2004, Journal of colloid and interface science.

[126]  K. Sefiane,et al.  Advancing and receding contact lines on patterned structured surfaces , 2010 .

[127]  T. Blake,et al.  Kinetics of displacement , 1969 .

[128]  Z. Barkay,et al.  Contact angle hysteresis on polymer substrates established with various experimental techniques, its interpretation, and quantitative characterization. , 2008, Langmuir : the ACS journal of surfaces and colloids.

[129]  Matthias Wessling,et al.  Porous ceramic mesoreactors: A new approach for gas–liquid contacting in multiphase microreaction technology , 2011 .

[130]  J. Long,et al.  Thermodynamic modeling of contact angles on rough, heterogeneous surfaces. , 2005, Advances in colloid and interface science.

[131]  Frieder Mugele,et al.  How to make sticky surfaces slippery: Contact angle hysteresis in electrowetting with alternating voltage , 2008 .