Electrical Double Layer And Zeta Potential Pdf

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Zeta Potential in Colloid Science: Principles and Applications covers the concept of the zeta potential in colloid chemical theory. The book discusses the charge and potential distribution at interfaces; the calculation of the zeta potential; and the experimental techniques used in the measurement of electrokinetic parameters. The text also describes the electroviscous and viscoelectric effects; applications of the zeta potential to areas of colloid science; and the influence of simple inorganic ions or more complex adsorbates on zeta potential.

Overview of the Zeta Potential

This article is part of the Thematic Series "Nanotribology". Guest Editor: E. Gnecco Beilstein J. In the present study, a modified Reynolds equation including the electrical double layer EDL -induced electroviscous effect of lubricant is established to investigate the effect of the EDL on the hydrodynamic lubrication of a 1D slider bearing.

Furthermore, the variation in the bulk electrical conductivity of the lubricant under the influence of the EDL is also considered during the theoretical analysis of hydrodynamic lubrication.

The results show that the EDL can increase the hydrodynamic load capacity of the lubricant in a 1D slider bearing. More importantly, the hydrodynamic load capacity of the lubricant under the influence of the EDL shows a non-monotonic trend, changing from enhancement to attenuation with a gradual increase in the absolute value of the zeta potential.

This non-monotonic hydrodynamic lubrication is dependent on the non-monotonic electroviscous effect of the lubricant generated by the EDL, which is dominated by the non-monotonic electrical field strength and non-monotonic electrical body force on the lubricant. The subject of the paper is the theoretical modeling and the corresponding analysis. Keywords: electrical double layer; electroviscous effect; hydrodynamic lubrication; zeta potential.

As one of the oldest techniques in modern engineering, lubrication is widely recognized and has inspired significant scientific interest []. The use of a layer of lubricant film, either in solid or fluid state, between frictional pairs can effectively reduce friction and wear. Among these interfacial properties, the effect of charged frictional pair—lubricant interface and the resulting electrical double layer EDL within the lubricant have been recognized and studied [].

The generation of surface charge at the frictional pair—lubricant interface is wide, especially for the frictional pairs of ceramics which have numerous applications of water as a lubricant. EDL is a physical structure spontaneously formed near the charged solid—liquid interface due to the electrostatic interaction between the charged interface and free ions within the liquid when the interface is charged due to different mechanisms [].

To explain the effect of the EDL on the hydrodynamic lubrication, one of the fundamental mechanisms is the influence of the EDL on the apparent viscosity of the lubricant, which is referred as the electroviscous effect [17]. Although the applications and studies of lubrication theory have a history dating back to hundreds of years, the role of surface-charge-induced EDL on the lubrication is a relatively new field.

This role was first considered for the study of thin film lubrication by Bike and Prieve [6]. Following them, Zhang and Umehara [7] introduced the effect of the EDL on modifying the conventional Reynolds equation, analyzing the hydrodynamic lubrication.

They found that the minimum lubricant film thickness increased with the increasing absolute value of zeta potential an important parameter of EDL to manifest the surface charge at the solid—liquid interface. Li [9] theoretically studied the combined roles of EDL and surface roughness on the hydrodynamic lubrication. Huang and his colleagues [8,10,13] systematically studied the effects of EDL on the hydrodynamic lubrication or elasto-hydrodynamic lubrication, where the effect of zeta potential was analyzed.

All these studies revealed that the EDL can significantly affect the lubrication capacity, especially when the Debye length an important parameter to manifest the thickness of the EDL of the EDL is similar to the thickness of the lubricant film.

To investigate the role on the hydrodynamic lubrication played by the EDL, it is needed to obtain the electrical potential and ion concentration within the lubricant affected by the EDL. It should be noted that zeta potential must be strictly limited to a small range normally, the magnitude of zeta potential should be smaller than 25 mV in these analyses based on DHA, otherwise, an unallowable error can be introduced [].

In such a small range of zeta potentials, the literature mainly revealed that the effect that the zeta potential has on lubrication, including minimum film thickness, pressure and load capacity, was a change in the form of a monotonic trend []. Actually, it was reported that the magnitude of zeta potential could be up to several hundred millivolts []. However, there are fewer studies regarding the dependence of the lubrication on the EDL with zeta potential over a wide range without the application of the DHA.

