COMMENTARIES The Water Repellency of Water-bird Feathers ARIE M. RIJKE• Elowson (1984) analyzed the physico-chemical or, by incorporatingEq. 1: principles involved in the water repellency of textile fabrics.Based partly on measurementsof the feather Ws, = %a (1 + cos 0). (2a) structureof 14 water-bird species,she concludedthat Adam (1956) pointed out that if a surfaceis rough or the "textile model" cannot be applied reliably to porous,large contactangles may causedrops to en- feathers, and does not account for the spread-wing trap air in the hollows and interstices,thereby form- behavioral differencesamong water birds. I present ing additional air-liquid interfaces.This will causea a rebuttal to Elowson's critique centering on three considerableincrease in contact angle becausethe main issues. work of adhesion between liquid and air is essen- First,the physicalprinciples of the water repellen- tially negligible. The work of adhesionbetween a cy of porous surfaces,originally applied to treated liquid and a poroussurface, W•, is analogousto Eq.2: textile fabricsto explain the mechanismof water re- pellency,generally have been acceptedin the orni- Wps,= f•(3'• - %,) + (1 - f2)3'•, (3) thologicaland textile-processingliterature (Moilliet 1963;Clark 1969; Kennedy 1969, 1972; Siegfried et where f• is the area of solid-liquid interface and f• al. 1975;Mahoney 1984). Elowson argued that textile that of liquid-air interface per unit macroscopicsur- fabrics and feather substructure are too dissimilar to face area. Substitutionof Eqs. 1 and 2a then yields justify comparison.More specifically,Elowson con- (Cassie and Baxter 1944): sideredthe conditionof parallel, perfectly cylindri- cal rows of rami and barbules essential for the valid- cos0^ = f•cos0 - f•, (4) ity of the "textile model" to predict the water where 0a is now the apparent contact angle as in- repellencyof feathers.Because the rami and barbules creasedby the formation of air-liquid interfaces. are not circularin crosssection, Elowson implicitly Equation4 has been derived solely from basicphys- rejectedthe applicability of the physicsof porous ico-chemical principles without reference to param- surfacesto feather structures, and, indeed, stopped eterspertaining specifically to textile fabricsor feath- just short of stating that feather structureis not a er structure.In addition, the values of f• and f2 are relevant factorin the water repellencyof the feather determined only by the solid-liquid and liquid-air coat. interfaces per unit of macroscopicsurface areas, When a drop of liquid is placedon a smooth,solid without dictating the shape, curvature, or configu- surface, the liquid either spreads into a continuous ration of theseinterfaces. The validity of Eq. 4, there- film or covers a limited area, with the liquid taking fore, extendsto any poroussurface that is coveredby the shapeof part of a sphere. In the latter case,the liquid for finite values of 0, i.e. larger than about 10ø. equilibrium positionof dropsis determinedby: Thesepremises have been testedexperimentally and found to be correctby Cassieand Baxter(1944) and cos 0 = ('rs - 'rs•)/'r,a, (1) by Rijke (1965)using paraffinated(0 = 114ø) and un- where 0 is the contactangle betweenthe tangent to coated(0 = 0) stainlesssteel wire cagesand grids. For the curved water surfaceat the point of contactwith these specificmodels, composedof parallel rows of the solid surface,measured through the liquid. perfectly cylindrical wires, a simple calculationfor %•, and 3•aare the solid-air, solid-liquid, and liquid- the values of f• and f2 can be made: air interfacialenergies per unit area (Moilliet 1963). Alternatively, the work of adhesion(W), i.e. the f• = [•rr/(r + d)] [1 - (0/180ø)] work required to separatea unit area of solid-liquid f2 = 1 - r sin O/(r + d), (5) interface into a solid-air and a liquid-air interface, can be expressedas: where r is the radius of the circular wires with their Ws•= 3'• + %a- %•, (2) axes 2(r + d) apart. Similar expressionscan be cal- culated if the cross section of the wires are assumed to be elliptical, square,rectangular, etc. without af- fecting the validity of Eq. 4. • Department of Radiology, School of Medicine, The contribution of the wire structure to the values University of Virginia, Charlottesville,Virginia 22908 of f• and f2 is determinednot by the absolutevalue USA. of the radii of the wires and their distancesapart, but 140 January1987] Commentaries 141 by the ratio (r + d)/r only. Large values of this ratio ized in raindropstrickling down a dirty window pane, imply large f2 and small f• values,which increasethe but this is incorrectas gravitationalforce dispropor- apparent contactangle in the manner describedby tionately increasesthe advancingfront and decreases Eq.4 and are independentof the cross-sectionalshape the following tail of the drop. An advancingangle is of the wires. established in the initial contact of water with the In the caseof feathers, there is an additional reason feather surface and also when water penetrates be- why conformityto a circularcross section of the rami tween the rami and barbules