Flow of water through channels filled with deformable polymer gels

A mathematical model is developed for the flow of water through a channel impregnated with a polymer gel that is treated as an elastic and deformable porous medium. The model uses a Brinkman equation along with an experimentally observed velocity-dependent permeability. Numerical and approximate analytical solutions are given. These results show that the gel intrinsic properties, i.e., gel reference permeability and elastic index, control the water flow. First, the permeability of water flow through the gel increases with an increase of gel reference permeability. Second, the velocity of water decreases when the gel velocity exponent increases. Our theoretical results show that the velocity-dependent permeability of water flow through polymer gels is in fact an intrinsic property of the gel rather than a property of the channel or some interaction between the gel and the pore walls.     

A contact mechanics method for characterizing the elastic properties and permeability of gels

When a saturated gel immersed in the same liquid is suddenly brought into contact with a smooth rigid indenter, the liquid cannot immediately flow out of the pores, and so the gel initially behaves as an incompressible material. This gives rise to a pressure gradient in the liquid phase and the liquid flows until the pressure in it goes to zero everywhere, and all the stresses are transferred to the elastic network. As a result of the flow, the force needed to maintain a constant contact area relaxes with time. In this work, we study the feasibility of using an indentation test to measure this time‐dependent force and to determine the elastic modulus, the Poisson's ratio, and the permeability, D_p, of the network. Specifically, we consider a two‐dimensional Hertz contact problem of a rigid circular cylinder indenting on a half space consisting of an elastic gel. The network of the gel is assumed to be linearly elastic and isotropic, and liquid flow within the gel is assumed to obey Darcy's law, which states that the flux is proportional to the pressure gradient. Exact expressions are obtained for the initial and final force required to maintain a given contact length. These expressions allow us to determine the elastic constants of the network. The permeability of the network can be obtained from the time‐dependent relaxation of the load, which is obtained by solving the exact continuum equations. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 359–370, 2006     

Yielding behavior of thermo-reversible colloidal gels

The breakdown of structure in gelled suspensions due to the application of an external stress results in flow. Here we explore the onset of flow by investigating the onset of nonlinear behavior in the elastic moduli of a widely studied class of thermo-reversible gels over a range of volume fractions. We employ the system composed of octadecyl-coated silica particles (radius = 24 nm) suspended in decalin that displays a transition from a liquid to a gel below a volume-fraction-dependent gel temperature, Tgel. The perturbative yield stress at which the gel modulus drops to 90% of its value in the linear viscoelastic limit is found to increase monotonically with volume fraction and decreasing temperature. The recently proposed activated barrier-hopping theory of Schweizer and co-workers1,2 presents a framework to capture the impact of external forces on the mechanical properties of structurally arrested systems. By characterizing particle interactions with a Yukawa potential and employing the resultant static structure factor as input into the activated barrier-hopping theory, we make predictions for how the elastic modulus evolves with the applied stress. Comparisons of these calculations with experiments reveal that the theory does an excellent job of quantitatively capturing the perturbative yield stresses over the entire range of volume fractions and temperatures explored in the study. The match of predictions with experimental results suggests that the theory not only captures particle localization but also how this localization is modulated in the presence of an external stress.     

新型刺激响应性纤维素基含能凝胶的流变性能

研究了以不同基团含量的羧甲基纤维素硝酸酯(CMCN)为胶凝剂的含能凝胶细微结构与流变行为的关系.探讨了凝胶的形成机理,并采用线性的流变学方法研究了凝胶的屈服性、触变性、蠕变性及温敏性等动态黏弹性质,分别利用Herschel-Bulkley模型、Burger模型及Carreau-Yasuda模型对凝胶的流动曲线、蠕变曲线和频率曲线进行了数据拟合.研究发现,CMCN凝胶是由其分子结构上两亲性基团通过分子链间氢键及疏水键等非共价键相互作用形成的一种结构均匀的物理交联网络型凝胶.凝胶的非牛顿系数n均小于0.5.随着亲水性羧酸基团含量的增加,凝胶的屈服应力逐渐增大,触变恢复性逐渐增强,弹性与黏性柔量均减小,但其比值增加,蠕变的黏性响应性逐渐减弱而弹性响应性逐渐增强.凝胶的温敏性变化有一个力学松弛转变区,随着羧酸基团含量的增加,松弛转变区愈发明显,凝胶的温敏性也逐渐增强.     

