Viscoelastic liquid bridge breakup and liquid transfer between two surfaces.

We studied experimentally the breakup of liquid bridges made of aqueous solutions of Poly(acrylic acid) between two separating solid surfaces with freely moving contact lines. For polymer concentrations higher than a certain threshold (~30 ppm), the contact line on the surface with the highest receding contact angle fully retracts before the liquid bridge capillary breakup takes place at its neck. This means that all the liquid remains attached to the opposing surface when the surfaces are separated. This behavior occurs regardless of the range of liquid volume and stretching speed studied. Such behavior is very different from that observed for Newtonian liquids or non-Newtonian systems where contact lines are intentionally pinned. It is shown that this behavior stems from the competition between thinning of bridge neck (delayed by extensional thickening) and receding of contact line (enhanced by shear thinning) on the surface with lower receding contact angle. If the two surfaces exhibit the same wetting properties, the upper contact line fully retracts before the capillary breakup due to the asymmetry caused by gravity, and, therefore, all the liquid remains on the lower surface.

Droplet impact: Viscosity and wettability effects on splashing.

HYPOTHESES: The wettability of a surface affects the splashing behavior of a droplet upon impact onto a surface only when surface exhibits either a very high or a very low contact angle. Viscosity affects the splashing threshold in a non-monotony way. EXPERIMENTS: To examine the roles of drop viscosity and surface wettability on splashing, a wide range of liquid viscosities (1-100 cSt), surface wettabilities (from hydrophilic to hydrophobic), drop velocities (0.5-3.3 m/s), and liquid surface tensions (∼20 and 70 mN/m) were examined. High speed imaging was used. FINDINGS: Wettability affects the splashing threshold at very extreme limits of the wettability i.e. at very high or very low contact angle values; however, the wettability effect is less prominent on spreading-splashing regime map. For drops of any surface tension impacting surfaces with any wettability, an increase in viscosity (up to ∼5 cSt or Reynolds number of 2000) promotes splashing; whereas using liquids with viscosities larger than 5 cSt, suppress splashing. We explained such behaviors using evolution of the lamella rim, dynamic contact angle, and velocity of the expanding lamella. Finally, to predict the splashing, we developed a general empirical relationship which explains all of ours, and previously reported data.

Contact angle measurement with a smartphone.

In this study, a smartphone-based contact angle measurement instrument was developed. Compared with the traditional measurement instruments, this instrument has the advantage of simplicity, compact size, and portability. An automatic contact point detection algorithm was developed to allow the instrument to correctly detect the drop contact points. Two different contact angle calculation methods, Young-Laplace and polynomial fitting methods, were implemented in this instrument. The performance of this instrument was tested first with ideal synthetic drop profiles. It was shown that the accuracy of the new system with ideal synthetic drop profiles can reach 0.01% with both Young-Laplace and polynomial fitting methods. Conducting experiments to measure both static and dynamic (advancing and receding) contact angles with the developed instrument, we found that the smartphone-based instrument can provide accurate and practical measurement results as the traditional commercial instruments. The successful demonstration of use of a smartphone (mobile phone) to conduct contact angle measurement is a significant advancement in the field as it breaks the dominate mold of use of a computer and a bench bound setup for such systems since their appearance in 1980s.

Asymmetric Spreading of a Drop upon Impact onto a Surface.

Study of the spreading of an impacting drop onto a surface has gained importance recently due to applications in printing, coating, and icing. Limited studies are conducted to understand asymmetric spreading of a drop seen upon drop impact onto a moving surface; there is no relation to describe such spreading. Here, we experimentally studied the spreading of a drop over a moving surface; such study also provides insights for systems where a drop impacts at an angle relative to a surface, i.e., drop has both normal and tangential velocities relative to the surface. We developed a model that for the first time allows prediction of time evolution for the asymmetric shape of the lamella during spreading. The developed model is demonstrated to be valid for a range of liquids and surface wettabilities as well as drop and surface velocities, making this study a comprehensive examination of the topic. We also found out how surface wettability can affect the recoil of the drop after spreading and explained the role of contact angle hysteresis and receding contact angle in delaying the recoil process.

Resolving an ostensible inconsistency in calculating the evaporation rate of sessile drops.

