Chemical and Rheological Characterization of Drag-Reducing Cationic Surfactant Systems

Strong Viscosity Increase in Aqueous Solutions of Cationic C22-Tailed Surfactant Wormlike Micelles

The viscoelastic properties and structure parameters have been investigated for aqueous solutions of wormlike micelles of cationic surfactant erucyl bis(hydroxyethyl) methylammonium chloride with long C22 tail in the presence inorganic salt KCl. The salt content has been varied to estimate linear to branched transition conditions due to screening of the electrostatic interaction in the networks. The local cylindrical structure and low electrostatic repulsion was obtained by SANS data. The drastic power law dependencies of rheological properties on surfactant concentrations were obtained at intermediate salt content. Two power law regions of viscosity dependence were detected in semi-dilute solutions related to “unbreakable” and “living” micellar chains. The fast contour length growth with surfactant concentration demonstrated that is in good agreement with theoretical predictions.

Interfacial Interaction Enhanced Rheological Behavior in PAM/CTAC/Salt Aqueous Solution-A Coarse-Grained Molecular Dynamics Study

Interfacial interactions within a multi-phase polymer solution play critical roles in processing control and mass transportation in chemical engineering. However, the understandings of these roles remain unexplored due to the complexity of the system. In this study, we used an efficient analytical method-a nonequilibrium molecular dynamics (NEMD) simulation-to unveil the molecular interactions and rheology of a multiphase solution containing cetyltrimethyl ammonium chloride (CTAC), polyacrylamide (PAM), and sodium salicylate (NaSal). The associated macroscopic rheological characteristics and shear viscosity of the polymer/surfactant solution were investigated, where the computational results agreed well with the experimental data. The relation between the characteristic time and shear rate was consistent with the power law. By simulating the shear viscosity of the polymer/surfactant solution, we found that the phase transition of micelles within the mixture led to a non-monotonic increase in the viscosity of the mixed solution with the increase in concentration of CTAC or PAM. We expect this optimized molecular dynamic approach to advance the current understanding on chemical-physical interactions within polymer/surfactant mixtures at the molecular level and enable emerging engineering solutions.

Wormlike micelles with a unique ladder shape formed by a C22-tailed zwitterionic surfactant bearing a bulky piperazine group

Wormlike micelles (WLMs) have been successfully constructed from many different C₂₂-tailed surfactants. Here, we creatively introduced a bulky piperazine group onto a C₂₂-tailed zwitterionic surfactant, N-erucamidopropyl-N,N-piperazine-N-methyl ammonium propanesulfonate (EDPS), and investigated the micellar structure and properties of the EDPS WLMs via molecular dynamics simulation, cryo-TEM and rheological techniques. It was found that 25 mM EDPS increased the zero-shear viscosity to as high as ∼10⁶ mPa s. Furthermore, abnormal rheological behaviors, such as an inflection in the shear thinning region of steady rheology and an abrupt decrease of the shear stress at a critical shear rate, were observed, which was attributed to the unique ladder shape micellar structure. The EDPS WLMs were superior to other C₂₂-tailed surfactants in many aspects, such as a low overlapping concentration, higher viscosity, stable viscosity over the whole pH range, and great temperature and salt (NaCl, CaCl₂ and MgCl₂) tolerance.

Effect of residual chemicals on wormlike micelles assembled from a C22-tailed cationic surfactant

HYPOTHESIS

Ultra-long-chain surfactants, particularly C₂₂-tailed ones, have attracted considerable attention because of their ease of self-assembly into wormlike micelles (WLMs). Commercial C₂₂-tailed surfactants often contain non-negligible amounts of chemical residues introduced during their production. Since the noncovalent driving force of wormlike self-assembly can be greatly affected by the composition, we hypothesized that the residual chemicals could play a significant role in tuning the micelle microstructure and macroscopic properties of the surfactants.

EXPERIMENTS

To confirm this hypothesis, a highly pure (>99%) C₂₂-tailed cationic surfactant, N-erucylamidopropyl-N,N,N-trimethylammonium iodide (EDAI) was synthesized, and various amounts of corresponding reactants (iodomethane or N-erucamidopropyl-N,N-dimethylamine) or solvents (acetone) commonly used in surfactant synthesis were introduced as residues. The impact of each individual residue on the macroscopic appearances, rheological properties, and micelle morphology of the surfactant solution were investigated.

FINDINGS

Increasing the residue fraction in the EDAI solution resulted in an initial increase, followed by a dramatic drop in solution viscosity. This behavior was described in terms of micellar structural transformations based on analysis of cryo-TEM observations and surface tension measurements. These findings are of crucial importance in understanding the sophisticated behaviors of WLMs and will benefit the industrial preparation of ultra-long-chain surfactants for commercial use.

