SPREADING OF HEAVY DROPLETS .1. THEORY

We study the spreading of a (nonvolatile) wetting liquid on a flat solid surface. For small droplets, capillary forces drive the spreading and the shape of the spreading liquid is well known to be close to a spherical cap, with a radius R(t) ∼ t 1 10 (where t is the spreading time). We investigate here the opposite case of "heavy droplets" (R > κ{script}-1, the capillary length), for which gravity controls the process. The velocity of spreading may be understood from the rate of conversion of gravitational energy into viscous losses. The latter process can be divided into two contributions, one from the advancing wedge and one from the central part (squashed under gravity). Depending on which dissipation mechanism is dominant, two different shapes of the spreading droplet can be observed; (a) For R < Rc (Rc = κ{script}-1ln(1/κ{script}a) ∼ few centimeters, where a is the molecular length), the dissipation in the wedge is dominant. The drop has a quasistatic shape, with a large flat portion of thickness h = κ{script}-1θd (where θd is the dynamical contact angle). (b) For R ≫ Rc, the dissipation in the bulk is dominant. The drop is not flat; most of the profile is described by a self-similar solution first postulated by Lopez et al. (1) (except for a "foot" of size κ{script}-1 at the droplet edge). The growth of the drop radius obeys a power law R(t) ∼ t 1 8 only in the asymptotic regime of very large droplets R ≫ Rc. © 1991.