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Influence of heterogeneous air entry pressure on large scale unsaturated flow in porous media
PublikacjaThe paper presents numerical simulations of water infiltration in unsaturated porous media containing coarse-textured inclusions embed- ded in fine-textured background material. The calculations are performed using the two-phase model for water and air flow and a simplified model known as the Richards equation. It is shown that the Richards equation cannot correctly describe flow in the presence of heterogeneities. How- ever, its...
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Numerical modelling and experimental verification of compressible squeeze film pressure
PublikacjaThe validity of using the Reynolds equation for compressible squeeze film pressure was tested with computational fluid dynamics (CFD). A squeeze film air bearing was instrumented with pressure sensors and non-contacting displacement probes to provide transient measurements of film thickness and pressure. The film thickness measurements also provided input parameters to the numerical prediction. However, numerical results showed...
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Analytical Buckling of FG Nanobeams on The Basis of A New One Variable First-Order Shear Deformation Beam Theory
PublikacjaIn this work, buckling analysis of functionally graded (FG) nanobeams based on a new refined beam theory has been analyzed. The beam is modeled as an elastic beam subjected to unidirectional compressive loads. To achieve this aim, the new obtained beam theory has only one variable which lead to one equation similar to Euler beam theory and also is free of any shear correction factor. The...
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Comparison of Average Energy Slope Estimation Formulas for One-dimensional Steady Gradually Varied Flow
PublikacjaTo find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is a discrete form of the differential energy equation. Such an approach requires the average energy slope between cross-sections to be estimated. In the literature, many methods are proposed for estimating the average energy slope in this case, such as the arithmetic mean, resulting in the standard step method, the harmonic mean and...
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Improvement of Thrust Bearing Calculation Considering the Convectional Heating within the Space between the Pads
PublikacjaA modern thrust bearing tool is used to estimate the behavior of tilting pad thrust bearings not only in the oil film between pad and rotating collar, but also in the space between the pads. The oil flow in the space significantly influences the oil film inlet temperature and the heating of pad and collar. For that reason, it is necessary to define an oil mixing model for the space between the pads. In the bearing tool, the solutions...
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DL_MG: A Parallel Multigrid Poisson and Poisson–Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution
PublikacjaThe solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential -- a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the...
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On local buckling of cold-formed channel members
PublikacjaThe paper deals with local buckling of the compressed flanges of cold-formed thin-walled channel beams subjected to pure bending or axially compressed columns. Arbitrarily shaped flanges of open cross-sections and the web-flange interactions are taken into account. Buckling deformation of a beam flange is described by displacement related to torsion of the flange about the line of its connection with the web. Total potential energy...
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ESTIMATING AVERSION TO RANK INEQUALITY UNDERLYING SELECTED ITALIAN INDICES OF INCOME INEQUALITY
PublikacjaIn this paper, we estimate aversion to rank inequality (ATRI) underlying selected Italian income inequality indices, I, notably the Pietra index, the Bonferroni index and the “new” Zenga index. We measure ATRI by the parameter v of the generalised Gini index G(v). ATRI is distinct from aversion to income inequality, as measured by parameter ε of Atkinson’s index A(ε). We propose eliciting v from the equation I = GE(v). As, in general,...
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Numerical Solution of the Two-Dimensional Richards Equation Using Alternate Splitting Methods for Dimensional Decomposition
PublikacjaResearch on seepage flow in the vadose zone has largely been driven by engineering and environmental problems affecting many fields of geotechnics, hydrology, and agricultural science. Mathematical modeling of the subsurface flow under unsaturated conditions is an essential part of water resource management and planning. In order to determine such subsurface flow, the two-dimensional (2D) Richards equation can be used. However,...
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A Quasi-2D MOSFET Model — 2D-to-Quasi-2D Transformation
PublikacjaA quasi-two-dimensional (quasi-2D) representation of the MOSFET channel is proposed in this work. The representation lays the foundations for a quasi 2D MOSFET model. The quasi 2D model is a result of a 2D into quasi 2D transformation. The basis for the transformation are an analysis of a current density vector field and such phenomena as Gradual Channel Detachment Effect (GCDE), Channel Thickness Modulation Effect (CTME), and...
