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Tomoya Omata
January 13, 2022


Tomoya Omata

January 13, 2022

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  1. Advanced CC Engineering Course, National Institute of Technology, Kisarazu College
    Department of Civil Engineering, National Institute of Technology, Kisarazu College
    Simulation of water droplet movements on the surface
    by means of MPS
    The deterioration on the structure by salt damage is being currently at issue and
    therefore numerical simulation on prediction of salt adhesion on the structure
    surface was performed. However, there are currently many studies that focus on
    the transportation of sea-salt particles caused by the wind. Salt damage impact
    that rainwater gives to the structure surface in seashore vicinity is different from
    that in the upcountry rejoin, but, in both areas, the deterioration degree of the
    structure tends to depend on the raindrop movements. In addition, its
    movements vary depending on droplet size, the adhesion behavior simulation
    that assumed every raindrop size is needed.
    The main influence of raindrop adhesion
    Seashore vicinity
    Upcountry region
    The sea
    Rainwater : Purifying action
    Sea salt particles By wind
    Rainwater : Salt damage
    By rain
    Young’s formula
    MPS Method : The calculation method to be able to reproduce a fluid interface clearly
    ▼ Governing equation
    p This method calculate by considering a distance between
    particles (𝑟) in effective radius (𝑟!
    ) as heaviness.
    𝛾! : Interfacial energy of solid
    𝑟" : Effective radius
    = −𝛻𝑃 + 𝜇𝛻!𝒖 + 𝒇
    implicit explicit
    ▼ Surface tension model
    𝑟#$%: Initial distance between
    ▼ Particle interaction model
    p The surface tension of the droplet on the surface is
    reproduced by using the potential between particles.
    ▼ Wettability model of the solid wall
    𝑷 𝒓 : Potential between the liquid particles
    𝑃 𝑟
    𝑃 𝑟
    𝑃 𝑟 : Attractive force
    𝑟 > 𝑟#$%
    𝑃 𝑟 : Repulsive force
    𝑟 ≤ 𝑟#$%
    p Wettability of the solid wall depicts in contact angle
    defined in Young’s formula.
    p The potential of wettability acts to form the contact
    angle inputted.
    − 𝛾#"
    − 𝛾#
    𝑐𝑜𝑠𝜃 = 0
    Solid wall
    𝑟 : Distance between particles
    𝛾&! : Interfacial energy between fluid and solid
    𝛾& : Interfacial energy of fluid
    ▼ Consideration
    0.1s later…
    Droplet size 𝐦𝐦𝟑 2-5
    Number of particles 125
    Mass density of the fresh water kg/m# 1000
    Mass density of the salt water kg/m# 1030
    Kinematic viscosity of fluid P + s
    Gravity acceleration m%/s 9.8
    Effective radius 2.1×𝑟&'(
    Effective radius of surface tension model 2.1×𝑟&'(
    Time step s 1.0×10$)
    Surface tension coefficient N/m 0.0728
    Contact angle ° 90
    Table.1 Calculation condition
    Fig.1. Measurement result of the droplet thickness for the droplet size
    ▼ Measurement result of droplet thickness
    (a) 𝑉 = 2mm3 (b) 𝑉 = 3mm3
    (c) 𝑉 = 4mm3 (d) 𝑉 = 5mm3
    (a) 𝑉 = 2mm3 (b) 𝑉 = 3mm3
    (c) 𝑉 = 4mm3 (d) 𝑉 = 5mm3
    ▼ Visualization of the adhesion behavior
    ▼ Condition
    Fig.2. Comparison of the fresh water droplet behavior by the droplet size
    Fig.3. Comparison of the salt water droplet behavior by the droplet size
    This research simulated the adhesion behavior of the droplet in different size by using means of MPS.
    And, I examined them as follows from the results (fig.1) (fig.2) (fig.3).
    - The attaching droplet become easily to spread and be crushed with increase of droplet volume.
    - The attaching droplet thickness is inversely proportional to the liquid density when the droplet size is more than capillary length.
    𝜅&' =
    capillary length : The droplet length that gravity
    becomes more dominant than surface tension
    𝜿&𝟏 (𝐓𝐡𝐞 𝐟𝐫𝐞𝐬𝐡 𝐰𝐚𝐭𝐞𝐫 ) : 2.726mm
    Given to capillary length, because the range of droplet size that the fresh water
    droplet cannot keep thickness is 2mm³-3mm³, gravity becomes more dominant than
    surface tension, and the droplet became easily to be crushed from this range. In
    addition, it was revealed that the droplet thickness is smaller than assumed when the
    fluid density went up because the droplet thickness of the salt water is smaller than
    that of the fresh water.
    #&''() *&''() $&''() +&''()
    𝜃 = 90°

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