Open AccessCapillary Torque on a Particle Rotating at an Interface
Author(s) -
Abhinav Naga,
Doris Vollmer,
HansJürgen Butt
Publication year - 2021
Publication title -
langmuir
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.042
H-Index - 333
eISSN - 1520-5827
pISSN - 0743-7463
DOI - 10.1021/acs.langmuir.1c00851
Subject(s) - capillary action , torque , surface tension , mechanics , capillary number , drop (telecommunication) , particle (ecology) , radius , contact angle , capillary surface , rotation (mathematics) , chemistry , classical mechanics , materials science , physics , composite material , thermodynamics , geometry , mechanical engineering , oceanography , computer security , mathematics , computer science , engineering , geology
Small particles attach to liquid-fluid interfaces due to capillary forces. The influence of rotation on the capillary force is largely unexplored, despite being relevant whenever particles roll at a liquid-fluid interface or on a moist solid. Here, we demonstrate that due to contact angle hysteresis, a particle needs to overcome a resistive capillary torque to rotate at an interface. We derive a general model for the capillary torque on a spherical particle. The capillary torque is given by M = γ RLk (cos Θ R - cos Θ A ), where γ is the interfacial tension, R is the radius of the particle, L is the diameter of the contact line, k = 24/π 3 is a geometrical constant, and Θ R and Θ A are the receding and advancing contact angles, respectively. The expression for the capillary torque (normalized by the radius of the particle) is equivalent to the expression for the friction force that a drop experiences when moving on a flat surface. Our theory predicts that capillary torque reduces the mobility of wet granular matter and prevents small (nano/micro) particles from rotating when they are in Brownian motion at an interface.