This paper resolves an ostensible inconsistency in the literature in calculating the evaporation rate for sessile drops in a quiescent environment. The earlier models in the literature have shown that adapting the evaporation flux model for a suspended spherical drop to calculate the evaporation rate of a sessile drop needs a correction factor; the correction factor was shown to be a function of the drop contact angle, i.e. f(θ). However, there seemed to be a problem as none of the earlier models explicitly or implicitly mentioned the evaporation flux variations along the surface of a sessile drop. The more recent evaporation models include this variation using an electrostatic analogy, i.e. the Laplace equation (steady-state continuity) in a domain with a known boundary condition value, or known as the Dirichlet problem for Laplace's equation. The challenge is that the calculated evaporation rates using the earlier models seemed to differ from that of the recent models (note both types of models were validated in the literature by experiments). We have reinvestigated the recent models and found that the mathematical simplifications in solving the Dirichlet problem in toroidal coordinates have created the inconsistency. We also proposed a closed form approximation for f(θ) which is valid in a wide range, i.e. 8°≤θ≤131°. Using the proposed model in this study, theoretically, it was shown that the evaporation rate in the CWA (constant wetted area) mode is faster than the evaporation rate in the CCA (constant contact angle) mode for a sessile drop.

Understanding the drop impact on moving hydrophilic and hydrophobic surfaces.

In this paper, a systematic study was performed to understand the drop impact on hydrophilic and hydrophobic surfaces that were moving in the horizontal direction. Drops (D0 = 2.5 mm) of liquids with three different viscosities were used. Wide ranges of drop normal velocity (0.5 to 3.4 m s-1) and surface velocity (0 to 17 m s-1) were studied. High speed imaging from the top and side was used to capture the impact phenomena. It was found that drop impact behavior on a moving surface significantly differs from that on a stationary surface at both the lamella extension stage (i.e. t ≤ tmax) and the retraction stage (t > tmax). Starting with the lamella extension stage, it was observed that the drop spreads asymmetrically over a moving surface. It was also found that the splashing behavior of the drop upon impact on a moving surface, unlike the understanding in the literature, is azimuthally different along the lamella contact line. In the case of the drop spreading over a moving surface, the surface movement stretches the expanded lamella in the direction of the surface motion. For hydrophilic surfaces, the stretched lamella pins to the surface and moves with the surface velocity; however, for hydrophobic surfaces, the lamella recoils during such stretching. A new model was developed to determine the splashing threshold of the drop impact on a moving surface. The model is capable of describing the azimuthally different behavior of the splashing which is a function of normal capillary and Weber numbers, surface velocity, and surface wettability. It was also found that the increase of the viscosity decreases the splashing threshold. Finally, comprehensive regime maps of the drop impact outcome on a moving surface were provided for both t ≤ tmax and t > tmax stages.

Impact of particle-laden drops: Particle distribution on the substrate.

The splat morphology after the impact of suspension drops on hydrophilic (glass) and hydrophobic (polycarbonate) substrates was investigated. The suspensions were mixtures of water and spherical hydrophobic particles with diameter of 200µm or 500µm. The impact was studied by side, bottom and angled view images. At Reynolds and Weber numbers in the range 150⩽We⩽750 and 7100⩽Re⩽16,400, the particles distributed in a monolayer on the hydrophilic substrates. It was found that the 200µm particles self-arranged as rings or disks on the hydrophilic substrates. On hydrophobic substrates, many particles were at the air-water interface and 200µm formed a crown-like structure. The current study for impact of particle-laden drops shows that the morphology of splats depends on the substrate wettability, the particle size and impact velocity. We developed correlations for the inner and outer diameter of the particle distribution on the hydrophilic substrates, and for the crown height on hydrophobic substrates. The proposed correlations capture the character of the particle distributions after drop impact that depends on particle volume fraction, the wettability of both particles and the substrate, and the dimensionless numbers such as Reynolds and Weber.

How pinning and contact angle hysteresis govern quasi-static liquid drop transfer.

This paper presents both experimental and numerical simulations of liquid transfer between two solid surfaces with contact angle hysteresis (CAH). Systematic studies on the role of the advancing contact angle (θa), receding contact angle (θr) and CAH in determining the transfer ratio (volume of the liquid transferred onto the acceptor surface over the total liquid volume) and the maximum adhesion force (Fmax) were performed. The transfer ratio was found to be governed by contact line pinning at the end of the transfer process caused by CAH of surfaces. A map based on θr of the two surfaces was generated to identify the three regimes for liquid transfer: (I) contact line pinning occurs only on the donor surface, (II) contact line pinning occurs on both surfaces, and (III) contact line pinning occurs only on the acceptor surface. With this map, an empirical equation is provided which is able to estimate the transfer ratio by only knowing θr of the two surfaces. The value of Fmax is found to be strongly influenced by the contact line pinning in the early stretching stage. For symmetric liquid bridges between two identical surfaces, Fmax may be determined only by θa, only by θr, or by both θa and θr, depending on the magnitude of the contact angles. For asymmetric bridges, Fmax is found to be affected by the period when contact lines are pinned on both surfaces.

