. JOURNAL OF COLWID AND INTERFACE SCIENCE 164, 252-259 ( 1994) . The Effect of Solid Surface Heterogeneity and Roughness on the Contact Angle / Drop (Bubble) Size Relationship JAROSLAW DRELICHI AND JAN D. MILLER Department0/ Metallurgical Engineering, Universityo/Utah, Salt Lake City, Utah 84112 ~ Received August 12, 1993; accepted December 2,1993 AI The contact angle for varyingsizes of dropsand air bubbles are n.°t fully ~ecognized. Until ~ecentIy, t~e position was that was measured on clean, heterogeneous, and rough solidsurfaces. the hn.e tensIon phenomenon IS responsIble for the effect of A linear correlation of the cosine of the contact angle vs recip- dropslZeon ~ntacta~gle (7,9, 10)according to the modified rocalof the drop (bubble) base radius was obtained for the tet- Young equatIon, WhIchwas presented in the literature as radecane / water / quartz and air / water / polyethylene systems in follows ( I, 16): which pure single-component liquidsandfreshly prepared cI;an soli~ surfaces wereused. It was found that solid surface imper- 'Ysv -'YSL = 'YLV cos 8 + ~ .[1] fectlons, heterogeneity and/or roughness, affect the contact an- ' r gle/ drop(bubble) size relationship. Thechange in contact angle with bubble sizedepended on the extent of solid surface heter- 'YLV, 'YSV, and 'YSL are the interfacial tensions,the L,S, and ogeneity, as was observed for the tetradecane/water/methylated V subscriptscorresponding to liquid, solid, and vapor, re- quart.z system with varyingdegrees of quartz methylation.For spectively; 8 is the contact angle; 'YSLV is the line tension the aIr/water/polyethylene and air/water/gold systems, it was which is attributed to the excess energy associated with the found that the slope of a plot of cos8vs 1/r increased for rough three-phase contactline; r is the drop base radius. Equation surfaces whencompared to that for smoothsurfaces, and that [ I] is often expressed as these experimentaldata qualitatively support the modified - Wenzelequation which includes the line-tension term. @ 1994 Academic Press, Inc. COS 8 = cos 800 -~ , [2] r 'YLV INTRODUCTION where 8 = 800 for r -00, which indicates that there should The nature of attachment and wetting of small drops or be a linear relationship betweenthe cosine of the contact bubbles is important in many particle separation and/or angle (cos 8) and the reciprocal of the drop base radius (1/ stabilization processes, which involve the interaction of dis- r). The line tension can then be calculated from the slope persedor suspended phases. Such information is necessary, of a plot of cos 8 vs 1/ r. Unfortunately, values of the line for example, in flotation, agglomeration, nucleation and tension calculated from contact angle data for varying drop condensation, detergency, stabilization of emulsions and size are much larger, 10-6-10-5 N (7,9, 14), than those ., foams by fine particles, and otherprocesses involving wetting expected from theoretical considerationof the excess energy .phenomena in orderto predictthe appropriateexperimental at the triple junction, 10-12_10-10 N (17-19), or obtained ! conditions for efficient separation or stabilization of the par- using other experimental approaches,10-11-10-9 N (20- ticulate phases.Measurements of contact angles for large 23). Only Wallace and Schurch( 10) obtained much lower r drops or bubbles, with diameters of 2-5 mm, may lead to values of the line tension, about 10-8 N, from the contact incorrect conclusions, which makes the identification of op- angle / drop size relationship. Why suchlarge values for the timal separationor stabilization conditions difficult. line tension ( 10 -6-10 -5 N) ascalculated from contactangle / The effect of drop (bubble) sizeon contactangle remained drop size data for certain systems were obtained was not controversial for a long time. However,the technical liter- clear. Leja and Poling (24) postulated that gravitational ature, especially during recentyears, has provided evidence forcescould contribute to the contact angle / drop (bubble) that this effect exists and is significant( 1-15). Nevertheless, size relationship. Shanahan (25) theoretically analyzedthe the factorsaffecting the contact angle / drop size relationship effect of solid microdeformation on contact angle and pos- tulated that solid strain in the vicinity of the triple wetting I To whom correspondence should be addressed. line for a system with a deformablesolid may explain a vari- 0021-9797/94 $6.00 252 Copyright @ 1994 by Academic Press, Inc. Allrights of reproduction in any form reserved.