Thermodynamic modeling of contact angles on rough, heterogeneous surfaces

Theoretical modelling for contact angle hysteresis carried out to date has been mostly limited to several idealized surface configurations, either rough or heterogeneous surfaces. This paper presents a preliminary study on the thermodynamics of contact angles on rough and heterogeneous surfaces by employing the principle of minimum free energy and the concept of liquid front. Based on a two-dimensional regular model surface, a set of relations were obtained, which correlate advancing, receding and system equilibrium contact angles to surface topography, roughness and heterogeneity. It was found that system equilibrium contact angles (theta(ES)) can be expressed as a function of surface roughness factor (delta) and the Cassie contact angle (theta(C)): costheta(ES) = deltacostheta(C). This expression can be reduced to the classical Wenzel equation.: theta(ES) = theta(W) for rough but homogeneous surfaces, and the classical Cassie equation theta(ES) = theta(C) for heterogeneous but smooth surfaces. A non-dimensional parameter called surface feature factor (omega) was proposed to classify surfaces into three categories (types): roughness-dominated, heterogeneity-dominated and mixed-rough-heterogeneous. The prediction of advancing and receding contact angles of a surface is dependent on which category the surface belongs to. The thermodynamic analysis of contact angle hysteresis was further extended from the regular model surface to irregular surfaces; consistent results were obtained. The current model not only agrees well with the models previously studied by other researchers for idealized surfaces, but also explores more possibilities to explain the reported experimental results/observations that most existing theories could not explain.     

Mercury Porosimetry: Contact Angle Hysteresis of Materials with Controlled Pore Structure

Mercury Porosimetry (MP) hysteresis is a commonly observed phenomenon in which mercury retention disguises further the overall hysteresis picture. This article introduces a new interpretation of the MP hysteresis based on the combined effect of pore structure networking and mercury contact angle variation occurring between the mercury penetration and retraction operations. To distinguish the contribution of each factor the following investigations were carried out. Nitrogen sorption (NP) and MP experiments were performed on samples of an anodic aluminum membrane and the results were interpreted in terms of the Corrugated Pore Structure Model (CPSM), i.e., CPSM-Nitrogen and CPSM-Mercury models, respectively. The simulation of the observed hysteresis data using the CPSM model enabled the evaluation of an identical for the two methods intrinsic pore size distribution (PSD) and cumulative surface area in perfect agreement with the respective BET value. Additionally, the CPSM analysis of data resulted in the evaluation of mercury contact angles, i.e., θ(p)=143 degrees and θ(r)=101.7 degrees for the MP penetration and retraction branches of the hysteresis loop, respectively. Moreover, CPSM-Mercury simulations of literature MP hysteresis data, valid for controlled-pore glasses and nuclepore membranes, led to the evaluation of contact angles, i.e., glasses: θ(p)=143 degrees, θ(r)=100.5-107.5 degrees and nuclepore: θ(p)=143 degrees, θ(r)=118- 121 degrees. The latter values are comparable with relevant literature data and approximate those determined for the anodic aluminum membrane. The CPSM model employed herein proved to be a flexible and reliable model for simulating the pertinent hysteresis loops by combining pore networking and contact angle hysteresis phenomena. Copyright 2001 Academic Press.     

Contact-Angle Hysteresis Caused by a Random Distribution of Weak Heterogeneities on a Solid Surface

A model according to which contact-angle hysteresis arises as the result of a random distribution of irregularities on the solid surface is investigated on the basis of probability theory. An estimate is obtained of the mathematical expectation of the number of stable equilibria when the effective angle between the liquid-gas surface and the solid surface with which the liquid is in contact deviates from the value, say theta(0), which would obtain if the solid surface were uniform, i.e., free from irregularities. It is found that when the effective contact angle deviates from theta(0) by less than a critical value, then the expected number of stable equilibria increases exponentially with the length of the contact line; therefore such a contact angle can occur under static conditions. But if the deviation of the contact angle from theta(0) exceeds the critical value, then the expected number of stable equilibria decreases exponentially with the length of the contact line, so a stable equilibrium is not possible for a macroscopic length of the contact line. The method is applicable only if the random deviations of the spreading power (defined as the solid-gas surface tension minus the sum of the liquid-gas and liquid-solid surface tensions) from its average are sufficiently small. It is found that the critical deviation of the contact angle from theta(0) is, apart from a slowly varying logarithmic factor, proportional to H(2)rho(s), where H is a measure of the amplitude of the surface irregularities and rho(s) is the surface density (i.e., number per unit area) of the irregularities. This qualitative feature agrees with the results previously obtained by several other authors, and, moreover, there is a surprisingly close agreement of the proportionality factor with the results of some earlier work in which the method of statistical analysis was much less elaborate than here. The effect of the logarithmic factor is to make the critical deviation of the contact angle increase more slowly than the first power of H(2)rho(s), and this is also in qualitative agreement with some earlier work. Copyright 2000 Academic Press.     