新型含能纤维素基凝胶推进剂的流变性能研究

制备了以羧甲基纤维素硝酸酯(CMCN)为胶凝剂的硝基甲烷(NM)凝胶, 系统研究了CMCN 修饰基团比例变化所引起NM/CMCN凝胶流变性能差异性的规律. 探讨了凝胶的形成机理并采用线性的流变学方法研究了NM/CMCN凝胶的屈服性、触变性、蠕变性、温敏性等动态粘弹性质, 分别利用Herschel-Bulkley 模型、Burger 模型、Carreau-Yasuda模型、Andrade-Eyring 模型对凝胶的流动曲线、蠕变曲线、频率曲线和温敏曲线进行了数据拟合. 研究发现, NM/CMCN凝胶是由CMCN 大分子链上两亲性基团与有机小分子基团间通过分子链间疏水键、氢键等非共价键相互作用形成的一种物理交联网络型凝胶. 凝胶的非牛顿系数n均小于0.60. 随着硝酸酯基团含量的减少, NM/CMCN 凝胶的结构强度变弱, 表现出屈服应力逐渐减小、触变恢复性逐渐增强、粘性与弹性柔量均减小但粘性柔量比例增加的趋势; 凝胶的弹性响应性逐渐减弱而粘性响应性渐强, 内耗也逐渐增大;凝胶的活化能总体上增大, 温度稳定性变弱.     

Clustering and mechanics in dense depletion and thermal gels

We report on the microstructure and mechanical properties (elastic modulus) of concentrated depletion and thermal gels of octadecyl-coated silica particles for different values of the strength of interaction--polymer concentration for depletion gels and temperature for thermal gels. The depletion gels are composed of dense clusters and voids, while the thermal gels are devoid of clusters. Shear breaks up clusters in depletion gels while it induces clustering in the thermal gels. In both of these gels, the microstructure recovers to the presheared state upon cessation of shear. The recovery of the elastic modulus mimics the microstructure in the sense that the elastic modulus recovers to the presheared sheared state after shearing is stopped. Calculations of the gel boundary by modeling the interactions with an effective one-component square-well model reveals that suspensions with similar ranges of attraction gel at the same volume fraction at a fixed strength of attraction. Calculations of the elastic modulus using the na?ve mode coupling theory for depletion gels are in good agreement with experimental measurements provided clustering is taken into account and have the same magnitude as the elastic moduli of thermal gels with similar strengths of attraction. These calculations, in addition to the experimental observations reinforce the point that the microscopic parameter determining the elastic modulus of dense gels and its recovery is the localization length which is only a fraction of the particle diameter and not the structure on the length scale of the particle diameter and larger.     

Stress generation by solvent absorption and wrinkling of a cross-linked coating atop a viscous or elastic base

An in-plane constrained cross-linked gel layer absorbs an equilibrium amount of solvent and experiences in-plane compressive stress. A stability analysis of such an elastic gel layer that is attached to either a viscous or an elastic bottom layer atop a rigid substrate is considered. The effects of the top and bottom layer moduli (E(t) and E(b)), the bottom-to-top layer thickness ratio (H/h), and the polymer solvent interaction parameter (chi) on the critical condition of wrinkling, wrinkle wavelength, and amplitude are examined. When the bottom layer is viscous, the compressed top layer is always unstable, and wrinkling is rate-controlled. The viscous flow of the bottom layer governs the rate and determines the fastest growing wavelength. As E(t) rises, the bending stiffness of the elastic layer does as well, and so the fastest growing wavelength (lambda(m)) rises and the equilibrium amplitude (A(e)) falls. As H/h rises, the constraint of the rigid substrate diminishes, and so lambda(m) and A(e) rise. As chi falls or as the solvent has higher affinity for the polymeric gel, lambda(m) falls and A(e) rises because better solvents create higher compressive strain that promote low-wavelength, high-amplitude wrinkles. When the bottom layer is elastic, a critical compressive stress exists. If the generated compressive stress by solvent absorption is greater than the critical stress, the top layer wrinkles. It was found that wrinkling is most likely at intermediate E(t), low E(b), high H/h, and low chi. Further, lower chi, higher H/h, and lower E(b) were found to promote higher equilibrium amplitude and higher wavelength wrinkles.     