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Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator
PublikacjaUsing the Mountain Pass Theorem we show that the problem \begin{equation*} \begin{cases} \frac{d}{dt}\Lcal_v(t,u(t),\dot u(t))=\Lcal_x(t,u(t),\dot u(t))\quad \text{ for a.e. }t\in[a,b]\\ u(a)=u(b)=0 \end{cases} \end{equation*} has a solution in anisotropic Orlicz-Sobolev space. We consider Lagrangian $\Lcal=F(t,x,v)+V(t,x)+\langle f(t), x\rangle$ with growth conditions determined by anisotropic G-function and some geometric conditions...
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Numerical Test for Stability Evaluation of Discrete-Time Systems
PublikacjaIn this paper, a new numerical test for stability evaluation of discrete-time systems is presented. It is based on modern root-finding techniques at the complex plane employing the Delaunay triangulation and Cauchy's Argument Principle. The method evaluates if a system is stable and returns possible values and multiplicities of unstable zeros of the characteristic equation. For state-space discrete-time models, the developed test...
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Subcritical bifurcation of free elastic shell of biological cluster
PublikacjaIn this paper we will investigate symmetry-breaking bifurcation of equilibrium forms of biological cluster. A biological cluster is a two-dimensional analogue of a gas balloon. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of biological cluster can be found as solutions of a certain second order ordinary functional-differential equation...
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Biomass estimation using a length-weight relationship in beetle larvae (Coleoptera: Aphodiidae, Histeridae, Hydrophilidae, Staphylinidae) obtained from cow dung
PublikacjaThis research enabled the relationship between length and dry body mass to be determined for 158 beetle larvaetaken from cow dung in north-eastern Poland. The larvae were divided into three morphological types, for which the power and linear function of the body length-weight relationship were determined. The linear regression equation characterizes the relationship between body weight and...
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Local buckling of compressed flange of cold-formed channel members made of aluminum alloy
PublikacjaThe paper deals with local buckling of a compressed single flange of thin-walled channel cold- formed columns and beams made of aluminum alloy. Material is described by means of the Ramberg-Osgood constitutive equation. Axial compression of the columns and beams undergoing bending is taken into consid- eration. A simple model of the member flange in the form a long beam elastically connected to the web is used to find the critical...
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Flexural buckling and post-buckling of columns made of aluminium alloy
PublikacjaThe paper concerns flexural buckling and initial post-buckling of axially compressed columns made of aluminium alloy described by the Ramberg-Osgood relationship. The non-linear differential equation of the problem is derived using the stationary total energy principle and the assumptions of classical beam theory within a finite range. The approximate analytical solution of the equation leading to the buckling loads and initial...
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Calculations of labyrinth seals with and without diagnostic extraction in fluid-flow machines
PublikacjaLabyrinth seals are essential components of steam turbine unit constructions. Two types of labyrinth seals can be named, the first of which is the seal without diagnostic steam extraction, and the second – with extraction. The distribution of flow parameters along the packing is affected remarkably by the average seal clearance. The presence of diagnostic extraction leads to the equation system which is determinable and can be...
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Symmetry-Breaking Bifurcation for Free Elastic Shell of Biological Cluster, Part 2
PublikacjaWe will be concerned with a two-dimensional mathematical model for a free elastic shell of biological cluster. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of the shell of biological cluster may be found as solutions of a certain nonlinear functional-differential equation with several physical parameters. For each multiparameter this...
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Buckling and initial post-local buckling behaviour of cold-formed channel member flange
PublikacjaThe initial post-buckling behaviour of a cold-formed channel member flange after its local buckling is investigated. An axially compressed column or beam subjected to pure bending is considered. The member material is assumed to follow a linear stress-strain relationship. The governing non-linear differential equation of the problem is derived using the minimum total potential energy principle. An approximate solution for the equation...
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Convergence of Monte Carlo algorithm for solving integral equations in light scattering simulations
PublikacjaThe light scattering process can be modeled mathematically using the Fredholm integral equation. This equation is usually solved after its discretization and transformation into the system of algebraic equations. Volume integral equations can be also solved without discretization using the Monte Carlo (MC) algorithm, but its application to the light scattering simulations has not been sufficiently studied. Here we present implementation...
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Analysis of Floodplain Inundation Using 2D Nonlinear Diffusive Wave Equation Solved with Splitting Technique
PublikacjaIn the paper a solution of two-dimensional (2D) nonlinear diffusive wave equation in a partially dry and wet domain is considered. The splitting technique which allows to reduce 2D problem into the sequence of one-dimensional (1D) problems is applied. The obtained 1D equations with regard to x and y are spatially discretized using the modified finite element method with the linear shape functions. The applied modification referring...
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Investigations On Water Circulation in Animal Sea-Water Basins – On the Example of Seals′ Breeding Pools
PublikacjaThis paper presents general comments concerning investigations on water circulation in animal breeding pools containing sea water. As an example are given results of computer simulation of water circulation in seals’ breeding pools situated in Marine Station at Hel, belonging to Oceanographic Institute, Gdansk University. A mathematical model of three main pools was prepared with taking into account their inflow and outflow water...
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Water uptake in protective organic coatings and its reflection in measured coating impedance
PublikacjaWater uptake in commercially available epoxy coating on mild steel using impedance spectroscopy and gravimetry was studied. The water content in the coating was determined using the Brasher-Kingsbury equation and various methods of coating capacitance calculation used in the literature. The obtained results were compared with reference gravimetric data. An overestimation of values obtained from impedance data in relation to gravimetric...
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Experimental and Numerical Analysis of Air Trapping in a Porous Medium with Coarse Textured Inclusions
PublikacjaThe paper presents a 2D upward infiltration experiment performed on a model porous medium consisting of fine sand background with two inclusions made of coarser sands. The purpose of the experiment was to investigate the effects of structural air trapping, which occurs during infiltration as a result of heterogeneous material structure. The experiment shows that a significant amount of air becomes trapped in each of the inclusions. Numerical...
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Directed pulse dynamics
PublikacjaIntroducing a projection method into a one-dimensional model of a pulse propagation in isotropic media, we derive and investigate a system of equation describing dynamics ultrashort pulses of opposite directions ofpropagation and ones with interaction of directed pulses with different polarization.
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Numerical Method for Stability Testing of Fractional Exponential Delay Systems
PublikacjaA numerical method for stability testing of fractional exponential systems including delays is presented in this contribution. We propose the numerical test of stability for a very general class of systems with a transfer function, which includes polynomials and exponentials of fractional powers of the Laplace variable s combined with delay terms. Such a system is unstable if any root of its characteristic equation, which usually...
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Local buckling of thin-walled channel member flange made of aluminum alloy
PublikacjaThe paper deals with local stability of the thin-walled compressed flange of channel columns and beams made of aluminum alloy. The aim of paper is to find critical stress of local buckling of the flange member taking into account the web-flange interaction in linear and nonlinear elastic range of the member material. The governing differential equation of the problem is derived with aid of the principle of stationary total potential...
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PROPERTIES OF ONE DIMENSIONAL OPEN-CHANNEL STEADY FLOW EQUATIONS
PublikacjaIn this paper properties of discrete forms of one dimensional steady gradually varied flow equations are discussed. Such forms of flow equations are obtained as a result of approximation of their differential forms, which is required to solve them numerically. For such purpose explicit or implicit numerical approximation schemes for ordinary differential equations can be applied. It turns out that dependently on the chosen approximation...
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Experimental investigation of two-phase thermosyphon heat exchanger charged with acetone
PublikacjaThis paper presents thermal characteristics of prototype of a two-phase thermosyphon heat exchanger (TPTHEx) charged with acetone as a working fluid. The TPTHEx consists of two horizontal cylindrical vessels connected by two risers and a downcomer. Tube bundles placed in the lower and upper cylinders work as an evaporator and a condenser, respectively. The tested TPTHEx operates in a vacuum. Therefore, the working liquid is boiled...
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Parametric method applicable in assessing breakout force and time for lifting slender bodies from seabed
PublikacjaThe article presents a parametric method applicable in assessing the suction force of a slender body to the seabed, and prognosing the body extrication time. Along with the body weight in water, the information on the suction force is essential for assessing the force needed to lift the object from the seabed. Based on the Foda theory and the resulting integral equation, which relates the maximum suction force with basic parameters...
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Projecting procedure for meta-material fiber
PublikacjaWe would like to show new way of derivation evolution equation for short pulses in dielectric waveguide including one model of metamaterial waveguide. This derivation model rely on projecting to the orthogonal basis. In our case to orthogonal basis for cylindrical waveguide.
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Air trapping problem during infiltration on the large areas
PublikacjaThe process of flow modeling in unsaturated porous medium is often found in many fields of sciences: geology, fluid mechanics, thermodynamics, microbiology or chemistry. Problem is relatively complicated due to complexity of the system which contains three phases: water, air and soil skeleton. The flow of water in such a medium can be described using two-phase (2PH) flow formulation, which accounts the inflow of air and water phases,...
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Determination of t8/5 cooling times for underwater local dry welding of steel
PublikacjaKnowledge of thermal history is the basic condition for studying the structure - properties of welded joints. The determinant of thermal history is the thermal cycle, whose in-situ measurements are still a big challenge. Water as the welding environment complicates this issue even more. The article presents a method to determine an equation for calculating t8/5 cooling times for underwater gas metal arc welding of unalloyed steels...
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Verification of algorithms determining wave loads on support structure of wind turbine
PublikacjaThe offshore wind turbines require determination of wave loads on their support structure. This structure is fixed and, therefore, this problem is reduced to solving only the diffraction problem, which is determined by Laplace equation and conditions on the following boundaries: on the support structure, on the sea free surface and on its bottom, and at infinity on free surface. The linear problem was applied to determine the wave...
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Newton’s Method for the McKendrick-von Foerster Equation
PublikacjaIn the paper we study an age-structured model which describes the dynamics of one population with growth, reproduction and mortality rates. We apply Newton’smethod to the McKendrick-von Foerster equation in the semigroup setting. We prove its first- and second-order convergence.
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Thermal ablation modeling via bioheat equation
PublikacjaWe consider Pennes’ bioheat equation and discuss an implicit numerical scheme which has better stability properties than other approaches. Our discussion concerns Carthesian geometry problems, however it carries over to spherical geometry models and more complicated shapes.
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Thermal ablation modeling via the bioheat equation and its numerical treatment
PublikacjaThe phenomenon of thermal ablation is described by Pennes’ bioheat equation. This model is based on Newton’s law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.
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The interpretation of the parameters of the equation used for the extrapolation of apparent molar volumes of the non-electrolyte (solutes) to the infinite dilution
PublikacjaThe paper discusses how to interpret the parameters of the basic equation used for the extrapolation of the apparent molar volume of the solute to infinite dilution. The common misunderstandings and oversimplifications have been pointed out. We present the alternative ways of the data interpretation that can be used to eliminate these obvious but frequent mistakes.
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Improvement of the thrust bearing calculation considering the convectional heating within the space between the pads
PublikacjaA modern thrust bearing calculation tool should consider not only the oil film between pad and rotating collar but also the space between the pads. The oil flow in the space has a significant influence on the oil film inlet temperature, the convectional cooling of pad and collar and should be included in the bearing calculation methods. The authors use a tool developed at Clausthal University of Technology in cooperation with the...
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Hyperelastic Microcantilever AFM: Efficient Detection Mechanism Based on Principal Parametric Resonance
PublikacjaThe impetus of writing this paper is to propose an efficient detection mechanism to scan the surface profile of a micro-sample using cantilever-based atomic force microscopy (AFM), operating in non-contact mode. In order to implement this scheme, the principal parametric resonance characteristics of the resonator are employed, benefiting from the bifurcation-based sensing mechanism. It is assumed that the microcantilever is made...