Una mirada al desarrollo de aditivos reductores de viscosidad y sus aplicaciones en el transporte de crudos pesados

La presente revisión aborda la problemática que presentan los crudos pesados debido a su alta viscosidad, lo cual dificulta su transporte por tubería y su directa relación con la fracción de asfaltenos, cuyo apilamiento genera cambios en la reología del crudo, altas caídas de presión y mayores requerimientos energéticos en el bombeo, e incluso taponamiento de tuberías. Las investigaciones reportadas se han enfocado en predecir y elucidar la composición estructural de los asfaltenos, de lo cual se resaltan modelos que describen a los asfaltenos como sistemas de anillos aromáticos policondensados, que pueden unirse por interacciones de Van der Waals formando agregados, o también como estructuras jerárquicas de sistemas de anillos de hidrocarburos aromáticos policíclicos (PAH), que finalizan en la formación de racimos (clúster). También se resalta el modelo termodinámico coloidal, el cual predice moléculas de asfaltenos suspendidas en una fase líquida, estabilizada por resinas adsorbidas en su superficie. Una alternativa para disminuir la viscosidad de los crudos es la inclusión de aditivos, los cuales mediante interacciones moleculares apropiadas, generan la dispersión de agregados asfalténicos, reflejándose en la disminución de la viscosidad. Por ello a la hora de diseñar aditivos reductores de viscosidad pare crudos, es importante diseñar estructuras moleculares con determinados grupos funcionales asociados a aminas, amidas, alcoholes, ácidos, entre otros, que favorezcan interacciones que generen la dispersión de asfaltenos. Por ellos y con el fin de brindar un panorama amplio de esta línea de investigación tan extensa, se finaliza este documento con una revisión de algunos aditivos reductores de viscosidad, implementados por diferentes investigadores.

Study of a Novel Gemini Viscoelastic Surfactant with High Performance in Clean Fracturing Fluid Application

Gemini surfactant, as a functionally flexible polymer-like material in the aqueous solution, has attracted increased attention in reservoir stimulation of hydraulic fracturing in recent decades. A new Gemini cationic viscoelastic surfactant named JS-N-JS, which has a secondary amine spacer group and two ultra-long hydrophobic tails, was synthesized from erucamidopropyl dimethylamine, diethanolamine, and thionyl chloride as a thickener for hydraulic fracturing fluid. Compared with some Gemini cationic surfactant with methylene spacer, JS-N-JS showed a lower critical micellar concentration (CMC) and higher surface activity due to the hydrogen bond formed between the secondary amine and water molecule intends to reduce electrostatic repulsion, which is more beneficial to be the fracturing fluid thickener. Moreover, the performance of JS-N-JS solution can be further improved by salts of potassium chloride (KCl) or sodium salicylate (NaSal), while organic salt behaved better according to the measurements. The SEM observation confirmed that JS-N-JS/NaSal system owned a tighter network microstructure, and JS-N-JS/NaSal system exhibited a distinct superior viscoelasticity system at a sweep frequency of 0.1⁻10 Hz. As a fracturing fluid, the solution with a formula of 30 mmol JS-N-JS and 100 mmol NaSal was evaluated according to the petroleum industrial standard and presented excellent viscoelastic properties, the viscosity of which can maintain above 70 mPa·s for 110 min under a shear rate of 170 s-1 at 120 °C. Meanwhile, the drag reducing rate of the formula could reach above 70% with the increase of shear rate. Finally, the viscous fracturing fluid can be broken into the water-like fluid in 1.2 h after being fully exposed to hydrocarbons and the water-like fluid presented a low damage to the tight sand reservoirs according to the core flooding experiments, in which the permeability recovery rate can reach 85.05%. These results fully demonstrate that the JS-N-JS solution fully meets the requirement of the industrial application of hydraulic fracturing.

Kinetics and Mechanism of Cationic Micelle/Flexible Nanoparticle Catalysis: A Review

The aqueous surfactant (Surf) solution at [Surf] > cmc (critical micelle concentration) contains flexible micelles/nanoparticles. These particles form a pseudophase of different shapes and sizes where the medium polarity decreases as the distance increases from the exterior region of the interface of the Surf/H2O particle towards its furthest interior region. Flexible nanoparticles (FNs) catalyse a variety of chemical and biochemical reactions. FN catalysis involves both positive catalysis ( i.e. rate increase) and negative catalysis ( i.e. rate decrease). This article describes the mechanistic details of these catalyses at the molecular level, which reveals the molecular origin of these catalyses. Effects of inert counterionic salts (MX) on the rates of bimolecular reactions (with one of the reactants as reactive counterion) in the presence of ionic FNs/micelles may result in either positive or negative catalysis. The kinetics of cationic FN (Surf/MX/H2O)-catalysed bimolecular reactions (with nonionic and anionic reactants) provide kinetic parameters which can be used to determine an ion exchange constant or the ratio of the binding constants of counterions.

A gemini surfactant-containing system with abundant self-assembly morphology and rheological behaviors tunable by photoinduction

The photoisomerization of OMCA affects the degree of OMCA participation in the formation of mixed micelles and results in the transformation of micellar morphologies.

