一种力–电协同驱动的细胞微流控培养腔理论模型

细胞培养液在微流控生物反应器中受到外界物理场(如压力梯度或者电场)作用流动而产生流体剪应力,并进一步刺激种子细胞调控其内部基因的表达,从而促进细胞的分化和生长,这个过程在自然生命组织内的微管中亦是如此.考虑到细胞培养微腔隙中液体流动行为很难实验量化测定,理论建模分析是目前可行的研究手段.因此建立了矩形截面的细胞微流控培养腔理论模型,将外部的物理驱动场(压力梯度与电场)与培养腔内液体的流速、切应力和流率联系起来,分别得到了压力梯度驱动(pressure gradient driven,PGD)、电场驱动(electric field driven,EFD)及力–电协同驱动(pressure-electricity synergic driven,P-ESD)三种驱动方式下的液体流动理论模型.结果表明该理论模型与现有的实验结果基本一致,即力–电协同作用下的解答为压力梯度驱动和电场驱动结果的叠加.细胞培养腔内的流体流速、剪应力及流率幅值均正比于外部物理场强幅值,但随着压力梯度驱动载荷频率的增大而减小,随着电场驱动频率的变化不明显.在压力梯度驱动作用下,细胞贴壁处的切应力随着腔高的增大而线性增大,流率则随着腔高的增大而非线性增大,而电场驱动下的结果不受腔高的影响.生理范围内的温度场变化对压力和电场驱动的结果影响不大.另外,在引起细胞响应的流体切应力水平,电场驱动能提供较大的切应力幅值而压力梯度驱动则能提供较大的流率幅值.该理论模型的建立为细胞微流控生物反应器实验系统的设计及参数优化提供理论参考,同时也为力–电刺激细胞生长、分化机理的研究的提供基础.     

一种骨小管中液体流动产生的流量及切应力模型

骨组织受力变形后其内部液体就会流动,同时在其微观结构——骨单元壁中扩散,并进一步产生一系列与骨液流动相关的物理效应,如流体剪切应力、流动电位等,这些物理效应被细胞感知并做出破骨或成骨等反应,来使骨适应外部载荷环境.鉴于骨组织产生的内部液体流动很难实验测定,理论模拟是目前的主要研究手段.基于骨单元的多孔弹性性质建立了骨小管内部液体的流动模型,该模型将骨单元所受的外部载荷与骨小管内部液体的压力、流速、流量和切应力联系起来,并进一步可以研究其力传导与力电传导机制.骨小管模型的建立分别基于中空和考虑哈弗液体的骨单元模型,并考虑了骨单元外壁的弹性约束和刚性位移约束两种边界条件.最终得到骨单元在外部轴向载荷作用下,骨小管内部液体的流量及流体切应力的解析解.结果表明:骨小管中的液体流量与流体切应力都正比于应变载荷幅值和频率,并由载荷的应变率决定.因此应变率可以作为控制流量和流体切应力的一种生理载荷因素.流量随着骨小管半径的增大而非线性增大,而流体切应力则随着骨小管半径的增大而线性增大.此外,在相同的载荷下,含哈弗液体的骨单元的模型中,骨小管中液体的流量和切应力均大于中空骨单元模型.     

局部狭窄血管中血液振荡流的速度和切应力

本文建立一种分析局部缓慢狭窄血管中血液振荡流的数学模型，给出了血液的轴向流速，径向流速和切应力的包含压力梯度项的解析表达式，并讨论了血管内由局部狭窄引起的压力梯度沿轴向变化的规律。文章以局部余弦狭窄为例进行数值计算，详细讨论上游均匀管段压力梯度的定常部分和不同次谐波对狭窄管段内流速和切应力的影响。数值结果表明，与均匀管情况相比，在狭窄段内，血液振荡流轴向流速无论平均值还是脉动幅值均明显增大，且径向流速不再为零。但径向流速仍远小于轴向流速。同时，切应力也不再仅由轴向流速梯度提供，径向流速梯度也将产生切应力，但是在计算管壁切向上的切应力时，径向流速梯度的贡献仍相当大。与均匀管管壁切应力沿流运方向保持恒定不同。狭窄管管壁切应力（平均值和脉动值）将随着狭窄高度的增大而增大，在狭窄最大高度处达到最大，因而沿流动方向产生了较大的切应力梯度。     

切应力协同下受热过冷层流液膜的破断特性

针对界面切应力协同下受热过冷层流液膜流动的破断过程, 建立了不同气液流向下的临界液膜厚度和最小润湿量的理论模型, 分析了不同驱动力作用下, 接触角、流体温度、界面切应力和壁面热流密度对液膜破断特性的影响. 研究表明: 临界液膜厚度和最小润湿量均随壁面热流密度的增加而增大; 重力驱动下的接触角影响在不同热流密度下有所不同, 流体温度在不同驱动力下对最小润湿量的影响截然相反; 同向切应力驱动下临界液膜厚度和最小润湿量随切应力增加而减小; 在重力和切应力协同驱动下, 同向切应力对最小润湿量的影响与重力和切应力所起作用的相对大小有关, 反向切应力使得临界液膜厚度和最小润湿量有所增大.      

