The spreading of liquid droplets on solid surfaces

Spreading and Infiltration of Inkjet-Printed Polymer Solution Droplets on a Porous Substrate

“…[3] are c = 54.1 ± 0.2, d = 0.04 ± 0.01, and n = 0.176 ± 0.008, resulting in the r s (t) dependence given by Eq. [7]: r s (t) = 54.1(0.04 + t) 0.176 . [7] R 2 for this fit is 0.96; 1.6 ms was chosen as the cutoff for the HPA 0.5 data simply because it is in this region that the spreading width plateaus; 0.8 ms was similarly chosen for the HPA 1.0 data because it is here that the droplet diameter begins to recede.…”

“…[7]: r s (t) = 54.1(0.04 + t) 0.176 . [7] R 2 for this fit is 0.96; 1.6 ms was chosen as the cutoff for the HPA 0.5 data simply because it is in this region that the spreading width plateaus; 0.8 ms was similarly chosen for the HPA 1.0 data because it is here that the droplet diameter begins to recede. The value of n (0.176) is clearly larger than the theoretical values predicted by bulk viscous force limited spreading dynamics (n = 0.1) or surface attachment limited dynamics (n = 0.14); however, it does fall well within the range of values reported in the literature.…”

An energy balance approach to modeling the hydrodynamically driven spreading of a liquid drop

“…It should be noted that the effect of the solid surface on which the drop is spreading, is accounted for in the above model by the solid -vapor and solid -liquid free energies, related to the equilibrium contact angle through Young's Eq. (11). Since the total mass of the drop, m as calculated from Eq.…”

“…Two major difficulties arise from the fluid mechanics approach: modeling the slip condition at the three-phase line and determining the relationship between the dynamic contact angle and the velocity of the advancing contact radius [6]. The surface physics approach has revealed that the spreading process is dependent largely on the interfacial tensions and contact angles as well as various chemical, physical and quantum mechanical parameters, which may or may not be possible to determine [11]. Models resulting from the combination of the two approaches have been successful, however they are generally largely dependent on empiricism to quantify the solution [11].…”

“…The surface physics approach has revealed that the spreading process is dependent largely on the interfacial tensions and contact angles as well as various chemical, physical and quantum mechanical parameters, which may or may not be possible to determine [11]. Models resulting from the combination of the two approaches have been successful, however they are generally largely dependent on empiricism to quantify the solution [11].…”