Fast Liquid Transfer between Surfaces: Breakup of Stretched Liquid Bridges.

In this work, a systematic experimental study was performed to understand the fast liquid transfer process between two surfaces. According to the value of the Reynolds number (Re), the fast transfer is divided into two different scenarios, one with negligible inertia effects (Re ≪ 1) and the other with significant inertia effects (Re > 1). For Re ≪ 1, the influences of the capillary number (Ca) and the dimensionless minimum separation (H(min)* = H(min)/V(1/3), where H(min) is the minimum separation between two surfaces and V is the volume of liquid) on the transfer ratio (α, the volume of liquid transferred to the acceptor surface over the total liquid volume) are discussed. On the basis of the roles of each physical parameter, an empirical equation is presented to predict the transfer ratio, α = f(Ca). This equation involves two coefficients which are affected only by the surface contact angles and H(min)* but not by the liquid viscosity or surface tension. When Re > 1, it is shown for the first time that the transfer ratio does not converge to 0.5 with the increase in the stretching speed.

Complex Drop Impact Morphology.

The aim of this work is to understand the changes in the observed phenomena during particle-laden drop impact. The impact of millimeter-size drops was investigated onto hydrophilic (glass) and hydrophobic (polycarbonate) substrates. The drops were dispersions of water and spherical and nearly iso-dense hydrophobic particles with diameters of 200 and 500 µm. The impact was studied by side and bottom view images in the range 150 ≤ We ≤ 750 and 7100 ≤ Re ≤ 16400. The particles suppressed the appearance of singular jetting and drop partial rebound but promoted splashing, receding breakup, and rupture. The drops with 200 µm particles spread in two phases: fast and slow, caused by inertial and capillary forces, respectively. Also, the increase in volume fraction of 200 µm particle led to a linear decrease in the maximum spreading factor caused by the inertia force on both hydrophilic and hydrophobic substrates. The explanation of this reduction was argued to be the result of energy dissipation through frictional losses between particles and the substrate.

Shedding of Water Drops from a Surface under Icing Conditions.

A sessile water drop exposed to an air flow will shed if the adhesion is overcome by the external aerodynamic forces on the drop. In this study, shedding of water drops were investigated under icing conditions, on surfaces with different wettabilities, from hydrophilic to superhydrophobic. A wind tunnel was used for experiments in a temperature range between -8 and 24.5 °C. Results indicate that the temperature has a major influence on the incipient motion of drop shedding. The critical air velocity (U(c)) at which a drop first starts to shed generally increases under icing conditions, indicating an increase in the adhesion force. The contact angle hysteresis (CAH) and the drop base length (L(b)) are found to be the controlling factors for adhesion. A correlation was also developed to deduce the drag coefficient, C(D) for the drop. It was found that C(D) can decrease under icing conditions. In general, a lower C(D) and higher adhesion together lead to a higher critical air velocity. However, there are systems such as water on Teflon for which the critical air velocity remains practically unaffected by temperature because of similar adhesion and C(D) values, at all temperatures tested.

Contact angles of surfactant solutions on heterogeneous surfaces.

Using Gibbs' adsorption equation and a literature isotherm, a new general model to predict the contact angle of surfactant solutions on (smooth or rough) chemically heterogeneous surfaces is constructed based on the Cassie equation. The model allows for adsorption at the liquid-vapor, solid-liquid, and solid-vapor interfaces. Solid-vapor adsorption is allowed in order to model the autophobic effect on hydrophilic surfaces. Using representative values for the coefficients which describe adsorption at each interface, model predictions for contact angles as a function of f parameters (area fractions) and surfactant concentration are made for heterogeneous surfaces made up of different materials. On smooth surfaces, the f parameters serve as weighting factors determining how to combine the effects of surfactant adsorption on each material to predict the behavior on the heterogeneous surface. Due to the non-linear nature of the model, the inclusion of a small amount of hydrophobic material has a greater effect on a predominantly hydrophilic material than vice versa, explaining the result seen in literature that a small amount of hydrophobic contamination (such as oil) significantly increases contact angle on a hydrophilic surface. The fact that even a small amount of heterogeneity can greatly change experimental results could lead to incorrect experimental conclusions about surfactant adsorption if a surface were wrongly assumed to be homogeneous. Model predictions rapidly become more complex as the number of differently wettable materials present on the surface increases. Also, an approximately equal weighting of different materials generally leads to more complex behaviors compared to heterogeneous surfaces composed largely of a single material. Rough heterogeneous surfaces follow previous results for surfactant wetting of rough homogeneous surfaces, leading to an amplification/attenuation of surfactant effects for penetrated/unpenetrated wetting, and further increasing the complexity of predictions. These potential complexities point to the importance of characterizing the heterogeneities of any surface under consideration. With proper characterization, the model described in this paper will allow for prediction of contact angles on all types of heterogeneous surfaces, and design of surfaces for specific interactions with surfactant solutions.

