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A liquid droplet placed on a non-uniformly heated solid surface will migrate from a high temperature region to a low temperature region. This study reports the development of a theoretical model and experimental investigation on the migration behavior of paraffin oil droplets induced by the unidirectional thermal gradient. Thin-film lubrication the...
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... measurement is based on the static sessile drop method, and the value is often quite close to the advancing contact angle. As shown in Figure 2, increasing the temperature leads to a rapid decrease in contact angle and the droplet is almost flattened as the temperature is increased to 140 °C, forming a pancake-shaped configuration. For the paraffin oil, the contact angle decreases significantly with the decreasing viscosity. ...
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On the basis of the Darcy's equations which define the lubrication flow in porous layers, and the Reynolds's modified equation, we solve the problem of an unsteady movement of viscous incompressible lubrication in the clearance of a porous damper. The peculiarity of this solution is a simultaneous account of dependence of lubrication viscosity and...
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... Specifically, we investigate the flow state and the resulting wetting dynamics of volatile liquids on thermal conductive substrates. In the numerical aspect, previous lubrication-type models usually consider boundary conditions with uniform heating (Anderson & Davis 1995;Ajaev 2005) or preset substrate temperature/temperature gradient (Karapetsas, Sahu & Matar 2013;Dai et al. 2016;Charitatos & Kumar 2020;Wang et al. 2021), which failed to illustrate the non-negligible role of non-isothermal heat conduction in the overall process. In addition, the numerical and experimental investigations have at large been developing in parallel without strict comparisons that consider the specific application scenarios. ...
Droplet spreading is ubiquitous and plays a significant role in liquid-based energy systems, thermal management devices and microfluidics. While the spreading of non-volatile droplets is quantitatively understood, the spreading and flow transition in volatile droplets remains elusive due to the complexity added by interfacial phase change and non-equilibrium thermal transport. Here we show, using both mathematical modelling and experiments, that the wetting dynamics of volatile droplets can be scaled by the spatial-temporal interplay between capillary, evaporation and thermal Marangoni effects. We elucidate and quantify these complex interactions using phase diagrams based on systematic theoretical and experimental investigations. A spreading law of evaporative droplets is derived by extending Tanner's law (valid for non-volatile liquids) to a full range of liquids with saturation vapour pressure spanning from 10 1 to 10 4 Pa and on substrates with thermal conductivity from 10 −1 to 10 3 W m −1 K −1. In addition to its importance in fluid-based industries, the conclusions also enable a unifying explanation to a series of individual works including the criterion of flow reversal and the state of dynamic wetting, making it possible to control liquid transport in diverse application scenarios.
... In other words, the substrate temperature at the center is higher than that at the edge, primarily due to the heat transfer from the high-temperature flame to the substrate. This directed motion of the burning droplet from the hot zone (center) to the cold zone (edge) is known as thermocapillary effect [19,20]. It should be noted that the evaporation of the burning droplets are at contact boiling [21,22] because the substrate temperature T s exceeds the boiling point of the liquid (for ethanol, T boil = 78 • C). ...
... The contact angles at which the transitions between these behaviours occur depend on the ratio of the viscosities of the ambient fluid to that of the droplet. Dai et al. 16 studied theoretically and experimentally the migration of a paraffin droplet and found that the migration velocity decreases quickly at first and then approaches zero gradually. Karapetsas et al. 17 performed 2D and 3D simulations for a wide range of wettabilities and demonstrated that the appearance of a critical thermal gradient to make possible the droplet migration is due to the contact angle hysteresis, and that the velocity of the droplet and its direction is the result of the combined effects of the forces along the contact line and the thermocapillary induced flow. ...
... In this case, v t follows a power-law, v t ∝ C 1.279 . This is a stronger dependence than that reported for droplets over a substrate (G ≥ 0), where the exponent is equal or smaller to 1, depending on the contact angle 7,8,16 . ...
The study focuses on the numerical evolution of a droplet, which hangs from a horizontal plane and moves due to thermocapillary effects. It is assumed that the liquid completely wets the substrate, that the surface tension of the liquid decreases linearly with temperature, that the imposed thermal gradient on the substrate is uniform, and that heat transport within the droplet is such that the temperature of its surface replicates that of the substrate. These assumptions, along with the lubrication approximation, allow for obtaining a differential equation that governs the evolution of the droplet. By introducing appropriate scales, this equation has a single dimensionless parameter, which expresses the ratio of gravitational to thermocapillary forces. Numerical solutions show that at sufficiently large volumes or weak thermal gradients, the droplet moves while maintaining a steady, slightly decreasing its volume, and leaving behind a tail whose width is uniform. By contrast, if the droplet is small or the thermal gradient is strong, it advances and stretches in the direction of movement.
