相互作用力及液膜排液动力学研究进展

邢耀文1,桂夏辉1,曹亦俊1,2,刘炯天1,2

(1.中国矿业大学 国家煤加工与洁净化工程技术研究中心,江苏 徐州 221116; 2.郑州大学 河南资源与材料产业河南省协同创新中心 河南 郑州 450000)

摘 要:颗粒气泡间相互作用力及液膜薄化破裂动力学是揭示浮选黏附机理的核心,也是近年来浮选胶体化学领域的研究热点。为深入明晰浮选黏附机理,对当前颗粒气泡间相互作用力及液膜排液动力学模型理论研究进展进行了系统综述。对于颗粒气泡间相互作用力,疏水引力可克服颗粒气泡间范德华力和静电斥力,诱发黏附。不同作用程范围内疏水力的来源机制不同:长程疏水力(>20 nm)主要源于固液界面亚微米/纳米气泡桥接,而短程疏水力(<20 nm)则主要源于固液界面水分子重排效应。由于疏水力强烈的吸引性和气液界面变形,颗粒气泡间疏水力的定量表征仍存在较大的挑战。对于颗粒气泡间液膜排液动力学模型,最具代表性的有Stefan-Reynolds平坦膜模型,Taylor模型和Stokes-Reynolds-Young-Laplace(SRYL)模型。Stefan-Reynolds及Taylor模型并未考虑排液过程中气泡表面曲率的变化,其应用存在着较大的局限性。SRYL模型则在描述液膜薄化速率的同时,兼顾了气泡表面在流体力和表面力等外力作用下的变形行为。在给定起始与边界条件下,SRYL模型通过数值迭代法与液膜排液试验测试结果对比,可以计算出颗粒气泡间的相互作用力信息;也可通过与相互作用力试验结果对比获得液膜排液数据。在今后的研究中,应重点将SRYL模型与试验测试相结合,对颗粒气泡间疏水力进行定量表征,揭示浮选黏附机理。

关键词:浮选;黏附;相互作用力;疏水力;排液动力学

颗粒气泡间相互作用力及液膜薄化破裂动力学是揭示浮选黏附机理的核心问题,也是近年来浮选胶体化学领域的研究热点。从热力学角度讲,水相中气泡会在固体表面形成有限接触角,其中气液固三相润湿周边铺展状态可由Young方程[1]描述:

γSG=γSL+γLGcos θ

(1)

式中,γSG为固气界面自由能;γSL为固液界面自由能;γLG为气液界面自由能;θ为接触角。

浮选气泡与固体颗粒发生黏附过程中的吉布斯自由能变化ΔG可由Dupre方程[1]来表示,联合Young方程可得

ΔG=γLG(1-cos θ)

(2)

由式(2)可知,一旦固体表面接触角大于0,气泡可在其表面成功黏附并达到热力学稳定状态。然而,在实际浮选中,只有疏水性颗粒才能被气泡捕获,造成此矛盾的原因是热力学方程没有考虑颗粒气泡黏附的动力学特性,黏附过程中的作用力及排液动力学不容忽视。基于此,对当前颗粒气泡间相互作用力及液膜排液动力学模型理论研究进展进行了系统综述。

1 颗粒气泡间相互作用力

1.1 DLVO力

根据经典DLVO理论,颗粒气泡黏附应由范德华力及双电层力共同支配[2-3]。当排斥力主导时,颗粒气泡间形成稳定液膜;当吸引力主导时,液膜会发生薄化破裂。对于颗粒气泡体系,单位面积的范德华力Πd通常可以由Hamaker方法或Lifshitz连续性理论表示。在不考虑延迟效应条件下有

(3)

其中,A132为以水相为中间介质的颗粒气泡间Hamaker常数,下标1代表颗粒,2代表气泡,3代表水相介质;h为分离距离。

A132可以由物质介电常数及光学折射率来确定,可近似为

(4)

式中,A11为颗粒在真空介质中的Hamaker常数;A22为气泡在真空介质中的Hamaker常数;A33为水在真空介质中的Hamaker常数。

对于单位面积的双电层力Πe,可以由恒定表面电势条件下的Hogg-Healy-Fuerstenau近似公式[3-4]计算:

(5)

