1983/01/01 by L. M. HOCKING, L. M. Hocking · 2 citations
Engineering · Materials Science · Mathematics · #Boundary layer #Computer science #Drop (telecommunication) #Fluid Dynamics Simulations and Interactions #Fluid Dynamics and Thin Films #Mathematics #Mechanics #Physics #Similarity solution #Slip (aerodynamics) #Surface Modification and Superhydrophobicity #Thermodynamics
paper · doi:10.1093/qjmam/36.1.55
crossref issued 1983/01/01 · crossref published 1983/01/01 · crossref published-print 1983/01/01 · openalex publication_date 1983/01/01 · crossref created 2007/01/05 · crossref deposited 2017/08/24 · openalex created_date 2025/10/10 · crossref indexed 2026/07/29 · openalex updated_date 2026/07/30
Solutions are given for the spreading of a thin drop using lubrication theory. The relative importance of gravity to capillarity in the spreading is measured by the Bond number and all values of this number are covered. As usual when a moving contact line is present, a slip boundary condition is applied. For moderate and low Bond numbers the solution is found by matching three asymptotic expansions, and numerical results are given for the rate of spread as a function of the radius. A very simple solution is obtained in the special case of zero Bond number, when the spreading is by capillarity alone. When the Bond number is large, a similarity solution exists for the drop as a whole, but it fails near the edge of the drop and when the drop is close to its equilibrium position. It is shown here that the similarity solution can be completed by a solution valid near the edge and the approach to equilibrium is also discussed.