Article pubs.acs.org/Langmuir
Fast Liquid Transfer between Surfaces: Breakup of Stretched Liquid Bridges H. Chen,† T. Tang,*,† and A. Amirfazli*,‡ †
Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 2G8, Canada Department of Mechanical Engineering, York University, Toronto, ON M3J 1P3, Canada
‡
S Supporting Information *
ABSTRACT: 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 (Hmin* = Hmin/V1/3, where Hmin 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 Hmin* 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.
α0) and does not change with the change in stretching speed. As demonstrated by several recent studies, with negligible viscous and inertia effects, surface contact angles (SCA), more specifically the receding contact angles, of the two surfaces are the only governing parameters for the value of α0.11−15 Compared to slow liquid transfer, the parameters governing the transfer ratio during fast transfer are still unclear. When a large U is applied, inertia and viscous forces become important. Therefore, besides SCA, five additional physical parameters can now play roles: γ, related to surface force; μ, related to the viscous force; V and ρ, related to the inertia force; and U, related to both viscous and inertia forces. In addition, the minimum separation between two surfaces (Hmin) which governs the initial shape of the liquid bridge could also affect the transfer process. In most practical situations, e.g., offset printing, small volumes (on the order of 10−3−10−6 μL) of viscous liquid are normally used,16 which results in a small Re for the system. Therefore, in the literature on the liquid transfer between two parallel surfaces, the inertia forces are typically neglected and only the surface and viscous forces are considered. By using the volume of fluid (VOF) method, Huang et al.17 studied the process of fast liquid transfer with a small inertia effect (Re in the range of 0.0008−0.04). The results showed that the transfer ratio could be significantly different when γ, U, SCA, and μ of the system were changed. On the other hand, how these parameters affect the surface or viscous forces was not thoroughly discussed. Dodded et al.18 investigated the effects
1. INTRODUCTION Methods of transferring a liquid drop from one solid surface (donor surface) to another (acceptor surface) have been investigated for more than 100 years. One of the most widely seen transfer methods is stretching liquid bridges formed between two surfaces. When stretched to a certain height, the liquid bridge breaks; hence, part of the liquid can be transferred from one surface to the other. Such a transfer process can be seen in many industrial applications, e.g., offset printing, drop deposition, the packaging industry, and electronic circuits printing1−6 as well as in nature.7,8 The transfer ratio (α), defined as the volume of liquid transferred to the acceptor surface over the total liquid volume, is particularly important in determining the product quality and work efficiency in the above applications. Therefore, understanding the governing parameters for the value of the transfer ratio has received considerable attention in the study of such liquid transfer processes. Chadov and Yakhnin9,10 for the first time identified that the transfer process can be governed by three different forces: surface, inertia, and viscous forces. In the literature, these three forces are typically described qualitatively by several dimensionless numbers: the capillary number (Ca = Uμ/γ, ratio of viscous to surface forces, where U is the stretching speed, μ is the liquid dynamic viscosity, and γ is the liquid surface tension), the Weber number (We =ρU2V1/3/γ, ratio of inertia to surface forces, where ρ and V are the liquid density and volume, respectively), and the Reynolds number (Re = ρUV1/3/μ, ratio of viscous force to the inertia forces). Shown in refs 9 and 10, when a very slow stretching speed is applied, the effects of viscous and inertia forces are negligible (both Ca and We ≪ 1). The value of the transfer ratio is a constant value (denoted by © 2015 American Chemical Society
Received: May 14, 2015 Revised: October 1, 2015 Published: October 6, 2015 11470
DOI: 10.1021/acs.langmuir.5b03292 Langmuir 2015, 31, 11470−11476
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Langmuir
Figure 1. Process of fast liquid transfer. (a) Drop of liquid placed on the donor surface. (b) Liquid bridge between two surfaces before transfer. (c) Liquid bridge stretched by applying a speed U to the acceptor surface. (d) Liquid bridge breaks.
