Based on the Church-Hoff model, the nonlinear oscillations of a single encapsulated microbubble with a finite thickness shell are theoretically studied. The effects of viscoelasticity on radial oscillations and the fu...Based on the Church-Hoff model, the nonlinear oscillations of a single encapsulated microbubble with a finite thickness shell are theoretically studied. The effects of viscoelasticity on radial oscillations and the fundamental and harmonic components are researched. The peaks of radial oscillations and magnitudes of power spectra of the fundamental and harmonic components all increase gradually with the shear modulus of shell varying from 0 to 10 MPa by an interval of 0. 1 MPa at the same shear viscosity, while they decrease as the shear viscosity increases from 0 to 1 Pa · s by an interval of 0. 01 Pa · s at the same shear modulus. The fluctuation ranges of subharmonic and ultraharmonic signals are much larger than both the fundamental and second harmonic components. It means that the effect of viscoelasticity on the subharmonic and ultraharmonic signals is greater than that on the fundamental and second harmonic components. So adjusting the viscoelasticity of the shell is a potential method to obtain a perfect microbubble contrast agent used for the subharmonic and ultraharmonic imaging. Four points with significant fundamental and harmonic components are chosen as an example： a shear viscosity of 0. 39 Pa · s with shear modulus of 3.9, 6. 6, and 8.6 MPa, respectively; a shear modulus of 6.6 MPa with a shear viscosity of 0.42 Pa · s.展开更多
BISHOP’s effective stress or two state stress variables are unsatisfactory for unsaturated soils where one of fluid phases is discontinuous, so new expressions of effective stress should be founded. The approach for ...BISHOP’s effective stress or two state stress variables are unsatisfactory for unsaturated soils where one of fluid phases is discontinuous, so new expressions of effective stress should be founded. The approach for derivation was according to the principle of equilibrium of forces (i.e., the stress-sharing principle), and it was firstly validated by demonstrating TERZAGHI’s principle of effective stress. And then, the derivations were subdivided into four parts according to different pore air states: 1) air bubbles were spherical and suspended in pore water; 2) air bubbles were bound on soil skeleton; 3) air bubbles held almost the single section of pore; 4) air phase was continuous. The different formulae of effective stress were presented. Conclusions are drawn as follows: 1) For nearly-saturated soils, the "real" effective stress would be a little smaller than TERZAGHI’s effective stress; 2) For soils in which air phase is discontinuous in the form of bubbles, a new concept of pore air elastic pressure is put forward, and the total stress can be constituted by effective stress, pore water pressure and pore air elastic pressure; 3) For soils in which air phase is continuous, effective stress is equal to the value of the total stress plus suction; 4) Suction can be divided into two parts: one is the effect caused by additional pressure, and the other is the contract action by the "skin".展开更多
基金The National Basic Research Program of China ( 973Program) ( No. 2011CB933503)the National Natural Science Foundation of China ( No. 50872021, 60725101, 31000453)
文摘Based on the Church-Hoff model, the nonlinear oscillations of a single encapsulated microbubble with a finite thickness shell are theoretically studied. The effects of viscoelasticity on radial oscillations and the fundamental and harmonic components are researched. The peaks of radial oscillations and magnitudes of power spectra of the fundamental and harmonic components all increase gradually with the shear modulus of shell varying from 0 to 10 MPa by an interval of 0. 1 MPa at the same shear viscosity, while they decrease as the shear viscosity increases from 0 to 1 Pa · s by an interval of 0. 01 Pa · s at the same shear modulus. The fluctuation ranges of subharmonic and ultraharmonic signals are much larger than both the fundamental and second harmonic components. It means that the effect of viscoelasticity on the subharmonic and ultraharmonic signals is greater than that on the fundamental and second harmonic components. So adjusting the viscoelasticity of the shell is a potential method to obtain a perfect microbubble contrast agent used for the subharmonic and ultraharmonic imaging. Four points with significant fundamental and harmonic components are chosen as an example： a shear viscosity of 0. 39 Pa · s with shear modulus of 3.9, 6. 6, and 8.6 MPa, respectively; a shear modulus of 6.6 MPa with a shear viscosity of 0.42 Pa · s.
基金Project(50878191) supported by the National Natural Science Foundation of ChinaProject(Y12E090030) supported by Zhejiang Provincial Natural Science Foundation, China
文摘BISHOP’s effective stress or two state stress variables are unsatisfactory for unsaturated soils where one of fluid phases is discontinuous, so new expressions of effective stress should be founded. The approach for derivation was according to the principle of equilibrium of forces (i.e., the stress-sharing principle), and it was firstly validated by demonstrating TERZAGHI’s principle of effective stress. And then, the derivations were subdivided into four parts according to different pore air states: 1) air bubbles were spherical and suspended in pore water; 2) air bubbles were bound on soil skeleton; 3) air bubbles held almost the single section of pore; 4) air phase was continuous. The different formulae of effective stress were presented. Conclusions are drawn as follows: 1) For nearly-saturated soils, the "real" effective stress would be a little smaller than TERZAGHI’s effective stress; 2) For soils in which air phase is discontinuous in the form of bubbles, a new concept of pore air elastic pressure is put forward, and the total stress can be constituted by effective stress, pore water pressure and pore air elastic pressure; 3) For soils in which air phase is continuous, effective stress is equal to the value of the total stress plus suction; 4) Suction can be divided into two parts: one is the effect caused by additional pressure, and the other is the contract action by the "skin".