Rheology and Permeability of Crosslinked Polyacrylamide Gel

Gels produced by crosslinking polyacrylamide solutions with chromium (III) have been characterized by dynamic rheology studies. To vary the gel strength, different polymer concentrations were used, while keeping the temperature, salinity, and crosslinker concentration constant. Both the loss and storage moduli increased with the polymer concentration for this gel system. The storage modulus at the end of the gelation was used to characterize the gel strength. Steady-state water flow experiments through gel-filled capillary tubes were performed, with the aim of linking the gel strength and flow behavior. The permeability was found to be a function of the water flow rate (velocity) and polymer concentration. Two parameters were used to characterize the flow behavior, intrinsic gel permeability and elasticity index, which are each functions of the polymer concentration. However, only one parameter is needed to fully identify the flow and rheological gel properties, as the elasticity index and storage modulus are linked by a power-law relationship. The loss modulus and intrinsic permeability are correlated with the storage modulus and elasticity index, respectively. A theoretical model for this behavior linking both gel properties based on the dual domain structure was used to demonstrate that the flow and rheological behavior of the gel are indeed related and that the gel strength controls the water permeability. Implications for prediction of flow of water through gels emplaced in a porous medium are discussed.     

Stress relaxation of deformed gel in a good solvent

A method for obtaining elastic moduli and frictional properties of gel chains, diagonal and off-diagonal elements of a friction tensor, from a tensile force relaxation of cylindrical gel that is stretched in a good solvent is presented. The theory to describe the relaxation is developed on the assumption that an off-diagonal element of the friction tensor is nonzero and compared with experimental results obtained for the poly(acrylamide) gel in water. The experiments revealed that the tensile force relaxation, F(t) at a long t, was described by a function: F(t)=A(Fi-FS) x exp(-t/tau)+FS, where Fi, FS, and A, respectively, were tensile forces at the initiation and the steady state, and a constant. The tau was found to be proportional to a square of radius of the gel. The experiments also revealed that the elastic force relaxation was synchronized with a change of the gel diameter. The theory well elucidates the experimental results to reveal the bulk and shear moduli, and the diagonal and off-diagonal elements of friction tensor.     

Relaxation of a viscoelastic gel bar: I. theory

When a rod of gel is deflected in 3-point bending, two types of relaxation process occur: hydrodynamic relaxation caused by flow of liquid within the gel network, and viscoelastic relaxation of the network itself. The kinetics of load relaxation have previously been analyzed for the case of hydrodynamic relaxation within a perfectly elastic network. That analysis describes, for example, the behavior of silica gel in a nonreactive solvent, such as acetone. When the liquid can attack the gel network, then true viscoelastic relaxation is superimposed on hydrodynamic relaxation, and that situation is examined in the present paper. To a very good degree of approximation, the total relaxation is equal to the product of the hydrodynamic and viscoelastic relaxation functions. In Part II, it will be shown that the present analysis describes the behavior of silica gel in an aqueous solvent and in an alcohol/amine solution.     

IPAAm凝胶在丙酮水溶液中溶胀行为的关联与预报

基于Maurer和Prausnitz的凝胶相平衡条件，建立了凝胶的溶胀模型.模型假设凝胶是以凝胶组分及凝胶吸收的溶液为核心，以弹性半渗透膜为壳的复合体.并采用UNIQUAC方程计算凝胶相及与之共存液相的Gibbs过剩自由能，采用“phantomnetwork”理论计算凝胶的弹性自由能，采用“自由体积”计算分子的尺度效应.同时以N-异丙基丙烯酰胺（IPAAm）为单体合成了IPAAm凝胶.研究了25 ℃时IPAAm凝胶在丙酮水溶液中的溶胀行为，并测定了丙酮在胶体相和与之共存液相中的分配，以检验模型的关联与预报能力.结果表明,模型预报的单体总量和交联剂浓度对凝胶溶胀的影响与实验符合得很好.而且凝胶溶胀时，能很好地预测丙酮在两相中的分配,表明模型具有很好的关联和预报能力.     