平行平板流动腔的数值优化设计

平行平板流动腔系统是研究切应力对细胞影响的体外实验装置之一。前期研究发现,流动腔的高度存在一个最佳高度,使用这个高度可以有效地减小或避免由于装配所引起的高度误差对切应力的影响。为了获得这一最佳高度,本文使用数值方法研究了平行平板流动腔的几何尺寸、流体粘度与集中液阻之间的关系,并拟合得到了集中液阻的函数关系式。利用液阻关系式和切应力计算公式,求得了对底部切应力影响最小的最佳高度的表达式。同时,研究还发现,对于相同的底部切应力,当高度取最佳高度时,所需的入(出)口压差最小。这样在流动腔底部沿轴向的压力梯度也就越小,沿轴向不同位置之间的压力差别也越小,这将有利于细胞力学实验结果之间的比较。     

具有切应力梯度的平行平板流动腔的构造

在近年来关于流体切应力与细胞力学行为之间关系的研究中,流体切应力梯度被认为是诱发动脉粥样硬化和内膜增生的重要因素之一.本文探讨如何利用常用的离体细胞力学实验工具--平行平板流动腔模拟具有梯度的定常流切应力环境.结果表明,根据Hele-Shaw流的原理和常用复势W(Z)=AZn(n＞1)的特性,可构造出具有各种切应力梯度分布的流动腔.与其它模拟切应力梯度的方法比较,本文的方法更加简洁、可行.     

刚性圆管中血液周期振荡流的切应力分布

本文通过求解圆管内血液振荡流的基本方程，求得圆管内血液流的压力梯度与切应力之间的关系式。在此基础上，详细讲座了圆管中轴向流速和切变率谐波的变化规律，指出流速谐波和切变率谐波的幅值都将随着谐波次数的增大而逐渐减小。为了使所得结果便于应用。文章通过管轴向中心线流速与压力梯度之间的关系式，进一步给出一种利用管轴向中心线流速计算管内切应力分布的简便方法。该方法用于检测活体血管内血液振荡流的切应力分布，具有操作简单，精度较高的优点。最后，以人体颈动脉为例，讨论血液周期振荡流的切应力的分布特性。发现在任意时刻，除了邻近管壁处切应力急剧增大到一定数值之外，沿管截面切应力分布相当均匀且接近于零，呈现出与定常流不同的切应力分布特征。     

微流控器件中的多相流动

微流控技术及微流控器件是近年来发展迅速的多学科交叉研究领域,相比于传统方法,微流控技术能够实现对微量多相流体的精准操控,可应用于化学分析、先进材料合成、蛋白质结晶、单细胞培育及检测、信息处理等领域。该文回顾微流控器件中的多相流动现象,概述其所涉及的流体力学机理,阐述实现多相微流控的各种方法,并分析多相微流控技术的应用现状及面临的挑战,最后总结针对多相微流动问题的数值模拟方法和实验测量技术,展望多相微流控器件的研究方向及应用前景。     

微流控器件中的多相流动

微流控技术及微流控器件是近年来发展迅速的多学科交叉研究领域.相比于传统方法, 微流控技术能够实现对微量多相流体的精准操控, 可应用于化学分析、先进材料合成、蛋白质结晶、单细胞培育及检测、信息处理等领域. 该文回顾微流控器件中的多相流动现象, 概述其所涉及的流体力学机理,阐述实现多相微流控的各种方法, 并分析多相微流控技术的应用现状及面临的挑战, 最后总结针对多相微流动问题的数值模拟方法和实验测量技术, 展望多相微流控器件的研究方向及应用前景.      

微流控通道内细胞及其初级纤毛的力传导行为

细胞处于复杂的生理环境之下,附着在细胞表面的初级纤毛被认为是重要的力学信号传感器,其与细胞的代谢、发育、分裂和增殖等生理活动密切相关.为了研究细胞及其初级纤毛在微流体环境下的力传导行为,本文建立了力-电协同驱动下的矩形微流控通道和含有多孔黏弹性属性的贴壁细胞有限元模型系统.考察了细胞的细胞质和细胞核在振荡层流下的应力、应变、孔隙压力和孔隙流速等力学信号响应,量化研究了初级纤毛作为细胞独特的力学感受器的生物力学行为. 结果表明:细胞在振荡层流下的力学响应表现出和外加力-电驱动载荷相同的震荡规律.渗透率是细胞多孔弹性力学行为的主要影响因素. 初级纤毛是细胞主要的力学感受器,细胞可以通过纤毛长度和直径调节其力学感受敏感性(应力影响区域),随着初级纤毛长度的增大, 其纤毛挠曲刚度减小, 但是敏感性增大.模型的建立为进一步研究微流体剪切作用下的细胞生长、分化等微观机理提供基础,同时也为检测细胞微结构器(纤毛等蛋白链)的力学性能提供了理论技术支持.      