式中,ε为水的介电常数;ε0为真空介电常数;κ-1为德拜长度;ψ1ψ2为颗粒及气泡表面电势。在计算中通常使用Zeta电位来替代表面电势。

一般来说,浮选颗粒气泡表面均呈电负性,体系Hamaker常数始终为正值,因此范德华及双电层力均表现为排斥作用,颗粒气泡间液膜应一直处于稳定状态。由此可见,经典DLVO理论可以诠释亲水性颗粒的浮选行为但并不能有效的解释疏水性颗粒气泡间的黏附机理,体系必须存在着第3种力(疏水力)以克服颗粒气泡间DLVO斥力诱发黏附。

1.2 疏水力及其来源机制

LASKOWSKI 和KITCHENER[5]首次发现了甲基化石英表面润湿膜的自发薄化破裂现象,并猜测疏水化石英基板与气泡间可能存在一种吸引力克服排斥性的范德华及双电层力。BLAKE 和KITCHENER[6]进一步测量了气泡与不同接触角的石英基板间的液膜临界破裂厚度,发现疏水性石英表面的润湿膜破裂厚度在60~220 nm变化,指出与传统DLVO力相比该吸引力具有更长的作用范围。1982年,PASHLEY和ISRAELACHVILI[7-8]首次实现了疏水力的定量表示,他们利用表面力仪(SFA)测量了十六烷基三甲基溴化铵(CTAB)存在体系中云母间的相互作用力,发现疏水力以1 nm的衰变长度按单指数模型衰减。自此,众多学者相继利用SFA,原子力显微镜(AFM)及薄膜压力平衡技术(TFB)对疏水力进行了测量[9-28]。然而,目前关于疏水力的来源机制及大小仍是一个充满争议的课题,疏水样品的制备方法及力测试手段均对结果有着很大影响,难以找到一个通用机制可以适用并概括所有的疏水力测试结果[29]

21世纪初期,CHRISTENSON和CLAESSON[27]、MEYER等[30]和XING等[29]详细探讨了疏水力的来源机制,其中较具代表性的来源机制有:固水界面水分子重排熵效应、局部电荷波动、纳米气泡桥接及亚稳态液膜分离诱导空化作用,如图1所示。

图1 疏水力来源机制[30]Fig.1 Possible mechanisms for hydrophobic force[30]

固水界面水分子重排可能是诱发短程疏水力的主要原因。水分子难以与疏水固体表面分子发生氢键作用,疏水界面的存在会打散体相水分子氢键笼形网状结构。因此,水分子趋向于恢复原有笼形配置使得疏水界面会受到“排挤”作用产生疏水力。MEZGER等[31]利用高能X射线反射技术对十八烷基三氯硅烷(OTS)覆盖的二氧化硅-水界面的水分子结构和密度云图进行了检测(图2),X射线穿过系列复合折射透镜(CRL)完成聚焦,发现界面存在0.5 nm左右的水分子排空区,这也直接说明了疏水性OTS与水分子间存在一定的排斥作用,界面水分子处于热力学不稳定状态。ERIKSSON等[32]则推导了基于水分子结构有序性的疏水力模型,随着分离距离的减小水分子有序性系数增加,模型能够很好的预测疏水力行为。HAMMER 等[33]指出疏水表面对界面水分子氢键排列顺序的影响仅在几个水分子层内起作用(0~1 nm),这意味着水分子重排只能诱发短程疏水力。TABOR 等[34]使用AFM对油滴间相互作用力进行了测试,通过配制与油滴折射率相等的溶剂来有效屏蔽范德华力,试验疏水力按0.3 nm(水分直径)的衰减长度衰减,进一步验证了基于水分子重排的短程疏水力假说,然而仍然存在部分文献结果与该假说相矛盾[12-13,35]。如熵起源力应受系统温度的影响,ISHIDA等[19]发现短程疏水力并不具有温度响应行为。

图2 MEZGER等实验系统及测试结果[31]
Fig.2 Experimental setup and results of MEZGER etc[31]

基于双分子层荷电补丁的静电作用是疏水力的另一种可能来源机制[36],但此假说主要针对表面活性体系。具体来说,覆盖在云母表面的表面活性剂单分子层逐渐向不完整的双层膜结构转变并最终形成荷正电双层膜与电负性裸露云母微区相间的新表面,如图1(c)所示。在云母相互靠近过程中,上下表面间电荷相反微区的对齐排列最终导致长程静电引力作用。MIKLAVCIC等[37-38]曾对恒定电势及恒定电量边界条件下非均质表面间的双电层力数学表达式进行了推导,表面电荷的非均匀排列可产生较强的引力作用。然而,表面活性剂系统中的短程吸引力来源仍然无法得到合理的解释。