parameters. Studies on cases with a large Re are particularly limited. In this work, an experimental study is performed on fast liquid transfer with both small and large inertia effects. A dimensional analysis is conducted to determine the dimensionless parameters that can affect the fast transfer process. When Re of the transfer system is small, the process is governed by SCA, Ca (which is a combination of U, μ, and γ), and Hmin* (defined as Hmin/V1/3, where Hmin is the minimum separation between two surfaces and V is the volume of liquid). Since the effects of SCA were well discussed in ref 20, the effects of Ca and Hmin* are the focus of this study. Experiments with large Re values were also performed to understand the inertia effects and address whether the transfer ratio still converges to 0.5 with increasing Ca under strong inertia effects.
of the viscous and surface forces during fast transfer, again neglecting the inertia force. Ca was used to characterize the liquid transfer process. It was found that the transfer ratio converged to 0.5 when Ca became sufficiently large, which agreed with the observations made in refs 9 and 10. In the above two studies, the contact angle was assumed to be constant on both surfaces during the entire process. As demonstrated by Bai et al.,19 the values of the contact angle during the process of fast transfer can have a complex dependence on the stretching speed, which can in turn affect the transfer ratio. A series of experiments and simulations were performed in our group to study the effects of SCA and U on fast liquid transfer.20 It was shown that the transfer ratio as a function of U converged from one plateau value (α0) to 0.5 with the increase in U and that the critical speeds at which the transfer ratio deviates from α0 to 0.5 are significantly affected by SCA. Although most studies so far have focused on liquid transfer with a negligible inertia effect (Re ≪1), situations with considerable inertia effects do exist. For example, when cats lap, water adheres to the tip of the tongue, forming a water bridge. By the retreat of its tongue (causing the liquid bridge to stretch), the cat can draw water into its mouth. As shown in ref 7, such a retreat speed can be up to ∼720 mm/s. Given the small viscosity of water, with such a fast speed, the Re of the system can be quite large (>500). Therefore, it is of interest to understand the transfer behavior under inertia effects. To do so, Dodded et al.21 performed a numerical study of liquid transfer from one surface (SCA = 70°) to another (SCA = 90°) with the same Ca (0.1) but five different Re values (0, 0.1, 1, 10, and 100). It was shown that when Re > 1 the formation of satellite drops upon bridge breakage could be observed, and the transfer ratio was found to increase from 0.08 to approximately 0.5 when Re increased from 0.1 to 100. In Park et al.,22 water transfer from a donor surface with an SCA of 60° to an acceptor surface with an SCA of 70° at different U values (10 to 250 mm/s) was simulated with the VOF method. Their results showed that the transfer ratio increased from 0.07 to 0.36 with the increase in U from 10 to 200 mm/s. However, when U was further increased to 250 mm/s (Re = 277), instead of staying at 0.5, the transfer ratio decreased to 0.33. Therefore, the observations made at small Re that the transfer ratio always converges to 0.5 at high speed may not be valid when the inertia effects become important. On the basis of the existing literature, there is a lack of systematic study which considers the effect of each physical parameter in fast liquid transfer. Some parameters were simply neglected, while for others no quantitative relation has been established between the transfer ratio and the physical
2. METHODS The experimental procedure is shown in Figure 1. A liquid drop was first placed on a donor surface. The acceptor surface was brought toward the drop so that a liquid bridge could form between the two surfaces. The compression stage was stopped when the separation between the two surfaces reached the minimum separation Hmin. After a short pause, the liquid bridge was stretched at a certain speed (U) until the liquid bridge broke. After this transfer process, part of the liquid was transferred from the donor surface to the acceptor surface. All experiments were performed at an ambient temperature of approximately 20.5 °C, and 2.0 μL of liquid was used. Phantom Miro M310 which can provide an imaging speed of 5000 fps with the resolution of 896 × 720 was used to record the process. The value of the transfer ratio is calculated by dividing the volume of the liquid transferred to the acceptor surface by the total liquid volume. Two different experimental setups were used. For the experiments with a relatively slow stretching speed (U < 20 mm/s), the motion of the acceptor surface was provided by a Motion Controller system (ILS100CC and XPS-C6 from Newport) (shown in Figure 2a). With this setup, the acceptor surface can be accelerated to a target velocity (