... As a result, the droplets migrate in the positive x axis direction from higher to lower temperatures. Specific experimental conditions can be obtained from the measurements of drop migration on a nonisothermal substrate with a unidirectional thermal gradient by Dai et al. 63 with temperatures of T m = 140°C and T * w0 ¼ 0 C for the heating and cooling elements, respectively, and an ambient temperature of 25°C. ...
... The physical parameters required for simulations were selected from the literature, 63 and the typical orders of magnitude and dimensionless parameter value ranges are listed in Tables III and IV, respectively. To make the two models consistent on the 52 we set h p = β = 0.01. ...
... The thermocapillary migration of a droplet was simulated by the two models and compared with the experimental results for the experiment on the migration of a paraffin oil droplet on a non-uniformly heated solid surface conducted by Dai et al. 63 As mentioned in the description of the experiments by Dai et al., the thermal gradient is Γ* = 3°C mm −1 and the dimensional parameters of paraffin oil are density ρ* = 8.29 × 10 3 kg m −3 , thermal conductivity λ* = 0.337 W m −1°C−1 , and surface tension coefficient α * T lg ¼ 0:082 mN mm À1 C. Based on these dimensional parameters, the dimensionless parameters were set to those listed in Sec. II E, which are ε = 0.1, C -1 = 0.03, Γ = 0.05, Bo = 0.5, and Bi = 0.01. ...
Moving contact line dynamics calculations include two models: precursor film models and slip models. The lubrication approximation method is used to establish a three-dimensional mathematical model to analyze the droplet thermocapillary migration behavior on a non-uniformly heated solid substrate with a wettability track. The contact line dynamics in the slip model and the disjoining pressure effect in the precursor model are proposed to regulate the substrate wettability. Both models are numerically implemented to investigate droplet spreading for three cases: free spreading on an isothermal substrate, thermocapillary migration on a uniform wettability substrate, and thermocapillary migration on a wettability-confined track. For the case of free spreading on an isothermal substrate, the three-dimensional results of the slip and precursor contact line models are essentially consistent with two-dimensional slip model results. For the case of thermocapillary migration on a uniform wettability substrate, the results of the two models essentially agree with the experimental results. Decreasing the thermal gradient reduces the discrepancies between the two models that result from the coordinate transformation method used in the slip model, which reduces the contact angles measured in the y-direction and enlarges the advancing contact angle in the migration direction. For the case of thermocapillary migration on a wettability-confined track, the slip model gradually shows a “dynamic-pinning” behavior with increasing equilibrium contact angle in the hydrophobic region. By contrast, the precursor film model maintains a stationary pinning behavior but separates a residual liquid outside the track. The precursor film model is preferred over the slip model in lubrication approximations for three-dimensional fluids when calculating complex moving contact dynamics caused by wettability differences. However, the precursor film model must be further optimized to prevent numerical instability.
... For example, thermal gradients can create stresses at the gas-liquid interface that drive the droplets to move. 2 Droplet's motion occurrs when both the amplitude and frequency of the mechanical vibration are suitable. 3 Furthermore, electrical wetting can improve the gravity-driven shedding of condensate droplets. ...
... (1) In Eq. (1), the capillary number is defined as Ca ¼ lU cl r , where U cl , l, and r are the contact line's spreading velocity, the dynamic viscosity, and the surface tension of the water. The empirical Hoffman's function is shown in Eq. (2). The DSJ boundary condition is applied as a velocity inlet with a cosine function. ...