Line energy and the relation between advancing, receding, and young contact angles

The line energy associated with the triple phase contact line is a function of local surface defects (chemical and topographical); however, it can still be calculated from the advancing and receding contact angles to which those defects give rise. In this study an expression for the line energy associated with the triple phase contact line is developed. The expression relates the line energy to the drop volume, the interfacial energies, and the actual contact angle (be it advancing, receding, or in between). From the expression we can back calculate the equilibrium Young contact angle, theta0, as a function of the maximal advancing, thetaA, and minimal receding, thetaR, contact angles. To keep a certain maximal hysteresis between advancing and receding angles, different line energies are required depending on the three interfacial energies and the drop's volume V. We learn from the obtained expressions that the hysteresis is determined by some dimensionless parameter, K, which is some normalized line energy. The value of K required to keep a constant hysteresis (thetaA-thetaR) rises to infinity as we get closer to theta0 = 90 degrees.     

Retention forces and contact angles for critical liquid drops on non-horizontal surfaces

Retention forces and drop parameters are investigated for drops on the verge of sliding on vertical and inclined surfaces. Using earlier observations of drop geometry, the retentive-force factor relating surface-tension forces to contact-angle hysteresis is reliably determined. The retention force for a drop is found to be insignificantly affected by the aspect ratio of its contour. The maximum size of a drop is predicted with good accuracy, based on the two-circle method for approximating shapes of drops. The Bond number of a critical drop is found to be constant for a given surface and liquid. A general relation is proposed between the characteristic advancing and receding contact angles. The relation is supported by a large set of contact-angle data. In the absence of theta R data, the relation allows estimating the receding contact angle and the critical drop size, using only the advancing angle.     

Ink-bottle effect in mercury intrusion porosimetry of cement-based materials

Mercury intrusion porosimetry (MIP) is a widely used method for studying porous materials, in particular, cement-based materials. The usual interpretation of such measurements is based on certain assumptions. One of these is that each pore is connected to the sample surface directly or through larger pores. Pores not meeting this assumption are called ink-bottle pores. The effect that sample size has on the MIP characteristics of concrete samples, like the ink-bottle effect and hysteresis, was studied by measuring additional extrusion and intrusion cycles. In order to characterize the extrusion and ink-bottle behavior, the amount of entrapped mercury chi(p) was estimated. Superimposition of extrusion and second intrusion curves is achieved if the contact angle theta is adjusted from theta(i), the intrusion contact angle, to theta(e), the extrusion contact angle. The threshold radius is often assumed to be a dominant pore radius, yet in this study the entrapped mercury content shows no evidence for the presence of a dominant pore radius. Even if characteristic properties of cement-based materials can be estimated with MIP, comparison of results is rendered difficult by the significant effects of sample preparation techniques and sample size and the ink-bottle effect due to randomly present air bubbles.     

The "lotus effect" explained: two reasons why two length scales of topography are important

Surfaces containing 4 x 8 x 40 microm staggered rhombus posts were hydrophobized using two methods. One, using a dimethyldichlorosilane reaction in the vapor phase, introduces a smooth modified layer, and the other, a solution reaction using methyltrichlorosilane, imparts a second (nanoscopic) length scale of topography. The smooth modified surface exhibits contact angles of thetaA/thetaR = 176 degrees /156 degrees . Arguments are made that the pinning of the receding contact line by the post tops (with thetaA/thetaR = 104 degrees /103 degrees ) is responsible for the hysteresis. The second level of topography raises the contact angles of the post tops and the macroscopic sample to theta(A)/theta(R) = >176 degrees />176 degrees and eliminates hysteresis. The increase in Laplace pressure due to the increase in the advancing contact angle of the post tops is a second reason that two length scales of topography are important.     