Relaxation of a viscoelastic gel bar: II. Silica gel

Silica gel is shown to be elastic in the presence of dry alcohol, but viscoelastic (VE) in aqueous media; the rate of VE relaxation increases with the concentration of water. At 25 vol% water in ethanol, the rate of viscoelastic relaxation decreases with pH, approaching zero (i.e., elastic behavior) at pH 1.5. Elastic behavior is also seen in methanol, but VE relaxation is rapid upon addition of 1% triethylamine. It is concluded that VE relaxation results from attack by the liquid on siloxane bonds in the gel network. The kinetics of relaxation are well described by the theory presented in Part I.     

Reversible switching of the sol-gel transition with ultrasound in rhodium(I) and iridium(I) coordination networks

Reversible coordination networks were prepared by combining diphenylphosphinite telechelic polytetrahydrofuran (2) with [RhCl(COD)]2 or [IrCl(COD)]2 in chloroform. Both systems resulted in stable gels at concentrations above 50 and 30 g/L for the rhodium(I) and iridium(I) networks, respectively. The rheological properties of the two coordination networks (100 g/L) were determined with oscillatory shear experiments, which showed that the elastic moduli are constant over a wide frequency range, indicating gel-like behavior; the iridium(I) gel has an elastic modulus distinctly higher (2.8x10(3) Pa) than that of the rhodium(I) gel (1.0x10(3) Pa). Ultrasonication of the rhodium(I) gel caused liquefaction after 3 min; regelation occurred 1 min after sonication was stopped. The iridium(I) gel was also liquefied after 3 min of sonication, but regelation took 1.5 h at room temperature and more than 10 days at -20 degrees C. 31P NMR measurements on model complexes showed that the large differences in gelation times are in agreement with the ligand exchange kinetics of the rhodium(I) and iridium(I) complexes. We propose that sonication of the gels results in ligand exchange, which changes the network topology without changing the coordination chemistry. Upon sonication, the fraction of metal centers in active cross-links decreases and thereby reduces the gel fraction to zero. The system is not at equilibrium, and upon standing the gel fraction increases at a rate that is determined by the exchange kinetics of the metal complex. The observed effects offer opportunities to use ultrasound in the activation of dormant transition metal catalysts.     

表面活性剂对氧化锰悬浮体系流变学振荡行为的影响

对介孔氧化锰的溶胶-凝胶法合成和用表面活性剂（脂肪醇聚氧乙烯醚, AEO_9)的模板合成过程中所得的悬浮体系的流变性质进行了对比研究。结果表明： 上述体系均具有触变性,且无论是否预剪切,其表观粘度均随时间作周期性振荡; 同时上述体系的储能模量G'和损耗模量G"亦具有周期性的振荡行为。但表面活性剂 AEO_9的引入使体系的触变性大为减弱,屈服值明显降低,凝胶结构强度减弱。同 时还发现引入AEO_9的模板合成过程中,不仅体系的表观粘度及G'大幅度下降,且 G'与G"的振荡周期显著增大,振幅亦明显减小。这说明体系中两亲分子与无机物存 在较强的相互作用,作者还对这些现象进行了讨论。     

The liquid crystalline state of polyimide precursors

The polyimide precursor poly(4,4′-methylenediphenylene pyromellitamic acid) (PMDPAA) in N-methyl pyrrolidone (NMP) was a lyotropic liquid crystal as evidenced by a DSC thermogram and x-ray spectrum on its gel, and optical properties by the existence of the critical concentration on the solution viscosity. The configuration of PMDPAA as shown by wide angle x-ray diffraction pattern was composed of regular meta pyromellitamic acid units. These units together with the rigid character of ? CH₂? linkage between two phenyl rings, and the hydrogen bonding of the intermesogenic units were surmised to be the driving force for liquid crystal formation. The liquid crystalline characters were dependent on molecular weight, solid content, temperature, and the extent of mechanical shearing flow. Data from rheometrics mechanical spectrometer (RMS) indicated that the elastic character of the melt of PMDPAA gel at room temperature shifted to lower frequency on standing and the complex dynamic viscosity increased with time.     