CHRISTENSEN和CLAESSON[26]认为疏水界面间亚稳态液膜空化作用是产生长程疏水引力的原因。利用SFA对碳氢化合物及氟碳化合物表面间的表面力进行了测量,通过监视中间介质的光学折射率变化发现了空化气泡的生成。但空化是在界面接触前还是在接触后产生仍存在一些争议,YAKUBOV等[39]及AZADI 等[40]发现AFM力曲线中疏水颗粒间的跳入黏附距离随着接近次数的增加逐渐增加至最大,如图3所示。这说明第1次颗粒间接触后的分离压降诱导了空化气泡的形成,再次接触时由于界面空化气泡的存在产生长程疏水力。FAGHIHNEJAD和ZENG[41]则使用SFA-正置光学显微镜连用系统对不同电解质浓度下的聚苯乙烯表面间的相互力进行了测试,在样品接近过程中观察到了空化气泡的形成。

图3 去离子水中不同接近次数下的疏水化石英小球与硅板
之间的力曲线[40]
Fig.3 Measured force curves for consecutive approaches in deionized water between silicon wafer and silica spheres after hydrophobic treatment[40]

纳米气泡桥接也是较具代表性的长程疏水力来源机制之一,并在21世纪开始受到了学者们的广泛关注。PARKER等[17]首次指出疏水固体表面的亚微米气泡是导致阶梯状AFM力曲线的原因。ISHIDA等[42]和LOU等[43]使用轻敲模式AFM实现了界面纳米气泡成像,采用非侵入性光学检测手段[44-46]也相继发现了纳米气泡使得其存在性已被学者们广为接受[23,47-51]。如果长程疏水力来源于纳米气泡桥接,那么水相中溶解气体及纳米气泡性质会对力学行为产生影响。TYRRELL和ATTARD[52]发现疏水石英胶体探针与玻璃基板间的黏附距离与表面纳米气泡的高度相当。一些研究也表明脱气处理会显著减小疏水力作用程[41,53-57],但脱气处理后仍然可以检测到一种明显强于范德华力的短程疏水力。此外,学者们发现毛细力数学模型可以很好的拟合长程疏水吸引力,间接证明了疏水力的纳米气泡起源[47,58-60]。MISHCHUK等[61-62]认为纳米气泡的存在会显著改变中间介质的介电常数,进而影响范德华力及双电层力,仅需对传统DLVO力进行适当修正即可对疏水力做出合理的解释。

FAGHIHNEJAD和ZENG[41]提出了一种三区段疏水力模型,不同的区域内的疏水力形成机制不同,如图4所示。包括:由微米及亚微米气泡桥接或荷电补丁引起的长程引力区(20 nm到几百纳米),纳米气泡桥接或Hamaker常数强化引起的中等作用区(几纳米到20 nm)及固液界面水分子结构效应造成的短程引力区。亚微米气泡及纳米气泡桥接从本质上讲同属于毛细作用力,同时考虑到荷电补丁假说的应用体系局限性,疏水力的来源机制可以更广义的概括为基于亚微米/纳米气泡桥接引发的长程力和基于固液界面水分子重排引发的短程力。

图4 三区段疏水力模型[41]
Fig.4 Three-region hydrophobic interaction model[41]

疏水力通常可以使用指数衰减或幂式衰减模型来表示。其中单位面积疏水力的双指数模型[2-3,63]表达式为

(6)

式中,Πh为单位面积疏水力;C1为长程疏水力常数;D1为长程疏水力衰变长度;C2为短程疏水力常数;D2为短程疏水力衰变长度;h为分离距离。

目前大部分疏水力来源机制及力行为研究均聚焦于固-固系统,但疏水力作为颗粒气泡间液膜薄化破裂的驱动力已经达成了共识[29]。目前的主要挑战是如何定量颗粒气泡间疏水作用力。一方面,由于其强烈的吸引性作用,传统力测试技术如AFM及SFA很难在准静态模式下操作,当吸引力梯度超过仪器的弹簧的弹性系数时,跳入黏附过程中的有效力信息难以提取。另一方面,由于气液界面的变形效应,颗粒气泡间绝对分离距离的确定存在困难。