Taking into account the benefits of the dual synthetic jet (DSJ) actuator's simple form, the absence of an air supply, and powerful jet momentum, as well as the low water adhesion force of the superhydrophobic surfaces, it is possible to make droplet shedding happen easily by combining these two methods. This paper studied the motion of water droplets under the action of the DSJ actuator with inclined outlets on three different kinds of surfaces with different wettability, namely, aluminum (hydrophilic), fluorinated silicon (hydrophobic), and superhydrophobic surfaces. Particle image velocimetry measurements were used to describe the flow field of the DSJ actuator. Then, high-speed photography was adopted to compare the critical air velocity for stable motion of the droplet on the three kinds of surfaces. The droplet mobility at three different surfaces when the jet velocity was the same was compared. The displacement and changes of the contact line of water droplets with different volumes on the superhydrophobic surface under the influence of jets were studied. Besides, choosing a typical case, the effect of the dual synthetic jet on the droplet was quantitatively examined, as well as the aerodynamic drag and lift forces. And some of the phenomenon observed in the experiment was explained using the simulation data. It is hoped that this research would lead to the development of a new method of facilitating droplet transport in applications such as anti-icing, drug delivery, self-cleaning surfaces, etc.
... 4−6 Precise control of droplets is even more important in lab-on-a-chip systems for combinatorial chemistry, 7 detection and analysis of biological cells, 5 and bioassays. 6 Over the past several decades, researchers have investigated numerous manipulative forces on droplets, 8−12 such as external temperature 13 and magnetic 14 and electric fields, 15 to control unidirectional transportation; however, in some cases, this condition is difficult to achieve and such factors affect the test results. Therefore, many researchers have focused on the self-driven movement of a droplet on a solid surface without any energy field using surface technology methods. ...
... They both obtained similar results: when the thermal gradient is below a critical value, droplets are pinned due to contact-angle hysteresis; when the thermal gradient is above this critical value, the migration speed of a droplet is proportional to the thermal gradient and inversely proportional to the dynamic viscosity of the fluid. Dai et al. 13 investigated the migration features of paraffinic oil droplets on a solid surface under a unidirectional thermal gradient. They found that the droplet velocity sharply decreased during the first 20% of the migration period, and this was followed by a slow decrease to be zero. ...
... Combining Eqs. (9) and (13) to integrate Eq. (5) yields the dimensionless temperature at the liquid-gas interface, given by ...
We report a study of the thermocapillary migration of droplets under a radial thermal gradient and in a wettability-confined track. A three-dimensional mathematical model is established based on the lubrication approximation. By considering the contact-line dynamics, a method for determining the velocity of the contact line in different directions is proposed for a three-dimensional droplet. Numerical simulations are performed to investigate the variations in the droplet profile, contact angle, and contact line. Three substrate-wettability cases are considered: uniform, temperature-dependent, and track-dependent wettability. The results show that when the substrate wettability is uniform, the droplet height initially decreases rapidly, and its center becomes concave and then gradually evolves into a ring-like morphology. Reducing the temperature sensitivity of the liquid–gas interfacial tension or increasing the temperature sensitivity of the liquid–solid interfacial tension decreases the equilibrium contact angle and accelerates thermocapillary migration. When a droplet spreads in a wettability-confined track, a wave-like peak is formed on each side of the droplet along the track direction until it finally separates into two distinct parts. As the track width is decreased, the time taken for a droplet to split into two smaller droplets advances, and the separation time presents a linear relationship with the track width.
... Droplet migration, together with separation, encapsulation, capture, fusion, transport, and suspension, constitute the droplet manipulation technique, which is used to generate stable and uniform droplets for biochemical reactions. The main manipulation methods used today are broadly: flow field manipulation, pressure manipulation, magnetic manipulation, electrical manipulation, thermal manipulation [1,2] and wetting gradient manipulation [3][4][5]. The wetting gradient manipulates microdroplet motion in such a way that the wetting gradient on the surface breaks the symmetry on the three-phase contact line, and the resulting imbalance forces drive the droplet toward a more wetting region to release free surface energy. ...
The motion of droplet on surface with discontinuous wetting gradient is of great importance for understanding lab-on-a-chip systems and other microfluidic devices. Different wetting gradients are known to be the main influencing factor in the droplet self- driven process, but the effect of different wall structures on the droplet migration process also deserves further investigation. In this paper, we analyze the self-driven process of liquid droplets on a local wetting gradient surface under microgravity conditions using front tracking method. The effects of different driving stripe lengths L_ΙΙx^*, different restrictive stripe lengths L_ΙΙΙy^*, and different surface wetting gradients ∆ cosθ on the droplet migration process and droplet morphology are analyzed. A theoretical formula that can predict the lateral spreading length of droplets is also proposed. The results show that different driving stripe length L_ΙΙx^* lengths and the wetting gradient ∆ cosθ have significant effects on the migration velocity of droplets, while different restrictive stripe length L_ΙΙΙy^* lengths have very significant effects on the final morphological characteristics of droplets. When restrictive stripe length L_ΙΙΙy^*≥1, the hindering effect generated by the restrictive region ΙΙΙ has more and more significant effects on the morphological structure of droplets in the migration process. When the correction factor ε=0.735 in the prediction equation, the predicted value calculated by the theoretical equation has a good degree of similarity with the numerical simulation results.