They found that the effect of the zeta potential on the load capacity resulted in a non-intuitive trend with increasing magnitude of zeta potential; however, further details and explanation were not given.

In addition, the electroviscous effect is dependent on the electrical conductivity of the lubricant [26,27] , which inevitably affects the hydrodynamic lubrication. However, most of the previous theoretical works neglected the variation of electrical conductivity of the lubricant considering the effect of the EDL.

To solve these problems, this paper presents a theoretical study on the effect of the EDL on the hydrodynamic lubrication with the additional consideration of the effect of the EDL on the electrical conductivity of the lubricant. On the basis of these assumptions, the effect of the zeta potential on the apparent viscosity of the lubricant is first studied and analyzed. Then, by combining the effects of the EDL on the electrical conductivity and apparent viscosity of the lubricant, the conventional Reynolds equation is modified to study the effect of the EDL on the load capacity of hydrodynamic lubrication.

In addition, the dependence of the apparent viscosity and load capacity on the bulk ion concentration of lubricant and lubricant film thickness are also investigated. The underlying mechanisms of these issues are analyzed. To analyze the effect of the EDL on the hydrodynamic lubrication, a hydrodynamic lubrication model in a 1D slider bearing with the effect of the EDL is considered. The following assumptions are made to carry out the modeling.

Figure 1: The schematic of hydrodynamic lubrication in a 1D slider bearing considering the effect of the EDL. To analyze the hydrodynamic lubrication under the effect of the EDL, the electrical potential within the EDL should first be analyzed. However, it should be noted that the classical PBE is derived based on the assumption that the free ions in the lubricant are point-like. Thus, the steric effect has been proposed and introduced to correct the classical PBE [12,28,29].

Based on the previous studies, in a certain range of zeta potential whose magnitude is normally smaller than mV for a dilute solution, the classical PBE can still effectively predict the electrical potential and ion concentration within an EDL with an allowable error when comparing with the prediction of theoretical model considering the steric effect [28]. Based on this analysis, in the present work, the PBE is still used to analyze the electrical potential distribution within the EDL. Furthermore, the zeta potential is strictly chosen during the simulation to reduce the error.

For a steady lubricant flow, the electrical field strength E x can be obtained on the basis of when the total current within the lubricant is zero [17,30]. There are three kinds of electrical current induced by the EDL: the streaming current, the conduction current and the sliding-wall-induced current, which can be expressed in the following forms, respectively [17,30] ,.

Based on the zero net current in the steady state, the electrical field strength E x can be given as,. Based on the previous studies, the bulk electrical conductivity of the lubricant under the influence of the EDL increases with the increasing absolute value of the zeta potential [26,27].

Hence, the EDL-dependent electrical conductivity of the lubricant must be considered during the analysis of the electroviscous effect and hydrodynamic lubrication. The average bulk electrical conductivity under the influence of the EDL can be obtained as [26,27,31] ,.

Normally, the electroviscous effect can be characterized by the apparent viscosity of the lubricant. Based on the apparent viscosity, the effect of the EDL on the flow can also be expressed by the following equation. The effect of the EDL on the hydrodynamic lubrication can be derived as follows.

Under the assumption of an incompressible lubricant, the mass conservation law gives the following modified Reynolds equation, which includes the effect of the EDL [7] ,. The hydrodynamic load capacity of the lubricant can be obtained by integrating the pressure over the 1D slider bearing length [7] ,. While solving for the hydrodynamic load capacity, the following pressure boundary conditions were used:.

After establishing the theoretical model regarding the effect of the EDL on the hydrodynamic lubrication, NaCl solution was chosen as the lubricant to carry out the analysis. Because the zeta potential at both the lower and upper bearing surfaces are the same, the electrical potential distribution within the EDL is symmetric.

It can be seen that the dimensionless electrical potentials obtained by the linear PBE remained constant with different values of zeta potential.

