question: How is it that water increases friction in small amounts, but decreases it in large amounts?
comment: Water is both cohesive (it sticks to itself) and adhesive (it sticks to other things) but these effects are relatively weak and more noticeable on a small scale. When you lick your finger to turn a page, there is a thin layer of molecules which is adhering to your finger and the page, making them sticky. When you have a larger amount of water, like on a water slide, the molecules are still adhering to your butt and to the slide, but there are now bazillions more water molecules in between. The fluid dynamic of them sliding over each other, amplified by gravity pulling you downhill, overpowers the weak forces of cohesion and adhesion.
passages: New models are beginning to show how kinetic friction can be greater than static friction. Kinetic friction is now understood, in many cases, to be primarily caused by chemical bonding between the surfaces, rather than interlocking asperities; however, in many other cases roughness effects are dominant, for example in rubber to road friction. Surface roughness and contact area affect kinetic friction for micro- and nano-scale objects where surface area forces dominate inertial forces.
   If the overall motion of the bodies is constant, then an overall steady state may be attained. Here the state of each surface particle is varying in time, but the overall distribution can be constant. This is formalised by using a coordinate system that is moving along with the contact patch.
  
  Section::::Solution of rolling contact problems.:Cylinder rolling on a plane, the (2D) Carter-Fromm solution.
   Section::::Laws of dry friction.
  
  The elementary property of sliding (kinetic) friction were discovered by experiment in the 15th to 18th centuries and were expressed as three empirical laws:
  
  BULLET::::- Amontons' First Law: The force of friction is directly proportional to the applied load.
  
  BULLET::::- Amontons' Second Law: The force of friction is independent of the apparent area of contact.
  
  BULLET::::- Coulomb's Law of Friction: Kinetic friction is independent of the sliding velocity.
  
  Section::::Dry friction.
   BULLET::::- At the macroscopic scale, it is applied for the investigation of the motion of contacting bodies (see Contact dynamics). For instance the bouncing of a rubber ball on a surface depends on the frictional interaction at the contact interface. Here the total force versus indentation and lateral displacement are of main concern.
   The two fundamental ‘laws’ of friction were first published (in 1699) by Guillaume Amontons, with whose name they are now usually associated, they state that:
  
  BULLET::::1. the force of friction acting between two sliding surfaces is proportional to the load pressing the surfaces together
  
  BULLET::::2. the force of friction is independent of the apparent area of contact between the two surfaces.
   The two main approaches for modeling mechanical systems with unilateral contacts and friction are the regularized and the non-smooth approach. In the following, the two approaches are introduced using a simple example. Consider a block which can slide or stick on a table (see figure 1a). The motion of the block is described by the equation of motion, whereas the friction force is unknown (see figure 1b). In order to obtain the friction force, a separate force law must be specified which links the friction force to the associated velocity of the block. 
  
  Section::::Modeling.:Non-smooth approach.
   Section::::Dry friction.:Normal force.
   BULLET::::- In laminar flow, losses are proportional to fluid velocity, "V"; that velocity varies smoothly between the bulk of the fluid and the pipe surface, where it is zero. The roughness of the pipe surface influences neither the fluid flow nor the friction loss.
   BULLET::::2. Dynamic friction, which occurs between surfaces in relative motion.
  
  The study of friction phenomena is a predominantly empirical study and does not allow to reach precise results, but only to useful approximative conclusions. This inability to obtain a definite result is due to the extreme complexity of the phenomenon. If it's studied more closely it presents new elements, which, in turn, make the global description even more complex.
  
  Section::::Physics.:Friction.:Laws of friction.
  
  All the theories and studies on friction can be simplified into three main laws, which are valid in most cases:
   BULLET::::1. First of all, there is the deformation of the separate bodies in reaction to loads applied on their surfaces. This is the subject of general continuum mechanics. It depends largely on the geometry of the bodies and on their (constitutive) material behavior (e.g. elastic vs. plastic response, homogeneous vs. layered structure etc.).
   This subdivision of the contact area into stick (adhesion) and slip areas manifests itself a.o. in fretting wear. Note that wear occurs only where power is dissipated, which requires stress and local relative displacement (slip) between the two surfaces.
  
  The size and shape of the contact patch itself and of its adhesion and slip areas are generally unknown in advance. If these were known, then the elastic fields in the two bodies could be solved independently from each other and the problem would not be a contact problem anymore.
  
  Three different components can be distinguished in a contact problem.
   BULLET::::- Historically, it is a concern in aqueducts of all kinds, throughout human history. It is also relevant to sewer lines. Systematic study traces back to Henry Darcy, an aqueduct engineer.
  
  BULLET::::- Natural flows in river beds are important to human activity; friction loss in a stream bed has an effect on the height of the flow, particularly significant during flooding.
  
  BULLET::::- The economies of pipelines for petrochemical delivery are highly affected by friction loss. The Yamal–Europe pipeline carries methane at a volume flow rate of 32.3 × 10 m of gas per year, at Reynolds numbers greater than 50 × 10.
   BULLET::::- Finally, at the microscopic and nano-scales, contact mechanics is used to increase our understanding of tribological systems (e.g., investigate the origin of friction) and for the engineering of advanced devices like atomic force microscopes and MEMS devices.
  