Study of model superoleophobic surfaces fabricated with a modified Bosch etch method.

A set of surfaces featuring pillars with overhanging cap structures, exhibiting superoleophobic behavior, were fabricated using a new method. While such structures have been previously reported, in contrast with previous literature this new method allows for the control of pillar cross-sectional diameter, pillar separation, and Cassie fraction independent from the pillar radius-to-height ratio. Once fabricated the contact angles of the surfaces were examined using water, ethylene glycol, and hexadecane. These surfaces were capable of maintaining a stable Cassie state with hexadecane where surfaces with similar Cassie fraction but vertical sidewalls we had examined previously collapsed into the Wenzel state. The overall behavior of the liquids conforms to prior experience with vertical sidewall structures, with the advancing contact angles tending to remain high and insensitive to changing Cassie fraction while the receding contact angles follow the trends predicted by the Cassie equation much more closely. All experimental evidence taken together, this seems to indicate that the cap structures increase the stability of the Cassie state, but at the expense of increasing drop pinning, over and above what such surface texturing already does.

Liquid transfer mechanism between two surfaces and the role of contact angles.

The transfer ratio of quasi-static liquid transfer was found to strongly depend on the difference between the receding contact angles of the two surfaces. In contrast to traditional thinking, the transfer ratio was quite insensitive to the adhesion force between the solid and the liquid when the liquid bridge broke.

Understanding (sessile/constrained) bubble and drop oscillations.

The diffuse literature on drop oscillation is reviewed, with an emphasis on capillary wave oscillations of constrained drops. Based on the review, a unifying conceptual framework is presented for drop and bubble oscillations, which considers free and constrained drops/bubbles, oscillation of the surface or the bulk (i.e. center of mass) of the drop/bubble, as well as different types of restoring forces (surface tension, gravity, electromagnetic, etc). Experimental results (both from literature and from a new set of experiments studying sessile drops in cross flowing air) are used to test mathematical models from literature, using a novel whole profile analysis technique for the new experiments. The cause of oscillation (cross flowing air, vibrated surface, etc.) is seen not to affect oscillation frequency. In terms of models, simplified models are seen to poorly predict oscillation frequencies. The most advanced literature models are found to be relatively accurate at predicting frequency. However it is seen that no existing models are reliably accurate across a wide range of contact angles, indicating the need for advanced models/empirical relations especially for drops undergoing the lowest frequency mode of oscillation (the order 1 degree 1 non-axisymmetric 'bending' mode that corresponds to a lateral 'rocking' motion of the drop).

Drop rebound after impact: the role of the receding contact angle.

Data from the literature suggest that the rebound of a drop from a surface can be achieved when the wettability is low, i.e., when contact angles, measured at the triple line (solid-liquid-air), are high. However, no clear criterion exists to predict when a drop will rebound from a surface and which is the key wetting parameter to govern drop rebound (e.g., the "equilibrium" contact angle, θeq, the advancing and the receding contact angles, θA and θR, respectively, the contact angle hysteresis, Δθ, or any combination of these parameters). To clarify the conditions for drop rebound, we conducted experimental tests on different dry solid surfaces with variable wettability, from hydrophobic to superhydrophobic surfaces, with advancing contact angles 108° < θA < 169° and receding contact angles 89° < θR < 161°. It was found that the receding contact angle is the key wetting parameter that influences drop rebound, along with surface hydrophobicity: for the investigated impact conditions (drop diameter 2.4 < D0 < 2.6 mm, impact speed 0.8 < V < 4.1 m/s, Weber number 25 < We < 585), rebound was observed only on surfaces with receding contact angles higher than 100°. Also, the drop rebound time decreased by increasing the receding contact angle. It was also shown that in general care must be taken when using statically defined wetting parameters (such as advancing and receding contact angles) to predict the dynamic behavior of a liquid on a solid surface because the dynamics of the phenomenon may affect surface wetting close to the impact point (e.g., as a result of the transition from the Cassie-Baxter to Wenzel state in the case of the so-called superhydrophobic surfaces) and thus affect the drop rebound.

