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Tortuosity and the Averaging of Microvelocity Fields in Poroelasticity

機(jī)譯：曲率和微流場(chǎng)的平均孔隙彈性

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The relationship between the macro- and microvelocity fields in a poroelastic representative volume element (RVE) has not being fully investigated. This relationship is considered to be a function of the tortuosity: a quantitative measure of the effect of the deviation of the pore fluid streamlines from straight (not tortuous) paths in fluid-saturated porous media. There are different expressions for tortuosity based on the deviation from straight pores, harmonic wave excitation, or from a kinetic energy loss analysis. The objective of the work presented is to determine the best expression for tortuosity of a multiply interconnected open pore architecture in an anisotropic porous media. The procedures for averaging the pore microvelocity over the RVE of poroelastic media by Coussy and by Biot were reviewed as part of this study, and the significant connection between these two procedures was established. Success was achieved in identifying the Coussy kinetic energy loss in the pore fluid approach as the most attractive expression for the tortuosity of porous media based on pore fluid viscosity, porosity, and the pore architecture. The fabric tensor, a 3D measure of the architecture of pore structure, was introduced in the expression of the tortuosity tensor for anisotropic porous media. Practical considerations for the measurement of the key parameters in the models of Coussy and Biot are discussed. In this study, we used cancellous bone as an example of interconnected pores and as a motivator for this study, but the results achieved are much more general and have a far broader application than just to cancellous bone.
機(jī)譯：多孔彈性代表體積元（RVE）中宏觀和微觀速度場(chǎng)之間的關(guān)系尚未得到充分研究。這種關(guān)系被認(rèn)為是曲折度的函數(shù)：定量測(cè)量孔隙流體流線偏離流體飽和的多孔介質(zhì)中筆直（而非曲折）路徑的影響。基于與直孔的偏離，諧波激勵(lì)或動(dòng)能損失分析，曲折度有不同的表達(dá)方式。提出的工作的目的是確定各向異性多孔介質(zhì)中多重互連開孔結(jié)構(gòu)的曲折性的最佳表達(dá)。作為研究的一部分，對(duì)Coussy和Biot在多孔彈性介質(zhì)的RVE上平均孔隙微速度的程序進(jìn)行了回顧，并確定了這兩個(gè)程序之間的重要聯(lián)系。基于孔隙流體粘度，孔隙率和孔隙結(jié)構(gòu)，確定孔隙流體方法中的庫西動(dòng)能損失是多孔介質(zhì)曲折性最吸引人的表達(dá)，從而獲得了成功?？椢飶埩渴强捉Y(jié)構(gòu)的3D度量，被引入到各向異性多孔介質(zhì)曲折張量的表達(dá)中。討論了在Coussy和Biot模型中測(cè)量關(guān)鍵參數(shù)的實(shí)際考慮。在這項(xiàng)研究中，我們以松質(zhì)骨為例，將其作為相互連通的毛孔并作為該研究的動(dòng)力，但所獲得的結(jié)果更為普遍，其應(yīng)用范圍遠(yuǎn)不止于松質(zhì)骨。

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