A fluid flow model in the lacunar-canalicular system under the pressure gradient and electrical field driven loads

The lacunar-canalicular system (LCS) is acknowledged to directly participate in bone tissue remodeling. The fluid flow in the LCS is synergic driven by the pressure gradient and electric field loads due to the electro-mechanical properties of bone. In this paper, an idealized annulus Maxwell fluid flow model in bone canaliculus is established, and the analytical solutions of the fluid velocity, the fluid shear stress, and the fluid flow rate are obtained. The results of the fluid flow under pressure gradient driven (PGD), electric field driven (EFD), and pressure-electricity synergic driven (P-ESD) patterns are compared and discussed. The effects of the diameter of canaliculi and osteocyte processes are evaluated. The results show that the P-ESD pattern can combine the regulatory advantages of single PGD and EFD patterns, and the osteocyte process surface can feel a relatively uniform shear stress distribution. As the bone canalicular inner radius increases, the produced shear stress under the PGD or P-ESD pattern increases slightly but changes little under the EFD pattern. The increase in the viscosity makes the flow slow down but does not affect the fluid shear stress (FSS) on the canalicular inner wall and osteocyte process surface. The increase in the high-valent ions does not affect the flow velocity and the flow rate, but the FSS on the canalicular inner wall and osteocyte process surface increases linearly. In this study, the results show that the shear stress sensed by the osteocyte process under the P-ESD pattern can be regulated by changing the pressure gradient and the intensity of electric field, as well as the parameters of the annulus fluid and the canaliculus size, which is helpful for the osteocyte mechanical responses. The established model provides a basis for the study of the mechanisms of electro-mechanical signals stimulating bone tissue (cells) growth.

     

MECHANOTRANSDUCTION OF THE CELL AND ITS PRIMARY CILIUM IN THE MICROFLUIDIC CHANNEL 1)

细胞处于复杂的生理环境之下,附着在细胞表面的初级纤毛被认为是重要的力学信号传感器,其与细胞的代谢、发育、分裂和增殖等生理活动密切相关.为了研究细胞及其初级纤毛在微流体环境下的力传导行为,本文建立了力-电协同驱动下的矩形微流控通道和含有多孔黏弹性属性的贴壁细胞有限元模型系统.考察了细胞的细胞质和细胞核在振荡层流下的应力、应变、孔隙压力和孔隙流速等力学信号响应,量化研究了初级纤毛作为细胞独特的力学感受器的生物力学行为. 结果表明:细胞在振荡层流下的力学响应表现出和外加力-电驱动载荷相同的震荡规律.渗透率是细胞多孔弹性力学行为的主要影响因素. 初级纤毛是细胞主要的力学感受器,细胞可以通过纤毛长度和直径调节其力学感受敏感性(应力影响区域),随着初级纤毛长度的增大, 其纤毛挠曲刚度减小, 但是敏感性增大.模型的建立为进一步研究微流体剪切作用下的细胞生长、分化等微观机理提供基础,同时也为检测细胞微结构器(纤毛等蛋白链)的力学性能提供了理论技术支持.     

Seismoelectric Fluid/Porous-Medium Interface Response Model and Measurements

Coupled seismic and electromagnetic (EM) wave effects in fluid-saturated porous media are measured since decades. However, direct comparisons between theoretical seismoelectric wavefields and measurements are scarce. A seismoelectric full-waveform numerical model is developed, which predicts both the fluid pressure and the electric wavefields in a fluid in which a porous disc is embedded. An experimental setup, in which pressure and electric signals in the fluid are simultaneously measured, is presented. The setup allows the detection of the EM field that is generated when an acoustic wave crosses the interface between the fluid and the thin porous disc, without interference of electrical fields that are present within seismic body waves. The predicted pressure wavefield agrees well with the measurements in terms of acoustic wave travel times, waveforms, and amplitudes. The electric wavefield predictions agree with the recordings in terms of travel times, waveforms, and spatial amplitude decay. A discrepancy in amplitude of the converted EM signal is observed. Theoretical amplitudes that are smaller than the measurements were also reported in previous literature. These results seem to validate seismoelectric theory.     

