Hysteresis of Contact Angle of Sessile Droplets on Smooth Homogeneous Solid Substrates via Disjoining/Conjoining Pressure

Abstract

A theory of contact angle hysteresis of liquid droplets on smooth, homogeneous solid substrates is developed in terms of shape of disjoining/conjoining pressure isotherm and quasi-equilibrium phenomena. It is shown that all contact angles, θ, in the range r θ <θ< a θ , which are different from the unique equilibrium contact angle θ ≠ e θ , correspond to the state of slow "microscopic" advancing or receding motion of the liquid if e θ <θ< a θ or r θ <θ< e θ , respectively. This "microscopic" motion almost abruptly becomes fast "macroscopic"advancing or receding motion after the contact angle reaches the critical values a θ or r θ , correspondingly. The values of the static receding, r θ , and static advancing, a θ , contact angles in cylindrical capillaries were calculated earlier, based on the shape of disjoining/conjoining pressure isotherm. It is shown now that both advancing and receding contact angles of a droplet on a on smooth, homogeneous solid substrate (i) can be calculated based on shape of disjoining/conjoining pressure isotherm, (ii) both advancing and receding contact angles depend on the drop volume and are not unique characteristics of the liquid-solid system. The latter is different from advancing/receding contact angles in thin capillaries. It is shown also that the receding contact angle is much closer to equilibrium contact angle than the advancing contact angle. The latter conclusion is unexpected and is in a contradiction with commonly accepted view that the advancing contact angle can be taken as the first approximation for the equilibrium contact angle. The dependency of hysteresis contact angles on the drop volume has a direct experimental confirmation.

Hysteresis of the Contact Angle of a Meniscus Inside a Capillary with Smooth, Homogeneous Solid Walls

“…8b) is observed. The calculation results of advancing contact angle ~ 57°, receding contact angle ~ 9° agree with calculated data for droplet 27 and with experimental data 14,16 . Parameters of the disjoining/conjoining pressure isotherm used for these calculations are similar to that for glass surfaces 16 .…”

“…The functional dependence (12) coincides with the corresponding expression for the static advancing contact angle in the case of drops 13,27 . However, the magnitude h 1 in (12) has a different numeric value, so the static advancing contact angle for meniscus differs from the case of drops 27 .…”

“…Note, if the structural component is taken into account then the shape of the disjoining/conjoining pressure dependency become more sophisticated 27 . The structural component is included below in the disjoining/conjoining pressure isotherms.…”

“…In capillaries the identical disjoining pressure isotherm was used as in 27 , however, in the case of capillaries P e >0. It is necessary to increase P e rather substantially in the region of low h values to have a small variation of h. This leads to a growth of positive area under the isotherm and to a decrease of the equilibrium contact angle according to Eq.…”

Generalized Young Equation for Contact Angles of Cylindrical Nanodrops Within a Homogeneous and Smooth Regular Triangular Prism

“…Wettability is one of the most significant behaviors of solid surfaces and is commonly expressed using contact angles. [7][8][9][10] The most well-known Young equation 11 describing the contact angle Y of a liquid drop on a chemically homogeneous and smooth solid surface can be obtained as cos Y = SV − SL LV (1) where SV , SL and LV are the surface tensions of solidvapor, solid-liquid, and liquid-vapor interfaces, separately. The Eq.…”