Nonlinear power loss in the oscillations of coated and uncoated bubbles: Role of thermal, radiation and encapsulating shell damping at various excitation pressures
Bibliographic record
Abstract
This study presents the fundamental equations governing the pressure dependent disipation mechanisms in the oscillations of coated bubbles. A simple generalized model (GM) for coated bubbles accounting for the effect of compressibility of the liquid is presented. The GM was then coupled with nonlinear ODEs that account for the thermal effects. Starting with mass and momentum conservation equations for a bubbly liquid and using the GM, nonlinear pressure dependent terms were derived for power dissipation due to thermal damping (Td), radiation damping (Rd) and dissipation due to the viscosity of liquid (Ld) and coating (Cd). The pressure dependence of the dissipation mechanisms of the coated bubble have been analyzed. The dissipated energies were solved for uncoated and coated 2–20 μm in bubbles over a frequency range of 0.25fr-2.5fr (fr is the bubble resonance) and for various acoustic pressures (1 kPa-300 kPa). Thermal effects were examined for air and C3F8 gas cores. In the case of air bubbles, as pressure increases, the linear thermal model looses accuracy and accurate modeling requires inclusion of the full thermal model. However, for coated C3F8 bubbles of diameter 1–8 μm, which are typically used in medical ultrasound, thermal effects maybe neglected even at higher pressures. For uncoated bubbles, when pressure increases, the contributions of Rd grow faster and become the dominant damping mechanism for pressure dependent resonance frequencies (e.g. fundamental and super harmonic resonances). For coated bubbles, Cd is the strongest damping mechanism. As pressure increases, Rd contributes more to damping compared to Ld and Td. For coated bubbles, the often neglected compressibility of the liquid has a strong effect on the oscillations and should be incorporated in models. We show that the scattering to damping ratio (STDR), a measure of the effectiveness of the bubble as contrast agent, is pressure dependent and can be maximized for specific frequency ranges and pressures.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".