Furthermore, there is a larger difference between the dimensionless electrical potentials obtained by the linear PBE and the nonlinear PBE when the zeta potential value is larger. Thus, the EDL-dependent lubrication analysis, based on the linear PBE, should be strictly limited to a small zeta potential range, otherwise, a large error will be introduced.

To reduce this error when the magnitude of the zeta potential is large, the nonlinear PBE is used in present work to carry out the EDL-dependent lubrication analysis. Figure 2: Dimensionless electrical potential distribution obtained by solving the linear PBE and the nonlinear PBE the model used in present work. Figure 2: Dimensionless electrical potential distribution obtained by solving the linear PBE and the nonlinea That is, the electrical potential shows a faster reduction.

The mechanism for this phenomenon is described as follows. For the case of the zeta potential with a larger absolute value, there is a larger surface charge density at the bearing surface—lubricant interface. This results in a larger local net ionic charge density near the interface by attracting many more counter ions to close the interface, leading to a faster reduction of dimensionless electrical potential.

When a constant electrical conductivity and the linear PBE based on DHA are used to analyze the effect of the zeta potential on the apparent viscosity, it can be found that the apparent viscosity of the lubricant monotonically increases with the increasing absolute value of the zeta potential.

This result is similar to the result reported by Li and Jin [11]. However, for the other three groups of results based on different assumptions, all of the three apparent viscosities show non-monotonic variations with the increasing absolute value of the zeta potential.

It is believed that the theoretical model based on the nonlinear PBE and changed electrical conductivity is much more reasonable, and this is the model established and used in the present work. Figure 3: The effect of the zeta potential on the apparent viscosity of the lubricant based on different assumptions and theoretical models. Figure 3: The effect of the zeta potential on the apparent viscosity of the lubricant based on different assu More interestingly, the EDL-enhanced apparent viscosity shows a non-monotonic trend from increasing to decreasing with the gradually increasing absolute value of the zeta potential, that is, the electroviscous effect exhibits a non-monotonic characteristic.

Figure 4: The effect of the zeta potential on the apparent viscosity of the lubricant and the dependence of the EDL-induced apparent viscosity on the lubricant film thickness and ion concentration of the lubricant based on the model of nonlinear PBE and modified electrical conductivity.

Figure 4: The effect of the zeta potential on the apparent viscosity of the lubricant and the dependence of t The non-monotonic electroviscous effect has been systematically studied in our previous study and can be analyzed on the basis of the modified Navier—Stokes equation [27,]. Based on the previous studies, the electrical body force applied on the flowing lubricant is dominated by the electrical field strength, which has a non-monotonic behavior with the increasing magnitude of the zeta potential.

This non-monotonic electrical field strength leads to a non-monotonic electrical field force on the lubricant, which then results in a non-monotonic variation of the velocity and a non-monotonic electroviscous effect.

In addition, the apparent viscosity increases with decreasing lubricant film thickness and decreasing ion concentration. These dependences of the electroviscous effect on the lubricant film thickness and ion concentration can also be explained on the basis of electrical field force applied on the lubricant, and have been studied in our previous works [27,]. Based on the influence of the EDL on the apparent viscosity, the effect of the EDL on the hydrodynamic load capacity of the lubricant can be analyzed.

W 0 is the hydrodynamic load capacity without the effect of the zeta potential. W is the hydrodynamic load capacity with the effect of the zeta potential. For example, when a constant electrical conductivity and the linear PBE are applied, the hydrodynamic load capacity of the lubricant monotonically increases with increasing absolute value of the zeta potential, even when the absolute value of the zeta potential is large. This result is similar to the reports of Li and Jin [11].

However, the other three types of hydrodynamic load capacities show non-monotonic variations with increasing zeta potential. The variation of the hydrodynamic load capacity is consistent with the variation of apparent viscosity. Among these models, the theoretical model based on the nonlinear PBE and varied electrical conductivity should be the most reasonable one, and this is the model used in the present work.

Figure 5: Comparison of the hydrodynamic load capacity of the lubricant including the effect of the zeta potential based on different assumptions and theoretical models. Figure 5: Comparison of the hydrodynamic load capacity of the lubricant including the effect of the zeta pote There is a non-monotonic relationship between the hydrodynamic load capacity and the zeta potential of the EDL. This result is similar to the result of Chakraborty and Chakraborty [12]. By considering the steric effect, they also found that the hydrodynamic load capacity followed a non-intuitive trend with increasing magnitude of zeta potential.