Water microdroplets on molecularly tailored surfaces: correlation between wetting hysteresis and evaporation mode switching

The evaporation of water microdroplets from solid surfaces was studied using digital contact angle analysis techniques. An inclusive trend for the evaporation process, that is, a switch from the initial constant contact area to the subsequent constant contact angle mode was observed for all surfaces examined, including mixed self-assembled monolayers (SAMs) on gold and "conventional" surfaces such as silicon wafers, polycarbonate, and Teflon. More importantly, it has been shown that the change in contact angle during the evaporation process (i.e., evaporation hysteresis, delta theta(evap), the difference between the initial and "equilibrated" contact angle) correlates well with the wetting hysteresis determined directly (i.e., measuring the advancing and receding contact angles on these surfaces by changing the drop volume). The comparison between mixed SAM surfaces and conventional solids revealed that the evaporation/wetting hysteresis is dominated by the roughness (from nanometer to micrometer scale) rather than the chemical heterogeneity of the surface. The evaporation rates of water microdroplets on these surfaces were also monitored and modeled.     

Wettability of Microstructured Hydrophobic Sol-Gel Coatings

The formation of appropriate surface patterns on hydrophobic surfaces leads to a general change in their wettability and the contact angle increases substantially. Such coatings are of great technical interest, especially if aqueous media are concerned as in the prevention of ice-adhesion. For this reason various fluorine containing nanocomposite coatings have been developed by sol-gel processing.The morphology of these hydrophobic surfaces has been controlled by varying the content of silica particles regarding size, degree of aggregation, and concentration. The wettability is characterized by the measurement of dynamic contact angles against water. The complete range of different wettability regimes is accessible, i.e. smooth surfaces (both low advancing contact angle and hysteresis between advancing and receding contact angle), surfaces within the Wenzel regime (high advancing contact angle and hysteresis), and superhydrophobic surfaces (high advancing contact angle and low hysteresis). The wettability is correlated with the surface roughness as determined using a profilometer or AFM.The wettability of superhydrophobic surfaces is greatly dependent on the surface tension of the liquid. By comparison of the tiltangle _t of a smooth and a superhydrophobic surface, a critical surface tension _c is identified, where _t (smooth surface) = _t (microstructured surface). The microstructured surface provides a better run-off of liquids _lg > _c 55 mN·m^–1.     

Anisotropic wetting characteristics on submicrometer-scale periodic grooved surface

Submicrometer-scale periodic structures consisting of parallel grooves were prepared on azobenzene-containing multiarm star polymer films by laser interference. The wetting characteristics on the patterned surfaces were studied by contact angle measurements. Macroscopic distortion of water drops was found on such small-scale surface structures, and the contact angles measured from the direction parallel to the grooves were larger than those measured from the perpendicular direction. A thermodynamic model was developed to calculate the change in the surface free energy as a function of the instantaneous contact angle when the three-phase contact line (TPCL) moves along the two orthogonal directions. It was found that the fluctuations, i.e., energy barriers, on the energy versus contact angle curves are crucial to the analysis of wetting anisotropy and contact angle hysteresis. The calculated advancing and receding contact angles from the energy versus contact angle curves were in good agreement with those measured experimentally. Furthermore, with the groove depth increasing, both the degree of wetting anisotropy and the contact angle hysteresis perpendicular to the grooves increased as a result of the increase in the energy barrier. The theoretical critical value of the groove depth, above which the anisotropic wetting appears, was determined to be 16 nm for the grooved surface with a wavelength of 396 nm. On the other hand, the effect of the groove wavelength on the contact angle hysteresis perpendicular to the grooves was also interpreted on the basis of the thermodynamic model. That is, with the wavelength decreasing, the contact angle hysteresis increased due to the increase in the number of energy barriers. These results may provide theoretical evidence for the design and application of anisotropic wetting surface.     

Removal of induced nanobubbles from water/graphite interfaces by partial degassing

Nanobubbles at an interface between a hydrophobic solid and water have a wide range of implications, but the evidence for their existence is still being debated. Here we artificially induced nanobubbles on freshly cleaved HOPG substrates in water using the protocol developed previously and subjected the system to moderate levels of degassing (approximately 0.1 atm for 0.5 to 3 h). The AFM images after the partial degassing revealed that some nanobubbles had coalesced and detached from the substrate because of buoyancy, whereas others apparently remained unaffected. The size and spatial distributions of the nanobubbles after the partial degassing suggest that there is a critical size for a nanobubble above which it may grow. The contact angle of water next to nanobubbles (approximately 160 degrees) is much larger than the advancing contact angle of a macroscopic water droplet on the same substrate (approximately 80 degrees) both before and after the partial degassing and concomitant growth and shrinkage of the nanobubbles. The contact angle of a nanobubble also remained unchanged as the nanobubble was moved along the substrate by the AFM tip. The apparent lack of contact angle hysteresis in the nanobubble systems may suggest that the very large contact angle may correspond to a local minimum of the free-energy landscape.     

