Fluid Mechanics

Spurk, Joseph H.; Aksel, Nuri

doi:10.1007/978-3-030-30259-7

Cited by 66 publications

(75 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In our system, Reynolds numbers ( Re ) for both rapid filling ( Re ≈ 20) and slow reaction flow rate ( Re ≈ 0.5) indicate laminar characteristics. [ 23 ] The decrease in flow rate is hence not able to induce a difference in the flow characteristics, which is proven in Figure 2 (see also Figure S7, Supporting Information). Conversion data taken from stationary operation yield almost identical values as for the nonstationary operation.…”

Section: Figurementioning

confidence: 74%

Continuous Kinetic Sampling of Flow Polymerizations via Inline UV–Vis Spectroscopy

Lauterbach

Abetz

2020

Macromol. Rapid Commun.

View full text Add to dashboard Cite

noninvasive way. Therefore, several online and inline methods in combination with flow chemistry have emerged during the last years. They range from analytic devices like size exclusion chromatography (SEC), [6,7] electrospray ionization mass spectroscopy [8] or NMR [9,10] to inline spectroscopic methods like IR [11,12] or UV-vis. [13] Most of these techniques are known from batch analytics, where especially NMR and SEC are obligatory for characterization of polymeric intermediates and products. Incorporation of these devices into flow reactors makes the life of every synthetic polymer chemist easier. It provides real-time and continuous information and makes optimization of any polymerization procedure less elaborate and, hence, more effective.In order to optimize homopolymerizations with certain desired molecular weights via controlled radical polymerizations, for instance, the experimentalist usually starts with an arbitrary set of intuitively chosen reaction conditions. Full monomer conversion is rarely targeted to suppress termination events and ensure a high chain end livingness. Consequently, it becomes inevitable to find the right conversion target and hence reaction time that yields the desired chain length. A widely used workflow to make such a kinetic screening in flow reactors is to set a specific flow rate (yielding the desired residence time) and collect the sample after equilibrating the reactor for a few residence times. [4] With a single run of this stationary approach, information about monomer conversion is obtained only at one individual reaction time, coincidently wasting a few reactor volumes of material. Complete kinetic screening is hence a brute force task and-discarding more material into waste than collectionhardly economically feasible. To gather information about all reaction times in a kinetic screening at once, the flow reactor needs to be operated in a nonstationary mode. Therefore, the whole volume is filled at a high flow rate and abruptly set to the desired rate. At this point, the sample collection can be started, and the residence time can be linearly calculated from the elapsed time. Although this approach has been widely used in academia, it is controversially discussed lately on the micro-and mesoscale. [9,10] Real-time data from inline SEC or NMR analysis are particularly helpful to find the desired molar mass as well as monomer conversion. Recently, notable studies showed how these methods can be automated to yield tailored polymer products with a minimum of experimentalist interaction. [7,10] However, the measurement volume of low-field NMR spectrometers is still big compared to other spectroscopic techniques, so that the reactor volume should be on the milliliter scale (or bigger) as well.Gapless monitoring of polymerization reactions is of paramount interest for academia and the polymer industry, allowing for efficient reaction screening and precise tailoring of the polymeric products. Herein, UV-visible spectroscopy (UV-vis) is employed as an operando measurement tech...

show abstract

Section: Figurementioning

confidence: 74%

Continuous Kinetic Sampling of Flow Polymerizations via Inline UV–Vis Spectroscopy

Lauterbach

Abetz

2020

Macromol. Rapid Commun.

View full text Add to dashboard Cite

show abstract

“…Here α and β are non-Newtonian material coefficients arising from the constitutive relation of a second-order liquid [6][7][8][9], namely…”

Section: Preparations For Transformation Of Ivpmentioning

confidence: 99%

“…For this purpose, real measurement values of the non-Newtonian contributions α and β from (4) are necessary to obtain results for the dimensionless ratio of the left-hand side of inequality (54). More precisely, the definitions of A * and B * from (3) associated with the nonlinear ODE (8) [or (9)] are applied for the computation.…”

Section: Connection Between Theory and Real Parametersmentioning

confidence: 99%

“…In [5], a two-phase system consisting of a small, spherical gas bubble in a highly viscous, incompressible liquid was theoretically examined by the conservation equations for mass and momentum at changing pressure conditions. The important point to note here is that the material law of a second-order liquid was applied for the stress tensor to take into account slow and slowly varying bubble motions [6][7][8][9]. The resulting nonlinear initial value problem (IVP) was numerically solved by a Runge-Kutta method of order four.…”

mentioning

confidence: 99%

“…A commonly used assumption is that the sum of both coefficients is zero [13,14]. Moreover, experimental measurements reveal that the coefficients differ from each other only by a negative sign [9]. The authors from [14] investigate steady motions of second-order and even third-grade fluids in aperture domains by analyzing existence and regularity of (weak) solutions.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Non-Newtonian coefficient condition for a stable long-time behavior of a single bubble: existence and characteristics of stable solutions

2020

View full text Add to dashboard Cite

The present paper takes up the underlying nonlinear initial value problem from a preceding author's work about the dynamics of a single bubble in a highly viscous liquid medium under different pressure impacts. The arising ordinary differential equation is mainly based on the constitutive relation of a secondorder liquid that in particular includes two non-Newtonian material constants. In this article, the significance of these coefficients is mathematically analyzed in detail by proving the existence of stable solutions of the named initial value problem. This is achieved by special transformations of the differential equation at hand and the introduction of appropriate Lyapunov functions. It particularly turns out that a combined condition of the non-Newtonian coefficients and diverse restrictions to the external pressure impact are decisive for the validity of the existence results. Furthermore, the convergence speed of solutions is investigated by considering the linearized equation associated with the present initial value problem and by applying a special variant of Gronwall's lemma. The main theoretical result, being the prementioned strong condition for the non-Newtonian coefficients, is finally compared to real data sets.

show abstract

Optimization of flow in additively manufactured porous columns with graded permeability

Salloum

Robinson

2022

AIChE Journal

View full text Add to dashboard Cite

Chemical engineering systems often involve a functional porous medium, such as in catalyzed reactive flows, fluid purifiers, and chromatographic separations. Ideally, the flow rates throughout the porous medium are uniform, and all portions of the medium contribute efficiently to its function. The permeability is a property of a porous medium that depends on pore geometry and relates flow rate to pressure drop. Additive manufacturing techniques raise the possibilities that permeability can be arbitrarily specified in three dimensions, and that a broader range of permeabilities can be achieved than by traditional manufacturing methods. Using numerical optimization methods, we show that designs with spatially varying permeability can achieve greater flow uniformity than designs with uniform permeability. We consider geometries involving hemispherical regions that distribute flow, as in many glass chromatography columns. By several measures, significant improvements in flow uniformity can be obtained by modifying permeability only near the inlet and outlet.

show abstract

Fluid Mechanics

Cited by 66 publications

References 0 publications

Continuous Kinetic Sampling of Flow Polymerizations via Inline UV–Vis Spectroscopy

Continuous Kinetic Sampling of Flow Polymerizations via Inline UV–Vis Spectroscopy

Non-Newtonian coefficient condition for a stable long-time behavior of a single bubble: existence and characteristics of stable solutions

Optimization of flow in additively manufactured porous columns with graded permeability

Contact Info

Product

Resources

About