  This page is mainly concerned with the second scale: getting basic insight in the stresses and deformations in and near the contact patch, without paying too much attention to the detailed mechanisms by which they come about.
  
  Section::::History.
  
  Several famous scientists,engineers and mathematician contributed to our understanding of friction.
   In many practical engineering applications, the fluid flow is more rapid, therefore turbulent rather than laminar. Under turbulent flow, the friction loss is found to be roughly proportional to the square of the flow velocity and inversely proportional to the pipe diameter, that is, the friction loss follows the phenomenological Darcy–Weisbach equation in which the "hydraulic slope" "S" can be expressed
  
  where we have introduced the Darcy friction factor "f" (but see "Confusion with the Fanning friction factor");
   The focus of research during the 20th century has been to understand the physical mechanisms behind friction. Frank Philip Bowden and David Tabor (1950) showed that, at a microscopic level, the actual area of contact between surfaces is a very small fraction of the apparent area. This actual area of contact, caused by asperities increases with pressure. The development of the atomic force microscope (ca. 1986) enabled scientists to study friction at the atomic scale, showing that, on that scale, dry friction is the product of the inter-surface shear stress and the contact area. These two discoveries explain Amonton's first law "(below)"; the macroscopic proportionality between normal force and static frictional force between dry surfaces.
   Consider a sphere that is pressed onto a plane (half space) and then shifted over the plane's surface. If the sphere and plane are idealised as rigid bodies, then contact would occur in just a single point, and the sphere would not move until the tangential force that is applied reaches the maximum friction force. Then it starts sliding over the surface until the applied force is reduced again.
   A drawback of the well-founded variational approaches is their large computation times. Therefore, many different approximate approaches were devised as well. Several well-known approximate theories for the rolling contact problem are Kalker’s FASTSIM approach, the Shen-Hedrick-Elkins formula, and Polach’s approach.
   Despite the relatively recent naming of the field of tribology, quantitative studies of friction can be traced as far back as 1493, when Leonardo da Vinci first noted the two fundamental ‘laws’ of friction. According to da Vinci, frictional resistance was the same for two different objects of the same weight but making contact over different widths and lengths. He also observed that the force needed to overcome friction doubles as weight doubles. However, da Vinci's findings remained unpublished in his notebooks.
   A more sophisticated approach is the non-smooth approach, which uses set-valued force laws to model mechanical systems with unilateral contacts and friction. Consider again the block which slides or sticks on the table. The associated set-valued friction law of type Sgn is depicted in figure 3. Regarding the sliding case, the friction force is given. Regarding the sticking case, the friction force is set-valued and determined according to an additional algebraic constraint. 
   In the 1970s, many numerical models were devised. Particularly variational approaches, such as those relying on Duvaut and Lion’s existence and uniqueness theories. Over time, these grew into finite element approaches for contact problems with general material models and geometries, and into half-space based approaches for so-called smooth-edged contact problems for linearly elastic materials. Models of the first category were presented by Laursen and by Wriggers. An example of the latter category is Kalker’s CONTACT model.
   Central in the analysis of frictional contact problems is the understanding that the stresses at the surface of each body are spatially varying. Consequently, the strains and deformations of the bodies are varying with position too. And the motion of particles of the contacting bodies can be different at different locations: in part of the contact patch particles of the opposing bodies may adhere (stick) to each other, whereas in other parts of the contact patch relative movement occurs. This local relative sliding is called micro-slip.
   BULLET::::2. Secondly, there is the overall motion of the bodies relative to each other. For instance the bodies can be at rest (statics) or approaching each other quickly (impact), and can be shifted (sliding) or rotated (rolling) over each other. These overall motions are generally studied in classical mechanics, see for instance multibody dynamics.
  
  BULLET::::3. Finally there are the processes at the contact interface: compression and adhesion in the direction perpendicular to the interface, and friction and micro-slip in the tangential directions.
   BULLET::::- Coefficients of Friction – tables of coefficients, plus many links
  
  BULLET::::- Measurement of friction power
  
  BULLET::::- Physclips: Mechanics with animations and video clips from the University of New South Wales
  
  BULLET::::- CRC Handbook of Chemistry & Physics – Values for Coefficient of Friction
  
  BULLET::::- Characteristic Phenomena in Conveyor Chain
  
  BULLET::::- Atomic-scale Friction Research and Education Synergy Hub (AFRESH) an Engineering Virtual Organization for the atomic-scale friction community to share, archive, link, and discuss data, knowledge and tools related to atomic-scale friction.
  
  BULLET::::- Coefficients of friction of various material pairs in atmosphere and vacuum.
   Section::::Contact forces.:Friction.
  
  Another important contact phenomenon is surface-to-surface friction, a force that impedes the relative motion of two surfaces in contact, or that of a body in a fluid. In this section we discuss surface-to-surface friction of two bodies in relative static contact or sliding contact. In the real world, friction is due to the imperfect microstructure of surfaces whose protrusions interlock into each other, generating reactive forces tangential to the surfaces.
   BULLET::::- At the intermediate scale, one is interested in the local stresses, strains and deformations of the contacting bodies in and near the contact area. For instance to derive or validate contact models at the macroscopic scale, or to investigate wear and damage of the contacting bodies' surfaces. Application areas of this scale are tire-pavement interaction, railway wheel-rail interaction, roller bearing analysis, etc.
  