Modeling liquid bridge between surfaces with contact angle hysteresis.

This paper presents the behaviors of a liquid bridge when being compressed and stretched in a quasi-static fashion between two solid surfaces that have contact angle hysteresis (CAH). A theoretical model is developed to obtain the profiles of the liquid bridge given a specific separation between the surfaces. Different from previous models, both contact lines in the upper and lower surfaces were allowed to move when the contact angles reach their advancing or receding values. When the contact angles are between their advancing and receding values, the contact lines are pinned while the contact angles adjust to accommodate the changes in separation. Effects of CAH on both asymmetric and symmetric liquid bridges were analyzed. The model was shown to be able to correctly predict the behavior of the liquid bridge during a quasi-static compression/stretching loading cycle in experiments. Because of CAH, the liquid bridge can have two different profiles at the same separation during one loading and unloading cycle, and more profiles can be obtained during multiple cycles. The maximum adhesion force generated by the liquid bridge is found to be influenced by the CAH of surfaces. CAH also leads to energy cost during a loading cycle of the liquid bridge. In addition, the minimum separation between the two solid surfaces is shown to affect how the contact radii and angles change on the two surfaces as the liquid bridge is stretched.

Trapezius muscle activity in using ordinary and ergonomically designed dentistry chairs.

BACKGROUND: Most dentists complain of musculoskeletal disorders which can be caused by prolonged static posture, lack of suitable rest and other physical and psychological problems. OBJECTIVE: We evaluated a chair with a new ergonomic design which incorporated forward leaning chest and arm supports. METHODS: The chair was evaluated in the laboratory during task simulation and EMG analysis on 12 students and subjectively assessed by 30 professional dentists using an 18-item questionnaire. EMG activity of right and left trapezius muscles for 12 male students with no musculoskeletal disorders was measured while simulating common tasks like working on the teeth of the lower jaw. RESULTS: Normalized EMG data showed significant reduction (p<0.05) in all EMG recordings of the trapezius muscle. Dentists also unanimously preferred the ergonomically designed chair. CONCLUSION: Such ergonomically designed chairs should be introduced as early as possible in student training before bad postural habits are acquired.

Understanding the edge effect in wetting: a thermodynamic approach.

Edge effect is known to hinder spreading of a sessile drop. However, the underlying thermodynamic mechanisms responsible for the edge effect still is not well-understood. In this study, a free energy model has been developed to investigate the energetic state of drops on a single pillar (from upright frustum to inverted frustum geometries). An analysis of drop free energy levels before and after crossing the edge allows us to understand the thermodynamic origin of the edge effect. In particular, four wetting cases for a drop on a single pillar with different edge angles have been determined by understanding the characteristics of FE plots. A wetting map describing the four wetting cases is given in terms of edge angle and intrinsic contact angle. The results show that the free energy barrier observed near the edge plays an important role in determining the drop states, i.e., (1) stable or metastable drop states at the pillar's edge, and (2) drop collapse by liquid spilling over the edge completely or staying at an intermediate sidewall position of the pillar. This thermodynamic model presents an energetic framework to describe the functioning of the so-called "re-entrant" structures. Results show good consistency with the literature and expand the current understanding of Gibbs' inequality condition.

The Cassie equation: how it is meant to be used.

A review of literature shows that the majority of papers cite a potentially incorrect form of the Cassie and Cassie-Baxter equations to interpret or predict contact angle data. We show that for surfaces wet with a composite interface, the commonly used form of the Cassie-Baxter equation, cosθ(c)=f(1)cosθ-(1-f), is only correct for the case of flat topped pillar geometry without any penetration of the liquid. In general, the original form of the Cassie-Baxter equation, cosθ(c)=f(1)cosθ(1)-f(2), with f(1)+f(2)≥1, should be used. The differences between the two equations are discussed and the errors involved in using the incorrect equation are estimated to be between ~3° and 13° for superhydrophobic surfaces. The discrepancies between the two equations are also discussed for the case of a liquid undergoing partial, but increasing, levels of penetration. Finally, a general equation is presented for the transition/stability criterion between the Cassie-Baxter and Wenzel modes of wetting.