... Darhuber et al. investigated the effect of a thermal gradient on low viscosity fluid flow to develop a tunable and elegant technique for fluid transport [33] and observed that induced thermocapillary stresses appropriately steered microfluid streams along lithographically characterized pathways. Moreover, the migration behavior of liquid droplets on a metal substrate has been studied using the thermocapillary effect [34]. The findings indicate the need for developing a viable method for predicting the migration velocity as a function of the heat gradient, which can also increase the mechanical stress on the capillary wall. ...
-Micropumps have attracted considerable interest in micro-electro-mechanical systems (MEMS), microfluidic devices, and biomedical engineering to transfer fluids through capillaries. However, improving the sluggish capillary-driven flow of highly viscous fluids is critical for commercializing MEMS devices, particularly in underfill applications. This study investigated the behavior of different viscous fluid flows under the influence of capillary and electric potential effects. We observed that upon increasing the electric potential to 500 V, the underfill flow length of viscous fluids increased by 45% compared to their capillary flow length. To explore the dynamics of underfill flow under the influence of an electric potential, the polarity of highly viscous fluids was altered by adding NaCl. The results indicated an increase of 20-41% in the underfill flow length of highly viscous conductive fluids (0.5-4% NaCl additives in glycerol) at 500 V compared to that at 0 V. The underfill viscous fluid flow length improved under the electric potential effect owing to the polarity across the substance and increased permittivity of the fluid. A time-dependent simulation, which included a quasi-electrostatic module, level set module, and laminar two-phase flow, was executed using the COMSOL Multiphysics software to analyze the effect of the external electric field on the capillary-driven flow. The numerical simulation results agreed well with the experimental data, with an average deviation of 4-7% at various time steps for different viscous fluids. Our findings demonstrate the potential of utilizing electric fields to control the capillary-driven flow of highly viscous fluids in underfill applications.
... When a liquid is placed on a non-isothermal solid surface, an unbalanced surface tension force at the liquid-gas surface is created due to the temperature difference, promoting the liquid to flow from warm to cold regions, and this interfacial phenomenon is known as thermocapillary motion [11][12][13][14][15][16][17][18][19][20][21][22][23]. We propose that it is possible to create a lifting force by manipulating the thermocapillary effect. ...
... This study proposed a manipulation strategy of adopting thermal gradients to control liquid motions and create lifting forces between two plates. The thermocapillary motion describes a flow of a viscous liquid from warm to cold regions on a nonisothermal solid surface [11][12][13][14][15][16][17][18][19][20][21][22][23]. Couette flow is a flow of a viscous fluid at the interface of two solid surfaces, one of which is moving tangentially relative to the other [4,5]. ...
Hypothesis: In this paper, we explore a concept and present the first experimental evidence to show that it is possible to form a stable liquid film and create lifting force at the interface via thermal gradient to minimize interfacial rubbing of surfaces and the associated wear.
Experiments: The approach is based on manipulating the flow behavior via thermocapillary, which describes how a liquid can be made to flow from warm to cold regions purely by inducing a thermal gradient. We show that liquid bridges between two parallel plates can be manipulated and stabilized under a combined effect of the thermocapillary flow and the Couette flow, which describes the motion of a viscous fluid between two parallel plates in a relative sliding motion.
Findings: The equilibrium stage is confirmed under different experimental conditions of a thermal gradient, interfacial gap, liquid viscosity, and liquid bridge volume. A strategy is proposed to control liquid motion and create lifting force between two plates. A theoretical model is also presented to illustrate the principle of the equilibrium stage. Creating lifting forces at the interface offers a new thermo-hydrodynamic tool for manipulating liquids behavior. This approach has the potential for controlling liquid motion in mechanical components and nature.
