Study On The Dynamics Behavior Of Finite Deformation For Protein Bubbles In Non-Newtonian Fluid

The protein bubble is being widely used in the fields of biomedicine, chemical industry, material industry, fire protection, oil and gas well cementing. In above engineering applications, the protein bubbles are immersed in fluid or flow with fluid as a whole. Because the protein film of bubble wall is viscoelastic, and the fluid immersing the protein bubble is non-Newtonian fluid in the majority of cases, the study on dynamic performance of protein bubble in fluid is complicated. Further, the dynamic performance of bubble will affect the survival time and the uniformity of bubble in fluid, and also affect the stability of system composed of fluid and protein bubbles. So the comprehensive and in-depth study on the dynamic performance of protein bubble in non-Newtonian fluid would be most meaningful for maximizing its efficiencies.Based on the study on the finite deformation of bubble formed by protein film, the equation describing the dynamic performance of protein bubble in non-Newtonian fluid is developed. The effect of viscoelasticity of protein film, the size of bubble, the properties of fluid and the interaction force between bubbles on the finite deformation of bubble are analyzed. These analyses would provide valuable reference for better engineering applications and for expanding the further application fields of protein bubble. The main contents and results in current research are described below.(1) According to the energy density function for finite deformation of viscoelastic material, to the relaxation function of Maxwell model and to the deformation gradient tensor of bubble, a nonlinear equation describing the relation between the stress and finite deformation of protein bubble is presented. And then by using above equation and equilibrium equation of bubble, another equation describing the relation between relative deformation ratio of inner radius and time is developed for finite deformation yielded by the pressure difference acted on bubble walls. The numeric results show that, under the action of different load, the radial deformation of protein bubble is nonlinear, the balance size of bubble and the time needed to reach balance state are both different. Increasing the thickness and viscosity of protein film can prolong the time needed to reach balance state, and enhance the load-bearing capacity of protein bubble obviously. (2) According to the equation describing the relation between the stress and finite deformation of protein bubble, and to the dynamics equation of bubble, another nonlinear equation describing the bubble wall vibration, which is yielded by the actions of pressure difference, the elastic finite deformation stress and the dissipation stress, is developed for a single bubble. The numeric results show that, under the action of different initial transient pressure difference, the variations of vibration frequency of bubble wall, the decrement velocity of amplitude, and the balance sizes of bubble are all diverse. Increasing the thickness and the viscosity of protein film can prohibit the vibration of bubble wall and thus can enhance the load-bearing capacity of protein bubble. The smaller bubble will vibrate with higher frequency, and the decrement of velocity is slower than that of a bigger one.(3) Considering the effect of viscosity of non-Newtonian fluid on the action acted on the outside wall of bubble, a nonlinear equation describing the dynamic performance in finite deformation for a single protein bubble in Bingham fluid is developed. The numeric results show that, increasing the plastic viscosity of liquid the protein bubble wall will vibrate with higher decrement velocity of amplitude, and lower frequency and lead to the bigger balance size of bubble. The dynamic performance of above single protein bubble is compared with that of a cavitation bubble in Bingham fluid, the results show that, under the condition of identical liquid pressure and bubble size, the protein bubble wall will vibrate with lower decrement velocity of amplitude, the lower frequency and the final size of bubble is bigger than that of cavitation bubble in the same fluid. The dynamic performance of single protein bubble in Bingham fluid is also compared with that of a single protein bubble, which is yielded by pressure difference. The numeric results show that, if the pressure of liquid is equal to the action on the outside bubble wall, the bubble wall in Bingham fluid will vibrate with a longer period, lower frequency and the balance bubble size is also bigger.(4) Based on the study on the dynamic performance of a single protein bubble in Bingham fluid, further study on vibration of two protein bubbles in non-Newtonian fluid is carried out. Considering the Bjerknes force between two vibrating bubbles, the nonlinear vibration equations for two identical size protein bubbles in Bingham fluid are built. The numeric results show that, under the same initial condition and boundary condition, the two bubbles in Bingham fluid will vibrate with higher frequency and higher decrement velocity of amplitude than that of a single bubble. Shortening the distance between bubbles, the bubble wall will vibrate with a higher frequency and decrement velocity of amplitude, further, the smaller the bubble size is, the higher the increment of frequency and decrement velocity of amplitude are.(5) To verify the static deformation of protein bubble, an engineering application of protein bubble in cementing slurry is taken as an example. By way of simulating the pressure yielded by the cementing slurry at any position below the wellhead, the density changes are tested and the contraction ratio of bubble is calculated according to density changes. The results show that, increasing the pressure acted on the bubble wall, the tested and numeric variation trends for contraction ratios of inner bubble wall are essentially uniform. It is proved that the theoretical study on the static deformation is correct.