and, therefore, deter- and barbules is not critical. When a drop of water is mines the water repellency and resistanceto water placed on a smoothsurface covered with a thin film penetration.The recedingangle determines the bead- of preening oil such as a rachisor a prepared micro- ing and eventualshedding of water drops. scopicslide, a contactangle of approximately 90ø is The ability of feathersto prevent water from pen- obtained. Inserting this value for the contact angle etrating to the skin is at least as important as water in Eq. 4 reducesthe first term on the right-hand side repellencyalone. A mathematicalexpression for the to zero or nearly so.As a result, the apparent contact pressurerequired to force water between the rami angle 0^ is essentiallydetermined by the value of f2 and barbules has been derived on premises similar alone. This conclusionis reachedwithout specifying to the ones referred to above (Baxter and Cassie 1945, the dimensions of the ramus-water or air-water in- Rijke 1970).Here, the absolutevalue of 2r and, there- terfaces.Its validity, therefore, extends to any such fore, the scale of the feather substructure come into interfaces irrespective of the cross-sectionalshape. effect, in addition to the ratio (r + d)/r and contact As in the caseof circular crosssections, it is easy to angle 0. Elowson claimed that the inherent assump- show that if the cross section of the rami would be tion of a zero pressuregradient acrossthe feather both continuousand elliptical, or square,or any in- surface at depth h is flawed becauseit ignores the termediate shape,the air-water interfacesunder zero considerablehydrostatic pressure, P = h x D x G (D hydrostatic pressurewould lie in the plane of the is the density of water and G is the gravitationalcon- long axes of the rami when 0 is 90ø. The term f2 is stant),to which the diving bird is exposed.This ar- then equal to d/(r + d), where 2r is the width of the gument, however, fails to take into accountthat the ramus as measured in the plane of the air-water in- air between the feather coat and skin, as well as air terface. The values of (r + d)/r range between 2.1 in the air sacs and respiratory tract, will be com- (penguins)and 6.0 (ducks).This meansthe apparent pressedso asto balancethe hydrostaticpressures sur- contact angle would vary between about 120ø and rounding the diving bird. Elowson'scase would be 150ø . This differencehas been advancedas the prox- valid if the air would communicate and the hydro- imate causeof a penguin'swet appearanceon the one staticpressures equilibrate, by meansof a tube for hand and the proverbial behavior of water drops on instance, with the atmospheric pressure above the a duck'sback on the other (Rijke 1970). water surface.The differencebetween Elowson'spre- I submit that Eq. 4 representsan expressionfor the sentation and a diving water bird is exactly why behavior of water drops on porous surfaces,deter- snorkelerscannot submerge much deeperthan 60 cm mined by contactangle and the relative areasof sol- below the water surface (provided the length of id-liquid and liquid-air interfaces,and basedon gen- snorkeling tube would permit this) without severe eral physico-chemical principles. When these respiratoryproblems, whereas pearl diversare known principlessubsequently are appliedto specificmodels, to function well at a depth of 20 m or more. such as feathers,certain simplifying assumptionsmay Finally, Elowson considered my 1968 and 1970 be helpful in estimatingthe values for f• and f2, but samplesizes too small and without sufficientelabo- thesedo not detractfrom the generalvalidity of Eq.4. ration on methods and measurements to permit a Second,in her discussionof water penetration and meaningful conclusion. In fact, as reported in the water repellency of the porous feather structure, 1970paper, feathers of at leastone speciesof 45 dif- Elowsonchose to distinguishbetween advancing and ferent aquaticfamilies were examinedand compared receding contactangles as two different entities, but with thoseof anotherspecimen or speciesof the same there is no physical basis for this. When a small family to ascertainthat the observedvalues were rep- quantity of water is added to a drop on a repellent resentative of the family. I included a total of 133 surface,the water-solidinterface will expandslightly different speciesand 426 different specimens.Of each and advancewith a contactangle that is larger than specimen,the dorsal and ventral aspectsof at least the recedingcontact angle observedwhen the water three breast feathers were examined for the dimen- is withdrawn. This difference reflectsany changesin sions of the rami and their distances apart, each at surfaceenergies from selectiveabsorption and con- nine different locations on the vane. The results were tamination of the water surfaceby selectivedissolu- compared with those of terrestrial birds. The data tion. It is usually small and unimportant in the ab- recently were analyzed statistically,and the differ- senceof absorptionor contamination,as for mercury encesbetwen the two groups were statisticallysig- drops on a glassslide.