Wetting transition on hydrophobic surfaces covered by polyelectrolyte brushes

We study the wetting by water of complex "hydrophobic-hydrophilic" surfaces made of a hydrophobic substrate covered by a hydrophilic polymer brush. Polystyrene (PS) substrates covered with polystyrene- block-poly(acrylic acid) PS- b-PAA diblock copolymer layers were fabricated by Langmuir-Schaefer depositions and analyzed by atomic force microscopy (AFM) and ellipsometry. On bare PS substrate, we measured advancing angles theta A = 93 +/- 1 degrees and receding angles theta R = 81 +/- 1 degrees . On PS covered with poorly anchored PS- b-PAA layers, we observed large contact angle hysteresis, theta A approximately 90 degrees and theta R approximately 0 degrees , that we attributed to nanometric scale dewetting of the PS- b-PAA layers. On well-anchored PS- b-PAA layers that form homogeneous PAA brushes, a wetting transition from partial to total wetting occurs versus the amount deposited: both theta A and theta R decrease close to zero. A model is proposed, based on the Young-Dupre equation, that takes into account the interfacial pressure of the brush Pi, which was determined experimentally, and the free energy of hydration of the polyelectrolyte monomers Delta G PAA (hyd), which is the only fitting parameter. With Delta G PAA (hyd) approximately -1300 J/mol, the model renders the wetting transition for all samples and explains why the wetting transition depends mainly on the average thickness of the brush and weakly on the length of PAA chains.     

Study of the advancing and receding contact angles: liquid sorption as a cause of contact angle hysteresis

Two types of experiments were used to study the behavior of both advancing and receding contact angles, namely the dynamic one-cycle contact angle (DOCA) and the dynamic cycling contact angle (DCCA) experiments. For the preliminary study, DOCA measurements of different liquids on different solids were performed using an automated axisymmetric drop shape analysis-profile (ADSA-P). From these experimental results, four patterns of receding contact angle were observed: (1) time-dependent receding contact angle; (2) constant receding contact angle; (3) 'stick/slip'; (4) no receding contact angle. For the purpose of illustration, results from four different solid surfaces are shown. These solids are: FC-732-coated surface; poly(methyl methacrylate/n-butyl methacrylate) [P(MMA/nBMA)]; poly(lactic acid) (DL-PLA); and poly(lactic/glycolic acid) 50/50 (DL-PLGA 50/50). Since most of the surfaces in our studies exhibit time dependence in the receding contact angle, a more extended study was conducted using only FC-732-coated surfaces to better understand the possible causes of decreasing receding contact angle and contact angle hysteresis. Contact angle measurements of 21 liquids from two homologous series (i.e. n-alkanes and 1-alcohols) and octamethylcyclotetrasiloxane (OCMTS) on FC-732-coated surfaces were performed. It is apparent that the contact angle hysteresis decreases with the chain length of the liquid. It was found that the receding contact angle equals the advancing angle when the alkane molecules are infinitely large. These results strongly suggest that the chain length and size of the liquid molecule could contribute to contact angle hysteresis phenomena. Furthermore, DCCA measurements of six liquids from the two homologous series on FC-732-coated surfaces were performed. With these experimental results, one can construe that the time dependence of contact angle hysteresis on relatively smooth and homogeneous surfaces is mainly caused by liquid retention/sorption. The results also suggested that the contact angle hysteresis will eventually approach a steady state, where the rate of liquid retention-evaporation or sorption process would balance out each other. If the existence of contact angle hysteresis can be attributed to liquid sorption/retention, one should only use the advancing contact angles (measured on a dry surface) in conjunction with Young's equation for surface energetic calculations.     