2 颗粒气泡间流体动力学排液模型

学者们通常使用雷诺润滑理论来描述颗粒气泡间液膜薄化动力学行为,其中流体力学边界条件对液膜排液动力学方程有着显著影响。对于气液界面,研究发现极微量的表面活性剂可使得气液界面变成无滑移界面[64]。对于固液界面,一般认为亲水性表面为无滑移界面[65];而疏水性表面则遵守Navier滑移准则[66],但仍有很多学者将疏水界面看做无滑移界面处理[67-68]。目前,经常使用的代表性排液模型包括:Stefan-Reynolds平坦膜模型,Taylor模型及Stokes-Reynolds-Young-Laplace(SRYL)模型。

Stefan-Reynolds模型是基于平行液膜假设的条件下获得的。在无滑移边界条件下,平坦液膜排液动力学方程可表示为

(7)

式中,t为时间;ΔP为液膜及液体体相压力差;μ为液体黏度;Rf为液膜半径。

众多排液试验发现在颗粒气泡接近过程中气液界面经常存在涟漪变形[69],Stefan-Reynolds模型未考虑涟漪形成后的流体阻力,因此会对排液速率产生过高估计。MANICA等[70]认为Stefan-Reynolds模型因其内在的不连续性不能准确描述液膜薄化动力学。

Taylor模型最早用于描述固体小球接近接近固体基板过程中的液膜薄化行为。在无滑移边界条件下有[71-73]:

(8)

式中,Fh为流体阻力;R为小球半径。

当固体小球被气泡所替代,并进一步考虑范德华力及静电力作用时[72],则有:

(9)

式中,ρ为水的密度;g为重力加速度。

Taylor模型的局限性同样在于没有考虑气泡接近过程中的变形效应,气泡内部的拉普拉斯压力难以克服排液过程中产生的流体阻力。对于Stefan-Reynolds和Taylor模型,均需要借助薄膜干涉技术观测液膜厚度的时空演化,通过拟合排液试验数据来获得颗粒气泡间相互作用力。

SRYL模型则在描述液膜薄化速率的同时,兼顾了气泡表面在流体力和表面力等外力作用下的变形行为。在给定起始与边界条件下,SRYL模型通过数值迭代法与液膜排液试验测试结果对比,可以计算出颗粒气泡间的相互作用力信息;也可通过与相互作用力试验结果对比获得液膜排液数据。IVANOV等[74]首次构建了SRYL控制方程。CHAN等[75]在此基础上将表面力项加入到了传统SRYL模型中。至此,SRYL模型使得力及液膜排液动力学真正意义上的实现了统一,其描述了颗粒气泡间作用力、界面变形及液膜排液3者间的动态耦合关系。模型控制方程主体为2部分:1部分是描述液膜排液的SR方程;另1部分是描述界面变形的YL方程。无滑移边界条件下,SR排液方程和YL变形方程可以表示为

(10)

(11)

式中,为等效半径;p(r,t)为液膜内部与外围体相的流体压力差;Π(r,t)为单位面积的总表面力,含范德华力,静电力及疏水力。

由YL方程可知,当流体力和表面力为排斥力时,气液界面为了维持力平衡状态将向气泡圆心方向变形,当流体压力和分离压力之和大于气泡内部拉普拉斯压力时,此时界面会形成浅凹变形。相反,当流体压力和分离压力之和为吸引力,气液界面将背离圆心方向形成凸起。

根据Derjaguin近似原理对流体压力和单位面积表面力在[0,∞]区间内积分可得颗粒气泡间的动态相互作用力,即

F(t)=2π[p(r,t)+Π(r,t)]rdr

(12)

其中,F(t)为颗粒气泡间相互作用力,在AFM体系下,探针所测得的力即为F(t)。

使用Matlab ODE15S标准软件包可完成对上述SRYL偏微分方程的数值求解,需要注意的是求解前需要使用毛细数对各变量进行无量纲化处理。

3 结 论

(1)对于颗粒气泡间相互作用力,疏水引力可克服颗粒气泡间范德华力和静电斥力,诱发黏附。不同作用程范围内疏水力的来源机制不同:长程疏水力(>20 nm)主要源于固液界面亚微米/纳米气泡桥接,而短程疏水力(<20 nm)则主要源于固液界面水分子重排效应。由于疏水力强烈的吸引性和气液界面的变形效应,颗粒气泡间疏水力的定量表征仍存在较大的挑战。

