Supplementary Information

Wetting failure of hydrophilic surfaces promoted by surface roughness

Menghua Zhao1, Xiaopeng Chen1*, Qing Wang2

1 School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an, 710072, China

2 School of Computer Science, Northwestern Polytechnical University, Xi'an, 710072, China.

Correspondence andrequests for materialsshould be addressed to X. -P. Chen. ()

Capillary rise

If the liquid is more viscous than g3/2r5/2-1/2, the capillary tube imbibition process of the liquid from the initial contact to the final steady state can be divided into three stages: acceleration, linear and Washburn regimes. Acceleration regime (I) is the duration when the liquid is assumed purely accelerated. Regime II fully forms when t comes to 0. In this regime, the height of the meniscus rise varies as t2. In the linear regime, from 0to *, fully developed viscous boundary layer forms, and the inertia and capillary predominate. The constant velocity, c, is estimated as (2cosd/r)1/2. Later after *, viscosity prevails inertia and the meniscus rise falls into the traditional Washburn regime where z varies as t1/2. Accordingly,  for a given system is calculated as follows:

It must be mentioned that there are several aspects of the liquid intrusion into capillary valleys on a rough surface different from the capillary rise: 1.Capillary force’s contribution to valleys’ intrusion is much smaller than the capillary rise in that the liquid-solid contact area in valleys’ intrusion case is smaller than that of the capillary rise in which case the liquid wets the whole inner perimeter of a capillary. 2. The liquid flow outside the capillary valleys leads to stronger vortexeswhich will strengthen the inhibitive effect of sharp edges in a capillary rise situation. 3. Once the inlet of a capillary valley is sealed by the flow over the rough surface, the air pressure inside the valley will increase with the continuing intrusion and be another resistance which doesn’t exist in a free capillary tube rise. Therefore, since c is calculated based on a free capillary tube rise, it’s rather an under-estimation to ensure the gas sealing when the liquid film passes over rough surfaces.

Model parameters

By numerically solving the relationships1 among the wetting velocity(Vf), static contact angle(0),dynamics contact angle(d),surface tension(), liquid viscosity(L) and gas viscosity(air), the dependence of C, g0on lis revealed as follows:


Supplementary Data

TableS1: Surface roughness measured by a roughmeter. Ra is the arithmetical mean roughness, and Rz is the ten-point mean roughness.

Table S2: Surface characteristic length of valleys measured by the Laser Scanning Confocal Microscope.

Table S3: Static contact angle detected by a Contact Angle Meter, OCA15EC of DataPhysics Instruments, using the standard sessile drop method.

Table S4: Proportion of solid tops calculated through images caputured by aLaser Scanning Confocal Microscope.

Table S5: Calculation of whether the air will be sealed when the water film dashes across surfaces with the critical velocity, Vf_critical. c is the intruding velocity in the linear regime. Lavg, Ra,and Rzare averaged from Table S1, 2, respectively. Lavg is taken as the radius of capillary. Rz is taken as the wetting height.dand F(s) are the dynamic contact angle and shift factor2 in the capillary tube, respectively.

Reference

  1. Duez, C. Effets du mouillage en hydrodynamique macroscopique: traînée, impacts et ruissellement. Thesis, Université Claude Bernard - Lyon I(2008).
  2. Hoffman R L. A study of the advancing interface. I. Interface shape in liquid—gas systems. J. Colloid Interface Sci. 50, 228-241(1975).