The variation of the hydrodynamic load capacity with zeta potential is consistent with the variation of the apparent viscosity with zeta potential. A larger apparent viscosity leads to a stronger hydrodynamic load capacity. This is because under the condition of a fixed lubricant film dimension, a smaller ion concentration of lubricant means a larger Debye length, and a larger range to affect the lubrication.

Overview of the Zeta Potential

In the present study, a modified Reynolds equation including the electrical double layer EDL -induced electroviscous effect of lubricant is established to investigate the effect of the EDL on the hydrodynamic lubrication of a 1D slider bearing. Furthermore, the variation in the bulk electrical conductivity of the lubricant under the influence of the EDL is also considered during the theoretical analysis of hydrodynamic lubrication. The results show that the EDL can increase the hydrodynamic load capacity of the lubricant in a 1D slider bearing. More importantly, the hydrodynamic load capacity of the lubricant under the influence of the EDL shows a non-monotonic trend, changing from enhancement to attenuation with a gradual increase in the absolute value of the zeta potential. This non-monotonic hydrodynamic lubrication is dependent on the non-monotonic electroviscous effect of the lubricant generated by the EDL, which is dominated by the non-monotonic electrical field strength and non-monotonic electrical body force on the lubricant. The subject of the paper is the theoretical modeling and the corresponding analysis.

Download the PDF version. This Technical Brief provides a general overview of the concept of the zeta potential ZP. We will discuss the two parameters that control the nature and behavior of every system in which one phase is dispersed in another phase. In a system, the first phase is called the disperse phase, or the phase forming the particles, and the second is the dispersion medium, or the fluid in which the particles are distributed. The two parameters we will focus on are the extent of the interface and the interfacial chemistry of the disperse phase. The physicomechanical and physicochemical characteristics that constitute the two respective fundamental parameters are summarized in Table 1.

The physical properties of colloids nanoparticles and suspensions are strongly dependent on the nature and extent of the particle-liquid interface. The behavior of aqueous dispersions between particles and liquid is especially sensitive to the ionic and electrical structure of the interface. Zeta potential is a parameter that measures the electrochemical equilibrium at the particle-liquid interface. It should be noted that that term stability, when applied to colloidal dispersions, generally means the resistance to change of the dispersion with time. We can regard zeta potential as the potential difference between the dispersion medium and the stationary layer of the fluid attached to the particle layer. Therefore, in experimental concerns, zeta potential is key factor in processes such as the preparation of colloidal dispersions, utilization of colloidal phenomena and the destruction of unwanted colloidal dispersions.


PDF | When clay particles are fully hydrated, the negative charge is balanced by the cations in the soil solution attracted by the Coulomb forces.


Electrical Characteristics of Interfaces. Electrical Double Layer and Zeta Potential

This article is part of the Thematic Series "Nanotribology". Guest Editor: E. Gnecco Beilstein J. In the present study, a modified Reynolds equation including the electrical double layer EDL -induced electroviscous effect of lubricant is established to investigate the effect of the EDL on the hydrodynamic lubrication of a 1D slider bearing.

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2.5: Zeta Potential Analysis

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Introduction

 Вы хотите дать взятку представителю закона? - зарычал. - Нет, конечно. Я просто подумал… - Толстяк быстро убрал бумажник.  - Я… я… - Совсем растерявшись, он сел на край постели и сжал руки. Кровать застонала под его весом.  - Простите.

Фильтры служили куда более высокой цели - защите главной базы данных АНБ. Чатрукьяну была известна история ее создания. Несмотря на все предпринятые в конце 1970-х годов усилия министерства обороны сохранить Интернет для себя, этот инструмент оказался настолько соблазнительным, что не мог не привлечь к себе внимания всего общества. Со временем им заинтересовались университеты, а вскоре после этого появились и коммерческие серверы. Шлюзы открылись - в Интернет хлынула публика. К началу 1990-х годов некогда тщательно охраняемый правительством Интернет превратился в перенаселенное пространство, заполненное общедоступными почтовыми серверами и порнографическими сайтами. Вскоре после не получившего огласки, но причинившего колоссальный ущерб государственной безопасности проникновения в базы данных Военно-морского флота стало абсолютно очевидно, что секретная информация, хранящаяся на компьютерах, подключенных к Интернету, перестала быть тайной.