Size-selective sliding of sessile drops on a slightly inclined plane using low-frequency AC electrowetting

When placed on an inclined solid plane, drops often stick to the solid surface due to pinning forces caused by contact angle hysteresis. When the drop size or the plane's incline angle is small, the drop is difficult to slide due to a decrease in gravitational force. Here we demonstrate that small drops (0.4-9 μL) on a slightly inclined plane (~12°, Teflon and parylene-C surface) can be mobilized through patterned electrodes by applying low-frequency ac electrowetting under 400 Hz (110-180 V(rms)), which has a mechanism different from that of the high-frequency ac method that induces sliding by reducing contact angle hysteresis. We attribute the sliding motion of our method to a combination of contact angle hysteresis and interfacial oscillation driven by ac electrowetting instead of the minimization of contact angle hysteresis at a high frequency. We investigated the effects of ac frequency on the sliding motion and terminal sliding of drops; the terminal sliding velocity is greatest at resonance frequency. Varying the electrowetting number (0.21-0.56) at a fixed frequency (40 Hz) for 5 μL drops, we found an empirical relationship between the electrowetting number and the terminal sliding velocity. Using the relationship between the drop size and ac frequency, we can selectively slide drops of a specific size or merge two drops along an inclined plane. This simple method will help with constructing microfluidic platforms with sorting, merging, transporting, and mixing of drops without a programmable control of electrical signals. Also, this method has a potential in heat transfer applications because heat removal capacity can be enhanced significantly through drop oscillation.     

Microscopic treatment of a barrel drop on fibers and nanofibers

The microscopic approach of Berim and Ruckenstein (J. Phys. Chem. B 108 (2004) 19330, 19339) regarding the shape and stability of a liquid drop on a planar bare solid surface is extended to a liquid barrel drop on the bare surface of a solid cylinder (fiber) of arbitrary radius. Assuming the interaction potentials of the liquid molecules between themselves and with the molecules of the solid of the London-van der Waals form, the potential energy of a liquid molecule with an infinitely long fiber was calculated analytically. A differential equation for the drop profile was derived by the variational minimization of the total potential energy of the drop by taking into account the structuring of the liquid near the fiber. This equation was solved in quadrature and the shape and stability of the barrel drop were analyzed as functions of the radius of the fiber and the microscopic contact angle theta(0) which the drop profile makes with the surface of the fiber. The latter angle is dependent on the fiber radius and on the microscopic parameters of the model (strength of the intermolecular interactions, densities of the liquid and solid phases, hard core radii, etc.). Expressions for the evaluation of the microcontact angle from experimentally measurable characteristics of the drop profile (height, length, volume, location of inflection point) are obtained. All drop characteristics, such as stability, shape, are functions of theta(0) and a certain parameter a which depends on the model parameters. In particular, the range of drop stability consists of three domains in the plane theta(0)-a, separated by two critical curves a=a(c)(theta(0)) and a=a(c1)(theta(0)) [a(c)(theta(0))h(m1) cannot exist, whereas in the third domain (between those curves) the drop can have values of h(m) either smaller than h(m1) or larger than h(m2), where h(m2)>h(m1) is a second critical height. For sufficiently large fiber radii, R(f)1 >/= microm, the critical curves almost coincide and only two domains, the first and the second, remain. The smaller the radius, the larger is the difference between the critical curves and the larger is the second domain of drop stability. The shape of the drop depends on whether the point (theta(0),a) on the theta(0)-a plane is far from the critical curve or near it. In the first case the drop profile has generally a large circular part, while in the second case the shape is either almost planar or contains a long manchon that is similar to a film on the fiber.     

Sliding of water droplets on hydrophobic surfaces with various hydrophilic region sizes

Four patterned surfaces with hydrophilic areas of different sizes were prepared using photolithography with a smooth octadecyltrimethoxysilane (ODS) hydrophobic coating. The hydrophilic area in the surfaces was aligned hexagonally with a constant area fraction. The sliding angle and contact angle hysteresis of the water droplets increased concomitantly with increasing pattern size. The increase of the contact line distortion between defects at the receding side plays an important role in this trend. The droplet sliding velocity also increased concomitantly with increasing pattern size. This trend was simulated by a simple flow model. The contribution of the interface between the ODS region and the hydrophilic area was deduced from this trend. This study demonstrated the different size dependency of the chemical surface defects for sliding behavior between the critical moment at which a droplet slides down and the period when a droplet is sliding.     