Mechanical Properties of Gel-Derived Materials

The mechanical behaviour of xerogels and aerogels is generally described in terms of brittle and elastic materials, like glasses or ceramics. The main difference compared to silica glass is the order of magnitude of the elastic and rupture moduli which are 10⁴ times lower. However, if this analogy is pertinent when gels are under a tension stress (bending test) they exhibit a more complicated response when the structure is submitted to a compressive stress. The network is linearly elastic under small strains, then exhibits yield followed by densification and plastic hardening. As a consequence of the plastic shrinkage it is possible to densify and stiffen the gel at room temperature. These opposite behaviours (elastic and plastic) are surprisingly related to the same two kinds of gel features: the silanol content and the pore volume. Both elastic modulus and plastic shrinkage depend strongly on the volume fraction of pores and on the condensation reaction between silanols. On the mechanical point of view (rupture modulus and toughness), it is shown that pores and silanols play also an important role. Pores can be considered as flaws in the terms of fracture mechanics and the flaw size, calculated from rupture strength and toughness is related to the pore size distribution. Different kinds of gels structure (fractal or not fractal) have been synthesized by a control of the different steps of transformation such as sintering and plastic compaction. The relationships between structural and the elastic properties are discussed in terms of the percolation theory and fractal structure.     

Yielding Behavior in Injectable Hydrogels from Telechelic Proteins

Injectable hydrogels show substantial promise for use in minimally invasive tissue engineering and drug delivery procedures.1,2 A new injectable hydrogel material, developed from recombinant telechelic proteins expressed in E. coli, demonstrates shear thinning by three orders of magnitude at large strains. Large amplitude oscillatory shear illustrates that shear thinning is due to yielding within the bulk of the gel, and the rheological response and flow profiles are consistent with a shear-banding mechanism for yielding. The sharp yielding transition and large magnitude of the apparent shear thinning allow gels to be injected through narrow gauge needles with only gentle hand pressure. After injection the gels reset to full elastic strength in seconds due to rapid reformation of the physical network junctions, allowing self-supporting structures to be formed. The shear thinning and recovery behavior is largely independent of the midblock length, enabling genetic engineering to be used to control the equilibrium modulus of the gel without loss of the characteristic yielding behavior. The shear-banding mechanism localizes deformation during flow into narrow regions of the gels, allowing more than 95% of seeded cells to survive the injection process.     

Thixotropic organogels based on a simple N-hydroxyalkyl amide: rheological and aging properties

The thixotropic properties ofthermoreversible organogels composed ofN-3-hydroxypropyl dodecanamide and various apolar fluids have been investigated by X-ray scattering, light microscopy, and rheo-optics experiments. This revealed that gel formation occurs via a precipitation process. Depending upon the cooling rate, large interconnected aggregates are formed and induce an elastic behavior. When submitted to a shear flow, these aggregates disentangled and became aligned in the direction of the velocity. Nevertheless, shear does not alter the structure of the individual aggregate and connections between the aggregates are quickly rebuilt due to gravity and thermal fluctuations when the applied flow is stopped. The alignment under flow and the reformation of the connections after the cessation of the shear induces the thixotropic behavior.     

Rheology of PVC Plastisol: Particle Size Distribution and Viscoelastic Properties

Plastisols of poly(vinyl chloride), PVC, are suspensions of fine particles in plasticizer with about 50% resin volume fraction. Typically, the gross particle size ranges from 15 to 0.2 &mgr;m and smaller, where the common practice of spray-drying these resins and subsequent grinding of larger particles dictate the size ranges including agglomerates as well as the primary particles. The plastisol is a pastelike liquid, which may be spread to coat substrates. The coated substrates are heated in an oven to gel and fuse the material for producing uniform, rubbery products. Because the first step of processing is spreading the plastisol on a substrate, rheology at room temperature is obviously important. The material is thixotropic under very low stress. The flow behavior is pseudoplastic and exhibits dilatancy and fracture at high shear rate. This work is concerned with the pseudoplastic behavior but the dynamic mechanical measurements are employed instead of the usual steady-state shear flow measurements. This is because the steady shear may break up agglomerates. The dynamic measurements with small strain-amplitude avoid the break-up of the agglomerates. This is important, because this work is concerned with the effects of the particle size distribution on the material behavior. The frequency dependence of both viscous and elastic behavior is recorded and presented with samples varying in particle size distribution. Copyright 2001 Academic Press.