Flow of electrolytes in a porous medium

A two-scale model of ion transfer in a porous medium is obtained for one-dimensional horizontal flows under the action of a pressure gradient and an external electric field by the method of homogenization. Steady equations of electroosmotic flows in flat horizontal nano-sized slits separated by thin dielectric partitions are averaged over a small-scale variable. The resultant macroequations include Poisson’s equation for the vertical component of the electric field and Onsager’s relations between flows and forces. The total horizontal flow rate of the fluid is found to depend linearly on the pressure gradient and external electric field, and the coefficients in this linear relation are calculated with the use of microequations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 162–173, July–August, 2008.     

On Thermodiffusion and Gauge Transformations for Thermodynamic Fluxes and Driving Forces

We discuss the molecular diffusion transport in infinitely dilute liquid solutions under nonisothermal conditions. This discussion is motivated by an occurring misinterpretation of thermodynamic transport equations written in terms of chemical potential in the presence of temperature gradient. The transport equations contain the contributions owned by a gauge transformation related to the fact that chemical potential is determined up to the summand of form (AT + B) with arbitrary constants A and B, where constant A is owned by the entropy invariance with respect to shifts by a constant value and B is owned by the potential energy invariance with respect to shifts by a constant value. The coefficients of the cross-effect terms in thermodynamic fluxes are contributed by this gauge transformation and, generally, are not the actual cross-effect physical transport coefficients. Our treatment is based on consideration of the entropy balance and suggests a promising hint for attempts of evaluation of the thermal diffusion constant from the first principles. We also discuss the impossibility of the “barodiffusion” for dilute solutions, understood in a sense of diffusion flux driven by the pressure gradient itself. When one speaks of “barodiffusion” terms in literature, these terms typically represent the drift in external potential force field (e.g., electric or gravitational fields), where in the final equations the specific force on molecules is substituted with an expression with the hydrostatic pressure gradient this external force field produces. Obviously, the interpretation of the latter as barodiffusion is fragile and may hinder the accounting for the diffusion fluxes produced by the pressure gradient itself.     

Thickness-averaged model for numerical simulation of electroosmotic flow in three-dimensional microfluidic chips

The microfluidic system is a multi-physics interaction field that has attracted great attention. The electric double layers and electroosmosis are important flow-electricity interaction phenomena. This paper presents a thickness-averaged model to solve three-dimensional complex electroosmotic flows in a wide-shallow microchannel/chamber combined (MCC) chip based on the Navier-Stokes equations for the flow field and the Poisson equation to the electric field. Behaviors of the electroosmotic flow, the electric field, and the pressure are analyzed. The quantitative effects of the wall charge density (or the zeta potential) and the applied electric field on the electroosmotic flow rate are investigated. The two-dimensional thickness-averaged flow model greatly simplifies the three-dimensional computation of the complex electroosmotic flows, and correctly reflects the electrookinetic effects of the wall charge on the flow. The numerical results indicate that the electroosmotic flow rate of the thickness-averaged model agrees well with that of the three-dimensional slip-boundary flow model. The flow streamlines and pressure distribution of these two models are in qualitative agreement.     

Simulation of flux expulsion and associated dynamics in a two-dimensional magnetohydrodynamic channel flow

We consider a plane channel flow of an electrically conducting fluid which is driven by a mean pressure gradient in the presence of an applied magnetic field that is streamwise periodic with zero mean. Magnetic flux expulsion and the associated bifurcation in such a configuration are explored using direct numerical simulations (DNS). The structure of the flow and magnetic fields in the Hartmann regime (where the dominant balance is through Lorentz forces) and the Poiseuille regime (where viscous effects play a significant role) are studied, and detailed comparisons to the existing one-dimensional model of Kamkar and Moffatt (J Fluid Mech 90:107–122, 1982) are drawn to evaluate the validity of the model. Comparisons show good agreement of the model with DNS in the Hartmann regime, but significant differences arising in the Poiseuille regime when nonlinear effects become important. The effects of various parameters like the magnetic Reynolds number, imposed field wavenumber etc. on the bifurcation of the flow are studied. Magnetic field line reconnections occurring during the dynamic runaway reveal a specific two-step pattern that leads to the gradual expulsion of flux in the core region.     

Unsteady hydromagnetic Couette flow of dusty fluid with temperature dependent viscosity and thermal conductivity

In the present paper the unsteady Couette flow and heat transfer of a dusty conducting fluid between two parallel plates with temperature dependent viscosity and thermal conductivity are studied. A constant pressure gradient and an external uniform magnetic field are applied. The governing coupled momentum and energy equations are solved numerically using finite differences. The effect of the variable viscosity and thermal conductivity of the fluid and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed.