A quest to extend friction law into multiscale soft matter: experiment confronted with theory—a review

Abstract This topical review focuses on applying the basics of the classical Coulomb–Amontons (CA) law of friction to describe bioinspired articulating systems of extremely low values of coefficients of friction (COFs). A quest to extend the CA law is thoroughly formulated and the complex biotribological circumstances are readily drawn. A starting conceptual platform is established to address the quest as belonging more to biological physics than physical-biology contexts. First, an applied-physics viewpoint is unveiled by presenting theoretical, experimental, and computer-simulation methods, pointing uniquely to the fact that the biological, mainly cellular, contribution to the problem cannot be solved satisfactorily by employing physical laws and tools only. However, a consecutive and systematic way of modifying the COFs by carefully expanding these quantities into series is sketched. Second, this viewpoint is compared with a nonequilibrium-thermodynamics framework up to the far-from-equilibrium, dissipative-structure addressing regime. This complex picture is corroborated with a random-walk type approach, mostly pertinent to the nanoscale, with an emphasis placed on the ubiquitous quantity, which is the huge number of hydrogen ions resulting from anomalous hydronium ions transport in water, changing in terms of pH values the acid-base solution conditions. The overall complex framework that is described, capable of unveiling kinetic-friction conditions (associated virtually with the random-walk of hydrogen ions), is supposed to mimic, or compensate, the biotribological contribution envisaged in terms of cellular productivity of chondrocytes/synoviocytes. Such productivity is necessary to maintain the friction-lubrication phenomenon as shown up in articular (bio)devices (knees, hips, jaws, elbows, etc) at ultralow COF-levels of 10 −3 or less, and is greatly facilitated due to reduced overall dissipation and often nonlinear pathways at the meso- and nanoscale. In this way, a novel insight into the biotribological phenomenon of practical interest concerning versatile viscosupplementation and arthroscopic reparation strategies is gained.