(2)对于颗粒气泡间液膜排液动力学模型,最具代表性的有Stefan-Reynolds平坦膜模型,Taylor模型和SRYL模型。Stefan-Reynolds及Taylor模型并未考虑排液过程中气泡表面曲率的变化,其应用存在着较大的局限性。SRYL模型则在描述液膜薄化速率的同时,兼顾了气泡表面在流体力和表面力等外力作用下的变形行为。在给定起始与边界条件下,SRYL模型通过数值迭代法与液膜排液试验测试结果对比,可以计算出颗粒气泡间的相互作用力信息;也可通过与相互作用力试验结果对比获得液膜排液数据。在今后的研究中,应重点将SRYL模型与试验测试相结合,对颗粒气泡间疏水力进行定量表征,揭示浮选黏附机理。

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Advance in the interaction force between bubble and particle and thethinning dynamics of thin liquid film

XING Yaowen1,GUI Xiahui1,CAO Yijun1,2,LIU Jiongtian1,2

(1.Chinese National Engineering Research Center of Coal Preparation and Purification,China University of Mining and Technology,Xuzhou 221116,China; 2.Henan Province Industrial Technology Research Institute of Resources and Materials,Zhengzhou University,Zhengzhou 450000,China)

Abstract:Interaction force and the thinning rupture dynamics between bubble and particle is the key to reveal the attachment mechanism of coal flotation.It is also a research hotspot in the field of flotation colloid chemistry in recent years.To understand the underlying mechanism of flotation,the recent development in the interaction force between bubble and particle and the hydrodynamic drainage models of the thin liquid film were reviewed systematically.For the interaction force,the hydrophobic force is the fundamental driving force overcoming the repulsive DLVO force between bubble and particle,inducing successful attachment.The origin mechanism of the hydrophobic force is not the same at different regimes.The long-ranged hydrophobic force (>20 nm) is mainly attributed to the bridge of submicron bubbles or nano-bubbles,while the short-ranged hydrophobic force (<20 nm) is mainly attributed to the re-arrangement of the interfacial water molecules.Due to the strong attraction characteristics of the hydrophobic force and the deformation effect of the gas-liquid interface,the quantitative characterization of the hydrophobic force between bubble and particle is experimentally challenging.For the hydrodynamic drainage model,the most representatives are Stef-an-Reynolds model,Taylor model,and the Stokes-Reynolds-Young-Laplace (SRYL) model.Variations in bubble surface curvature during film thinning are not taken into consideration in Stefan-Reynolds and Taylor models,and hence their applications have great limitation.However,the SRYL model describes not only the film thinning dynamics between bubble and particle,but also the air-water interface deformation under surface forces and hydrodynamic force.Under a given initial and boundary condition,the force information can be obtained through iterative method when the theoretical film profile is consistent with experimental results.Also the film drainage profile could be obtained using SRYL model by comparing with experimental force results.In the future investigations,SRYL model should be combined with experimental tests to quantify the hydrophobic force between bubble and particle,revealing the mechanism of flotation attachment.

Key words:flotation;attachment;interaction force;hydrophobic force;drainage dynamics

中图分类号:TD94

文献标志码:A

文章编号:0253-9993(2019)10-3185-08

移动阅读

邢耀文,桂夏辉,曹亦俊,等.相互作用力及液膜排液动力学研究进展[J].煤炭学报,2019,44(10):3185-3192.doi:10.13225/j.cnki.jccs.2018.0445

XING Yaowen,GUI Xiahui,CAO Yijun,et al.Advance in the interaction force between bubble and particle and the thinning dynamics of thin liquid film[J].Journal of China Coal Society,2019,44(10):3185-3192.doi:10.13225/j.cnki.jccs.2018.0445

收稿日期:2018-04-02

修回日期:2019-09-16

责任编辑:常明然

基金项目:国家重点研发计划资助项目(2018YFC0604702);中国博士后科学基金特别资助项目(2019T120482);第四届中国科协青年人才托举工程资助项目(2018QNRC001)

作者简介:邢耀文(1989—),男,河北秦皇岛人,副研究员。Tel:0516-83591116,E-mail:cumtxyw@126.com

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