Entrapped MicroBubble Dynamics

Calculates the natural frequencies and vibration modes of a micro-bubble with multiple circular openings doi.org/10.1063/5.0075876

% Citation instructions

If you use this function or its variations you are kindly requested to cite:

1) "Dynamics of entrapped microbubbles with multiple openings"

doi.org/10.1063/5.0075876

2) File Exchange detail page

% Description

Entrapped_MicroBubble_Dynamics calculates the natural frequencies and vibration modes (cosine only) of a micro-bubble with multiple circular openings as described in the manuscript "Dynamics of entrapped microbubbles with multiple openings" by Amit Dolev, Murat Kaynak, and Mahmut Selman Sakar. doi.org/10.1063/5.0075876

To use the function the user should download the following toolbox:

Bessel Zero Solver (https://www.mathworks.com/matlabcentral/fileexchange/48403-bessel-zero-solver), MATLAB Central File Exchange.

[fn, PHI_O] = Entrapped_MicroBubble_Dynamics(a, alphaV, V0)

[fn, PHI_O] = Entrapped_MicroBubble_Dynamics(a, alphaV, V0, NoModes, sigma, rho, kappa, p0, Modal_damping, M, N, BC)

% Inputs

a (m)- The opening radius.

alphaV - Nondimentional vector of the openings' radius.

V0 (m^3)- The volume of the bubble.

NoModes - The number of modes to plot

default value = length(alphaV)*2

sigma (N/m)- Fluid-gas surface tension.

default value = 0.0720 N/m

rho (kg/m^3)- Fluid density.

default value = 998.2 kg/m^3

kappa - Gas polytropic coeficient.

default value = 1.4

p0 (Pa)- Ambient pressure.

default value = 101325 Pa

Modal_damping - Assumed uniform modal damping.

M - Number of bessel fnctions to be used for building the basis functions

default value = 4

N - Number of bessel zeroes

default value = 3

BC - Boundary conditions 'baff' for a baffled bubble or 'free'

default value = 'baff'

% Outputs

fn (Hz)- All the computed natural frequencies

PHI_O - All the computed linear vibration modes

The function plots the NoModes first vibration modes

If Modal_damping is provided, the function plots the bubble's FRF when

subjected to a uniform pressure.

% Example

Example 1 - Compute the first natural frequencies and vibration modes of

a spherical bubble R=25um with a single opening a=10um, using the default

parameters;

a = 10e-6;

alphaV = 1;

R = 25e-6;

V0 = 4/3*pi*R^3;

[fn,PHI_O] = Entrapped_MicroBubble_Dynamics(a, alphaV, V0);

Example 2 - Compute the first 10 natural frequencies and vibration modes of

a spherical bubble R=15um with a two opening a1=8um a2=9um, assuming free

boundary conditions. And plot the FRF for a modal damping of 10%;

a = 8e-6;

alphaV = [1 9/8];

R = 15e-6;

V0 = 4/3*pi*R^3;

[fn,PHI_O] = Entrapped_MicroBubble_Dynamics(a, alphaV, V0, 10, [], [], [], [], 0.1, [], [], 'free');

Originally written by

Written by: Amit Dolev - 10/01/23

Contact: amit(dot)dolev(at)epfl(dot)ch