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Coalescence Dynamics of Drops over a Hydrophobic Surface

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Drop Dynamics and Dropwise Condensation on Textured Surfaces

Part of the book series: Mechanical Engineering Series ((MES))

Abstract

Fluid motion arising from the coalescence of two liquid drops is discussed. Experiments are described in which two small water drops are placed on a chemically textured hydrophobic surface (apparent contact angle ~150°), either in sessile or in pendant modes, respectively, just touching each other, under atmospheric conditions. Equal and unequal drop volumes have been studied. The Bond number of the combined drop falls within 0.01–0.04. The resulting coalescence process has been imaged by a high-speed camera, till the combined drop reaches equilibrium. The sequence of images arising from coalescence is analyzed. The position of the center of mass of the combined drop is determined, with displacement yielding the velocity components. The centroid displacement data show that two timescales describe the harmonic content of flow oscillations. These are related to the high initial flow velocities generated, followed by viscous relaxation of the fluid at later times. Scale analysis in terms of force pairs and energy components delineate experimental trends in velocity and wall shear stress. Shear stresses are momentarily developed at the wall at the short timescale, with a magnitude depending on the drop volumes. These are smaller in the pendant mode compared to the sessile. The possibility of including the coalescence details of individual droplet pairs in a complete dropwise condensation model is then discussed.

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Abbreviations

A :

Gas-liquid interface area (m2)

E :

Surface energy (J)

E ∗ :

Excess surface energy function (−)

E CL :

Contact line dissipation (W)

E g :

Change of potential energy with time (W)

E k :

Change of kinetic energy rate with time (W)

E s :

Surface energy rate of a coalesced drop (W)

E vis :

Viscous dissipation (W)

f :

Roughness factor (−)

\( \overset{\rightharpoonup }{g} \) :

Acceleration due to gravity (m/s2)

m :

Spring stiffness (N/m)

m :

Mass (kg)

M, N:

Number of images and number of pixels in each image (−)

N p :

Number of pixels at the interface of a combined drop (−)

p :

Pressure (N/m2)

r :

Radius of the drop (m)

R :

Characteristic length (m)

Ravg = 1/RC:

Average instantaneous radius of the combined drop (m)

R b :

Radius of the combined drop footprint (m)

(RC):

Radius of curvature averaged over the air-water interface (m−1)

t :

Time (s); suffix IS is inertia-surface tension; IV is inertia-viscous; VS is viscous-surface tension

U :

Velocity scale (m/s)

u c :

x-component of centroid velocity (m/s)

\( {u}_{\mathrm{c}}^{\ast } \) :

Non-dimensional x-component of centroid velocity (−)

\( {u}_{\mathrm{res}}=\sqrt{u_{\mathrm{c}}^2+{v}_{\mathrm{c}}^2} \) :

Resultant velocity of the centroid (m/s)

V, Vcomb drop:

Volume and volume of the combined drop (m3)

v c :

y-component of centroid velocity (m/s)

\( {v}_{\mathrm{c}}^{\ast } \) :

Non-dimensional x-component of centroid velocity (−)

w i :

Area function for the ith pixel (−)

xc, yc:

x- and y-coordinates of centroid (m); time-average is indicated by an overbar

\( {x}_{\mathrm{c}}^{\ast },{y}_{\mathrm{c}}^{\ast } \) :

Non-dimensional x- and y-coordinates of centroid (−);

Bo:

Bond number, \( \frac{\rho {gR}^2}{\sigma } \)

We:

Weber number, \( \frac{\rho {U}^2R}{\sigma } \)

Fr:

Froude number, \( \frac{U^2}{gR} \)

Re:

Reynolds number, \( \frac{\rho UR}{\mu } \)

Oh:

Ohnesorge number, \( \frac{\mu }{\sqrt{\rho R\sigma}} \)

\( \dot{\gamma} \) :

Shear rate (s−1)

γ ∗ :

Non-dimensional hear rate (−)

θ :

Contact angle (°)

μ, ν:

Dynamic and kinematic viscosity (Pa s; m2/s)

ρ :

Fluid density (kg/m3)

σ :

Coefficient of surface tension (N/m)

τ :

Dimensionless time (−)

ζ :

Damping ratio (−)

1 :

Drop placed below (−)

2 :

Drop placed above (−)

3 :

Combined drop after coalescence (−)

c:

Critical (−)

CB:

Cassie-Baxter state (−)

eq:

Equilibrium (−)

lg:

Liquid-gas interface (−)

sg:

Solid-gas interface (−)

sl:

Solid-liquid interface (−)

W:

Wenzel state (−)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, India

    Praveen Somwanshi, K. Muralidhar & Sameer Khandekar

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  1. Praveen Somwanshi
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  2. K. Muralidhar
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  3. Sameer Khandekar
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Somwanshi, P., Muralidhar, K., Khandekar, S. (2020). Coalescence Dynamics of Drops over a Hydrophobic Surface. In: Drop Dynamics and Dropwise Condensation on Textured Surfaces. Mechanical Engineering Series. Springer, Cham. https://doi.org/10.1007/978-3-030-48461-3_3

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  • DOI: https://doi.org/10.1007/978-3-030-48461-3_3

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