| Abstrakt: |
We report an experimental and theoretical study of the collapse time of a gas bubble injected into an otherwise stagnant liquid under quasi-static conditions and for a wide range of liquid viscosities. The experiments were performed by injecting a constant flow rate of air through a needle with inner radius a into several water/glycerine mixtures, providing a viscosity range of 20 cP ≲ μ ≲ 1500 cP. By analyzing the temporal evolution of the neck radius, R0(t), the collapse time has been extracted for three different stages during the collapse process, namely, Ri/a = 0.6, 0.4, and 0.2, being Ri = R0(t = 0) the initial neck radius. The collapse time is shown to monotonically increase with both Ri/a and with the Ohnesorge number, Oh = μ/ √ ρσRi, where ρ and σ represent the liquid density and the surface tension coefficient, respectively. The theoretical approach is based on the cylindrical Rayleigh-Plesset equation for the radial liquid flow around the neck, which is the appropriate leading-order representation of the collapse dynamics, thanks to the slenderness condition R0(t) r1(t) ≪ 1, where r1(t) is half the axial curvature of the interface evaluated at the neck. The Rayleigh-Plesset equation can be integrated numerically to obtain the collapse time, τcol, which is made dimensionless using the capillary time, tσ = √ ρR3 i /σ.We present a novel scaling law for τcol as a function of Ri/a and Oh that closely follows the experimental data for the entire range of both parameters, and provide analytical expressions in the inviscid and Stokes regimes, i.e., τcol(Oh → 0) → √ 2 lnC and τcol(Oh → ∞) → 2Oh, respectively, where C is a constant of order unity that increases with Ri/a.ρR3 i /σ.We present a novel scaling law for τcol as a function of Ri/a and Oh that closely follows the experimental data for the entire range of both parameters, and provide analytical expressions in the inviscid and Stokes regimes, i.e., τcol(Oh → 0) → √2 ln C and τcol(Oh → ∞) → 2Oh, respectively, where C is a constant of order unity that increases with Ri/a. [ABSTRACT FROM AUTHOR] |
