A diagram showing a fluctuating droplet and its parametrization in terms of . The total area of the droplet is fixed and equal to .
Combined contour and velocity field plots showing the solutions for the velocity field given by Eqs. (34) and (35). The droplet contour is overlayed on the field plots for (a) standing and (b) traveling waves. The amplitude of the oscillations is chosen large enough so that the undulations can be observed. Parameters: and .
The dimensionless frequency , obtained by taking the square root of Eq. (47), is plotted as a function of for (a) and (b) . The open circles (○), bullets (●), and open squares (◻) show the positive and negative real parts, and the imaginary part, respectively.
The dynamic structure factor, , as a function of for . The solid (blue), dashed (red), dotted (green), and dashed-dotted (black) lines correspond to , 19.76, 0.1976, and 0.001 976, respectively. The dynamic structure factor scales as at intermediate frequencies for small and as at large angular frequencies.
Snapshot of a fluctuating droplet simulated using the particle-based simulation technique (Ref. 36) with 20% -80% particles. Average density in units of inverse . Parameters: , , and .
The averaged Fourier coefficients, and , for and . The deviation at indicates the presence of fourfold anisotropy due to the cubic cell structure. Bullets (●, ○) and squares (◻, ◼) correspond to and, , respectively. The results are independent of the viscosity of the fluid as expected (filled symbols: SRD collisions every time step, open symbols: SRD collisions every tenth time step). Parameters: , , , and .
Static structure factor, , as a function of mode number for and . The SRD collisions are performed at every time step [shown in bullets (●)], and at every tenth time step [shown in squares (◻)]. The corresponding average radii are given by and , respectively. The solid line is a fit to Eq. (16) which yields . Parameters: , , , and .
Dynamic structure factor, , as a function of time for large damping . The bullets (●), open circles (○), and filled squares (◻) correspond to , 3, and 4, respectively. The solid lines are obtained by numerically integrating Eq. (48). The average droplet radius is , , and . Parameters: , , , , and .
Dynamic structure factor, , as a function of time for moderate damping . The bullets (●), open circles (○), and filled squares (◻) correspond to , 3, and 4, respectively. The solid lines are obtained by numerically integrating Eq. (48) using . The viscosity is lowered by performing SRD collisions every tenth time step. The average droplet radius is and . Parameters: , , , , and .
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