Fabrication of surfaces with extremely high contact angle hysteresis from polyelectrolyte multilayer

High contact angle hysteresis on polyelectrolyte multilayers (PEMs) ion-paired with hydrophobic perfluorooctanoate anions is reported. Both the bilayer number of PEMs and the ionic strength of deposition solutions have significant influence on contact angle hysteresis: higher ionic strength and greater bilayer number cause increased contact angle hysteresis values. The hysteresis values of ~100° were observed on smooth PEMs and pinning of the receding contact line on hydrophilic defects is implicated as the cause of hysteresis. Surface roughness can be used to further tune the contact angle hysteresis on the PEMs. A surface with extremely high contact angle hysteresis of 156° was fabricated when a PEM was deposited on a rough substrate coated with submicrometer scale silica spheres. It was demonstrated that this extremely high value of contact angle hysteresis resulted from the penetration of water into the rough asperities on the substrate. The same substrate hydrophobized by chemical vapor deposition of 1H,1H,2H,2H-perfluorooctyltriethoxysilane exhibits high advancing contact angle and low hysteresis.     

Liquid Drops on an Inclined Plane: The Relation between Contact Angles, Drop Shape, and Retentive Force

Contact angle hysteresis, drop shape, and drop retention were studied with a tiltable plane. Contact liquids were water and ethylene glycol. Four polymers and silicon wafers were used as substrates. When the plane was inclined, the shape of drops distorted, exhibiting advancing and receding contact angles. Drops remained stationary until a critical angle of tilt was exceeded, and then they began to move. The difference in the advancing and receding contact angles, or contact angle hysteresis, ranged from 9° to 66°, depending on the liquid and the substrate. Roughness did not seem to influence the hysteresis as much as the chemical nature of the surfaces. Elongation and back-to-front asymmetry were greater on surfaces with high hysteresis. We found a linear correlation between the aspect ratio of drops and their contact angle hysteresis. Also, the retentive force increased with elongation of the drops.     

Patterned nonadhesive surfaces: superhydrophobicity and wetting regime transitions

Nonadhesive and water-repellent surfaces are required for many tribological applications. We study mechanisms of wetting of patterned superhydrophobic Si surfaces, including the transition between various wetting regimes during microdroplet evaporation in environmental scanning electron microscopy (ESEM) and for contact angle and contact angle hysteresis measurements. Wetting involves interactions at different scale levels: macroscale (water droplet size), microscale (surface texture size), and nanoscale (molecular size). We propose a generalized formulation of the Wenzel and Cassie equations that is consistent with the broad range of experimental data. We show that the contact angle hysteresis involves two different mechanisms and how the transition from the metastable partially wetted (Cassie) state to the homogeneously wetted (Wenzel) state depends upon droplet size and surface pattern parameters.     

Cylindrical droplet on nanofibers: a step toward the clam-shell drop description

The existence and shape of a cylindrical (infinitely long) liquid drop on a fiber of arbitrary radius are examined using a microscopic approach based on the interaction potentials between the molecules of the system. A differential equation for the drop profile was derived by the variational minimization of the total potential energy by taking into account the structuring of the liquid near the fiber. This equation was solved by quadrature, and the existence conditions and the shape of the drop were examined as functions of the radius of the fiber, microscopic contact angle theta(0), which the actual drop profile makes with the fiber, and a certain parameter, a, which depends on the interaction potential parameters. Angle theta(0) is defined in the nanoscale range near the leading edge where the interactions between the liquid and solid are strong. It differs from the macroscopically measured wetting angle (theta(m)) that represents the extrapolation of the profile outside the range of liquid-solid interaction to the solid surface. Expressions for both theta(0) and theta(m) are established in the paper. For any given fiber radius, the range of drop existence involves two domains in the plane theta(0) - a, separated by a critical curve a = a(c)(theta(0)). In the first domain, below the curve a = a(c)(theta(0)), the drop always exists and can have any height, h(m). In the second domain, above the curve a = a(c)(theta(0)), there is an upper limit of h, h(m1), such that drops with h(m) > h(m1) cannot exist. The shape of the drop depends on whether the point (theta(0), a) on the theta(0) - a plane is far from the critical curve or near to it. In the first case, the drop profile has generally a circular shape, with the center of the circle not located on the fiber axis, whereas in the second case the shape is "quasi planar", that is, most of the drop profile lies on a circle concentric with the fiber profile. Comparing the potential energies of a cylindrical drop on a fiber and a film of uniform thickness covering the fiber and having the same volume as the drop, the energetically preferred configuration was determined for various conditions. Considering the cylindrical drop as a limiting case of a clam-shell one, and the film as a limiting case of a barrel drop, the obtained analytical results could be employed to examine the barrel-drop-clam-shell-drop transformation (roll-up transition).