В качестве штатного ангела-хранителя компьютерных систем АН Б Джабба ходил по отделам, делал замечания, что-то налаживал и тем самым постоянно подтверждал свое кредо, гласившее, что профилактика-лучшее лекарство.

Никаких ограничений - только свободная информация. Это шанс всей вашей жизни. И вы хотите его упустить. - Следи за мной, - холодно парировал Стратмор. - А как же Сьюзан? - Хейл запнулся.

Эту проклятую машину так или иначе следует объявить вне закона. Стратмор вздохнул. - Оставь эти штучки детям, Грег. Отпусти. - Чтобы вы меня убили.

Стратмор шагнул вперед, нащупывая ногой место, где начинались ступеньки узенькой лестницы. Переложив берет-ту в левую руку, правой он взялся за перила. Он прекрасно знал, что левой рукой стрелял так же плохо, как и правой, к тому же правая рука была ему нужна, чтобы поддерживать равновесие. Грохнуться с этой лестницы означало до конца дней остаться калекой, а его представления о жизни на пенсии никак не увязывались с инвалидным креслом.

И он задвигал крошечными металлическими контактами на кончиках пальцев, стремясь как можно быстрее сообщить американским заказчикам хорошую новость. Скоро, подумал он, совсем. Как хищник, идущий по следам жертвы, Халохот отступил в заднюю часть собора, а оттуда пошел на сближение - прямо по центральному проходу. Ему не было нужды выискивать Беккера в толпе, выходящей из церкви: жертва в ловушке, все сложилось на редкость удачно. Нужно только выбрать момент, чтобы сделать это тихо.

 Около двадцати минут. Их надо использовать с толком. Фонтейн долго молчал. Потом, тяжело вздохнув, скомандовал: - Хорошо.

 Я готов рискнуть. - Чепуха. Вы жаждете обладать ею еще сильнее, чем Цифровой крепостью. Я вас знаю.

Офицер был шокирован. - Вы же только что прибыли. - Да, но человек, оплативший авиабилет, ждет. Я должен доставить эти вещи. На лице лейтенанта появилось оскорбленное выражение, какое бывает только у испанцев.

Он же вас ненавидит. - Он позвонил и предупредил, что заканчивает работу над алгоритмом, создающим абсолютно стойкие шифры. Я ему не поверил.

Все подняли головы. - Три! - крикнула Сьюзан, перекрывая оглушающую какофонию сирен и чьих-то голосов. Она показала на экран.

Хотя смерть Энсея Танкадо спасет в будущем тысячи жизней, Сьюзан никогда не примет ничего подобного: она убежденная пацифистка. Я тоже пацифист, - подумал Стратмор, - я просто не могу позволить себе роскошь вести себя как пацифист. У него никогда не возникало сомнений по поводу того, кто убьет Танкадо. Танкадо находился в Испании, а Испания - вотчина Халохота.

В девяноста футах внизу, распростертый на острых лопастях главного генератора, лежал Фил Чатрукьян. Тело его обгорело и почернело. Упав, он устроил замыкание основного электропитания шифровалки. Но еще более страшной ей показалась другая фигура, прятавшаяся в тени, где-то в середине длинной лестницы.

Статуя без изъянов, которую не нужно было подправлять, называлась скульптурой sin cera, иными словами - без воска. С течением времени это выражение стало означать нечто честное, правдивое. Английское слово sincere, означающее все правдивое и искреннее, произошло от испанского sin сега - без воска.

Подумать. - Что вы имеете в виду. - Да он смеялся над нами.

2 Response
  1. Tremhunkace1964

    Management information system managing the digital firm 12th edition pdf panasonic lumix fz200 manual pdf

  2. Gaudencio V.

    A double layer DL , also called an electrical double layer , EDL is a structure that appears on the surface of an object when it is exposed to a fluid.

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