Foldy according to which bubbles do interact with the average pressure field but not with each other’s field. Note that the sound pressure is assumed to be harmonic, i.e. ~ . pS The equation relating the liquid pressure to the gas pressure is given by (2.13) also yields the following equation for the equilibrium state: (2.14) To complete the formulation, an equation for the internal pressure is needed. It could be either derived from the enthalpy equation , (2.15) where is the thermal conductivity or from the polytrophic equation for the K expansion of perfect gas: (2.16) is the ratio of specific heats. When equation (2.16) is used for the thermal γ equation of state, it refers to an isothermal process for the value of and adiabatic γ=1 process when =1.4. Further can have complex values which describe other γ γ physical phenomena. A more detailed formulation regarding the thermal phenomena can be found in the work of Prosperetti . Instead of using the polytrophic equation of the gas which does not account for the thermal losses, an ad hoc dissipative term is added to that equation by Prosperetti in order to simulate thermal viscous losses.
Foldy according to which bubbles do interact with the average pressure field but not with each other’s field. Note that the sound pressure is assumed to be harmonic, i.e. pS ~ . The equation relating the liquid pressure to the gas pressure is given by (2.13) also yields the following equation for the equilibrium state: (2.14) To complete the formulation, an equation for the internal pressure is needed. It could be either derived from the enthalpy equation , (2.15) where K is the thermal conductivity or from the polytrophic equation for the expansion of perfect gas: (2.16) γ is the ratio of specific heats. When equation (2.16) is used for the thermal equation of state, it refers to an isothermal process for the value of γ=1 and adiabatic process when γ =1.4. Further γ can have complex values which describe other physical phenomena. A more detailed formulation regarding the thermal phenomena can be found in the work of Prosperetti . Instead of using the polytrophic equation of the gas which does not account for the thermal losses, an ad hoc dissipative term is added to that equation by Prosperetti in order to simulate thermal viscous losses.
Thesis_Hakan_Dogan.docx