Lateral retention of water droplets on solid surfaces without gravitational effect
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Research Letter
Lateral retention of water droplets on solid surfaces without gravitational effect Sirui Tang, Dan F. Smith Department of Chemical Engineering, Lamar University, Beaumont, TX 77710, USA Chun-Wei Yao , Department of Mechanical Engineering, Lamar University, Beaumont, TX 77710, USA Rafael Tadmor, Dan F. Smith Department of Chemical Engineering, Lamar University, Beaumont, TX 77710, USA; Department of Mechanical Engineering, Ben Gurion University of the Negev, Beer Sheva 8410501, Israel Divine Sebastian, Department of Mechanical Engineering, Lamar University, Beaumont, TX 77710, USA Address all correspondence to Chun-Wei Yao at [email protected] (Received 22 April 2020; accepted 26 May 2020)
Abstract Gravity is commonly considered negligible when the surface tension is dominant; i.e., the Bond number is less than 1. In this paper, however, the authors present a technique in which drops slide over surfaces with zero effective gravity. Our study compared the sliding motion of water drops on hydrophilic and hydrophobic surfaces in scenarios: one in which effective gravity = 1 (1 g) and one in which it = 0 (0 g). The authors found that the lateral retention force was greater under 1 g than it was under 0 g. Also, the results showed that retention forces calculated by Furmidge equation are higher than the measured forces.
Introduction Droplet-based microfluidics has attracted a lot of attention due to its relevance in various applications, such as biochemical assays,[1–3] drug development,[4,5] medical diagnostics,[6] and fabrication of electronic devices.[7] For many of these applications, an understanding of interfacial sliding of droplets on solid substrates is crucial. More recently, the motion of water droplets has been investigated.[8–12] The droplet dynamics has been extensively studied in normal gravity conditions. As drop size decreases, the influence of gravity diminishes and is often considered to be negligible when the surface tension force is dominant, especially for small droplets.[13,14] However, more accurate force representation is necessary for some applications, such as the design of microfluidic devices.[15] The dimensionless Bond number,[16] defined as Bo = ΔρgL 2/γ, is often used to express the influence of gravity on different droplet sizes. Bo < 1 implies that adhesion forces are dominant over gravity, and the drop remains attached to the substrate. Also, the droplet shape is assumed to maintain as part of a sphere, as this shape minimizes the free energy of the system.[17,18] Ravi Annapragada et al.,[19] however, showed the spherical shape assumption for low Bond numbers (Bo < 1) underpredicts the droplet length and the contact area. Additionally, existing models demonstrate the effect of gravity on the height of the droplet and the contact radius for droplet sizes on the order of the capillary length of the liquid (Bo < 1).[17] In this paper, we investigate how small droplets move with and without gravity. Previous studies have examined the
motion of a droplet under different conditions
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