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Interaction between acoustic and non-acoustic mode in bubbly liquid
PublikacjaThe nonlinear interaction of acoustic and entropy modes in a bubbly liquid is the subject of investigation. Thedynamic equation governing an excess density of the entropy mode is derived. Nonlinearity and dispersion are the reasons forexcitation of the entropy mode. The nonlinear interaction of modes as a reason for bubble to grow due to sound, is discovered.Some numerical examples of the modes interactions are made.
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The application of Monod equation to denitrification kinetics description in the moving bed biofilm reactor (MBBR)
PublikacjaIn this paper, the kinetic constants Vmax and KCOD occurring in the Monod equation, which describe the denitrification process in the moving bed, are determined. For this purpose, a laboratory moving bed biofilm reactor (MBBR) was used. The filling of the reactor consisted of EvU Perl carriers. The experiment was carried out with an excess of nitrate, and denitrification rate was dependent on the concentration of external organic...
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MODELLING OF TOXIC COMPOUNDS EMISSION IN MARINE DIESEL ENGINE DURING TRANSIENT STATES AT VARIABLE PRESSURE OF FUEL INJECTION
PublikacjaTransient states are an important part of the spectrum of engine loads, especially the traction engines. In the case of marine diesel engines, transient states are of particular importance in reducing the analysis of motion units for special areas and maneuvering in port, the participation of transient states in the load spectrum significantly increases, also, the emission of toxic compounds from this period increases proportionally....
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Improved model of isothermal and incompressible fluid flow in pipelines versus the Darcy–Weisbach equation and the issue of friction factor
PublikacjaIn this article, we consider the modelling of stationary incompressible and isothermal one-dimensional fluid flow through a long pipeline. The approximation of the average pressure in the developed model by the arithmetic mean of inlet and outlet pressures leads to the known empirical Darcy–Weisbach equation. Most importantly, we also present another improved approach that is more accurate because the average pressure is estimated...
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Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
PublikacjaIn this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained...
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Verification of baffle factor for straight pipe flow
PublikacjaDuring the water disinfection devices designing, it is often assumed that the baffle factor for a straight pipe reactors is equal to one. It would be possible only for the plug flow, which is a simplified model of the flow and does not appear in real situations. The paper contains an equation which enables calculation of the real value of the baffle factor for the pipe flow.
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Model of pressure distribution in vortex flow controls
PublikacjaThe paper is devoted to the vortex valve. Existing devices are described by CFD-methods, or by means of simple empirical relations. A rational method of the considered object design is proposed, on the base of the input and dissipation energy balance., what gives a simple algebraic equation. Conformity between calcul;ated and measured parameters of the vortex valve allows for acceptation of the proposed concept.
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Mountain pass type periodic solutions for Euler–Lagrange equations in anisotropic Orlicz–Sobolev space
PublikacjaUsing the Mountain Pass Theorem, we establish the existence of periodic solution for Euler–Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part and a forcing term. We consider two situations: G satisfying at infinity and globally. We give conditions on the growth of the potential near zero for both situations.
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Local buckling of composite channel columns
PublikacjaThe investigation concerns local buckling of compressed flanges of axially compressed composite channel columns. Cooperation of the member flange and web is taken into account here. The buckling mode of the member flange is defined by rotation angle a flange about the line of its connection with the web. The channel column under investigation is made of unidirectional fibre-reinforced laminate. Two approaches to member orthotropic...
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Rhamnolipid CMC Prediction
PublikacjaRelationships between the purity, pH, hydrophobicity (log Kow) of the carbon substrate, and the critical micelle concentration (CMC) of rhamnolipid type biosurfactants (RL) were investigated using a quantitative structure–property relationship (QSPR) approach and are presented here for the first time. Measured and literature CMC values of 97 RLs, representing biosurfactants at different stages of purification, were considered....