Filtration of aerosol particles by elliptical fibers: a numerical study

Filtration is an important technology for nanoparticle control and reduction of human exposure to nanoparticles. Filtration by non-circular fibers is gaining more attention in search for better filter quality; elliptical fibers have extra significance because they may be used in simple models of dust loading. We carry out numerical simulation to investigate filtration by fibers with elliptical cross-sections. The drag force on individual fibers is in good agreement with analytical solutions for elliptical fibers obtained from the cell model. Our simulation covers mechanisms for particle capture due to interception, inertial impaction, and diffusion. Single-fiber efficiencies of different elliptical fibers are computed. The figure of merit, which is an indicator of the ratio of the collection efficiency to the pressure drop, is used to evaluate the performance of different elliptical fibers. It is found that blunt and close to circular fibers perform better for particles dominated by the effects of interception and inertial impaction, whereas long and slim fibers perform better for particles dominated by the diffusion effect. For very small nanoparticles, the diffusion effect is important and long and slim elliptical fibers may improve the filter performance.     

一类非线性渗流方程的Cauchy问题

讨论具有强非线性源和对流项的一般渗流方程以ＲＮ中某有界连续函数ｕ０（ｘ）或某一Ｒａｄｏｎ测度为初值的Ｃａｕｃｈｙ问题弱解的存在性，得到关于解的一系列重要估计．     

Quantitative stability of multistage stochastic programs via calm modifications

In this paper, we revisit the quantitative stability of multistage stochastic programs. Different from the single calm modification used in Küchler (2008), we introduce two types of calm modifications which leads to a much simpler proof and tighter upper bound for the difference of optimal values of multistage stochastic programs under different stochastic processes than those of Küchler (2008). In addition, we avoid those restrictive assumptions in Küchler (2008) and the filtration distance in Heitsch et al. (2006). Finally, we illustrate our results with two numerical examples.     

Observation and modelling of barrel droplets on vertical fibres subjected to gravitational and drag forces

Extensive experimental investigation of the wetting processes of fibre/liquid systems during air filtration (when drag and gravitational forces are acting) has shown many important features, including droplet extension, oscillatory motion, and detachment or flow of drops from fibres as airflow velocity increases. A detailed experimental study of the aforementioned processes was conducted using glass filter fibres and H(2)O aerosol, which coalesce on the fibre to form barrel droplets with small contact angles. The droplets were predominantly observed in the Reynolds transition (or unsteady laminar) flow region. The droplet oscillation appears to be induced by the onset of vortexes in the flow field around the droplet as the increasing droplet size increases the Reynolds number. Flow in this region is usually modelled using the classical two-dimensional Karman vortex street, and there exist no 3D equivalents. Therefore to model such oscillation it was necessary to create a new conceptual model to account for the forces both inducing and inhibiting such oscillation. The agreement between the model and experimental results is acceptable for both the radial and transverse oscillations.     

溶剂浸泡对驻极体空气过滤材料性能的影响

通过过滤效率的跟踪测试,研究了聚丙烯熔喷非织造布驻极体空气过滤材料经各种不同溶剂浸泡后过滤性能的变化规律,比较了不同过滤效率测试方法对测试结果的影响。结果表明：溶剂浸泡后聚丙烯熔喷无纺布驻极体空气过滤材料的过滤效率都有不同程度的下降,下降幅度随水、甲醛、乙醇、异丙醇和丙酮的顺序逐渐增加,其下降规律与溶剂浸泡后滤材表面电位的衰减规律相一致,并与溶剂和聚丙烯分子间相互作用（溶胀作用）程度相关联。过滤效率对驻极体电场有很强的依赖性,其大小还与测试方法有关。     

Unconditional martingale difference sequences in Banach spaces

For a Banach space Y, the question of whether Lp(μ,Y) has an unconditional basis if 1<p<∞ and Y has unconditional basis, stood unsolved for a long time and was answered in the negative by Aldous. In this work we prove a weaker, positive result related to this question. We show that if (yj) is a basis of Y and (di) is a martingale difference sequence spanning Lp(μ) then the sequence (di⊗yj) is a basis of Lp(μ,Y) for 1?p<∞. Moreover, if 1<p<∞ and (yj) is unconditional then (di⊗yj) is strictly dominated by an unconditional tensor product basis. In addition, for 1<p<∞, we show that if (di)⊂Lp(μ) is a martingale difference sequence then there exists a constant K>0 so that

     

Homogeneous liquid‐phase microextraction followed by filtration‐based phase separation coupled to high‐performance liquid chromatography

A simple homogenous liquid‐phase microextraction methodology applying octanoic acid as the extraction phase was introduced for determination of chlorobenzenes. In this approach, phase separation phenomenon occurred by changing pH of the solution. The extraction phase was isolated based on filtration of emulsion instead of centrifugation and it was introduced to the high‐performance liquid chromatography instrument as an on‐line procedure. This method was used for extraction and determination of five chlorobenzenes in different samples. Experimental design and response surface methodology were used for the optimization of various parameters influencing the extraction efficiency of the method. Under optimal conditions, chlorobenzenes were effectively extracted, and preconcentration factors of 255–294 were obtained. The calibration curves were investigated in the concentration range of 1–200 μg/L and good linearity was achieved with coefficient of determinations better than 0.997. Limits of detection of 0.1 and 0.3 μg/L and suitable precision with relative standard deviations better than 5.1% (n = 5) were attained. Finally, the proposed method was applied to determine the concentration of chlorobenzenes in different samples and acceptable recoveries were gained.     

SOME TYPICAL BEHAVIORS OF WEAK SOLUTIONS OF LAYERED POROUS MEDIA EQUATION

1.IntroductionThefiltrationproblemoflayeredporousmediacanbedescribedasfollows(see[21):whereHisHeavisidefunction.u(x,t)isthecapillarypiezometrichead,oi(u)(i~l,2)thevolumetricmoisturecontentandK4(u)thehydraulicconductivityinupperlayer(x6(1,21).Theassumptionsarethesameasthosein[2]:(0KI)oi(r),Ki(r)EC' '(R).(0K2)oi(r)>0,Ki(r)>0,6:(r)>0andK:(r)20forrE(--co,u'.),whereu"thesaturatedcapillarypiezometricheadoftheithlayer.Whenr2u",oi(r)=osiandKi(r)~K'i,whereof'andK8iaresaturatedvaluesofthemoisturec…     

Radial filtration during constant-force squeeze flow of soft solids

Various soft solid suspensions were squeezed at constant force between polished and roughened circular glass plates and the time-dependence of the interplate separation was measured. The filterability of suspensions was quantified by their desorptivity S obtained from measurements of capillary suction time. The squeeze flow (SF) of suspensions for which S < 2 μm s^−1/2 was largely consistent with rheological theory, which neglected radial filtration: the relative motion between the liquid and solid phases of the suspension in the radial pressure gradient. Suspensions having S > 2 μm s^−1/2 showed SF behavior that was consistent with the presence of radial filtration.     

Use of thiopropyl sepharose for preparation of 2-nitro-5-thiobenzoic acid

A simple method is described for preparation of 2-nitro-5-thiobenzoic acid (NTB), a compound with versatile applications but is commercially unavailable. In this method, NTB is produced by the reduction of 5,5′-dithiobis(2-nitrobenzoic acid) (DTNB) with thiopropyl sepharose, which is then separated from NTB by filtration. Two molecules of NTB can be generated from each molecule of DTNB when a large excess of thiopropyl sepharose is used. Thiopropyl sepharose is commercially available and can be readily regenerated for repeated use in the preparation of NTB. This method is simple and more effective than any other reported methods of NTB preparation.