Responsive, switchable wormlike micelles for CO2/N2 and redox dual stimuli based on selenium-containing surfactants

A dual-stimuli responsive, wormlike micelle system was developed using a switchable selenium-containing surfactant, dihendecylcarboxylic acid sodium selenide (C₁₁-Se-C₁₁), and a commercially available surfactant, cetyltrimethyl ammonium bromide (CTAB). The solution showed a viscoelastic characteristic at low shear frequencies, and the synergism was significant when the concentrations of CTAB and C₁₁-Se-C₁₁ were 145 mM and 25 mM, respectively. Additionally, the system was fast and reversibly responded to CO₂ and redox dual stimuli, and it showed a circulatory gel/sol transition, which reflected changes in the self-assembly from entangled worms to rodlike micelles. Moreover, these transitions were switchable at least three times. The dual responsiveness of the solution allowed for precise control of the wormlike micelles, and these micelles will have a wide range of applications in the development of functional materials for pharmaceutical or biomedical materials.

Giant vesicles (GV) in colloidal system under the optical polarization microscope (OPM)

This paper discusses the unprecedented microscopic findings of micellar growth in colloidal system (CS) of catalyzed piperidinolysis of ionized phenyl salicylate (PS^-). The giant vesicles (GV) was observed under the optical polarization microscope (OPM) at [NaX]=0.1M where X=3-isopropC₆H₄O^-. The conditions were rationalized from pseudo-first-order rate constant, k_obs of PS^- of micellar phase at 31.1×10^-3s^-1 reported in previous publication. The overall diameter of GV (57.6μm) in CS (CTABr/NaX/H₂O)-catalyzed piperidinolysis (where X=3-isopropC₆H₄O) of ionized phenyl salicylate were found as giant unilamellar vesicles (GUV) and giant multilamellar vesicles (GMV). The findings were also validated by means of rheological analysis.

pH-regulated surface properties and pH-reversible micelle transition of a zwitterionic gemini surfactant in aqueous solution

A zwitterionic gemini surfactant, called 2,2'-(1,4-phenylenebis(oxy))bis(N,N-dimethyl)-N-carboxyethyl-N-(alkylamide propyl) ammonium chloride (C₁₄-B-C₁₄), was synthesized successfully. The surfactant molecule exhibits various states at different pH values due to the two pH-sensitive carboxylate groups in the molecule. The surface activity and aggregate behaviors of C₁₄-B-C₁₄ in the aqueous solution were investigated under different pH conditions. The surface activities of the surfactant decrease with the increase in pH due to higher hydrophilic properties under basic conditions. The aggregate behaviours were also studied in acidic, near neutral and alkaline solutions, respectively. When the pH values of the solutions increased from acidic conditions to near neutral conditions (6.80), the samples immediately transformed from water-like solutions to viscoelastic fluids and remained gel-like under basic conditions. The changes in the appearance of the solution were due to the transition of the micelle structure from spherical to worm-like. Furthermore, this transition was reversible and repeated for at least 4 cycles. Finally, a reasonable mechanism of the appearance and transition of micelles was proposed based on the molecular states, viscoelastic properties and micelle structures.

pH-Regulated surface property and pH-reversible micelle transition of a tertiary amine-based gemini surfactant in aqueous solution

A series of tertiary amide-based gemini surfactants, 2,2'-(1,4-phenylenebis(oxy))bis(N-(3-(dimethylamino)propyl)alkylamide), abbreviated as Cm-A-Cm (m = 8; 10; 12; 14), were synthesized. The surface property and aggregation behaviors of the Cm-A-Cm aqueous solutions were studied in detail. The Cm-A-Cm exhibited high and pH-regulated surface activity at the air/water interface; i.e., the critical micelle concentration was 5.6 × 10(-6) mol L(-1) at pH = 2.50 when m = 14 and was further regulated to 1.8 × 10(-6) mol L(-1) by altering the pH to 6.50. When the pH was tuned from 2.0 to 12.0, the appearance of the C12-A-C12 aqueous solution (35 mM) underwent 5 states: transparent water-like solution, viscous fluid, gel-like fluid, turbid liquid and dispersion system with white precipitate. The results of rheology, cryogenic transmission electron microscopy, and dynamic light scattering characterization revealed that the transition from water-like to viscous or gel-like liquid was actually due to aggregate microstructure transition from spherical to worm-like micelles. This transition was completely reversible between pH = 2.50 and 6.81, tuned by adding HCl and NaOH solutions for at least 4 cycles. Similar micellar transitions regulated by pH were also found for m = 8 and 10, whereas only worm-like micelles were formed for m = 14 at both acidic and nearly neutral conditions. Finally, a reasonable mechanism of aggregate behavior transition was proposed from the viewpoint of the molecular states, molecular structures, and the intra- and inter-molecular interactions.

Investigation on the aggregation behavior of photo-responsive system composed of 1-hexadecyl-3-methylimidazolium bromide and 2-methoxycinnamic acid

Mechanism of the aggregation behavior for the photo-responsive system composed of 1-hexadecyl-3-methylimidazolium bromide and 2-methoxycinnamic acid.

Kinetics and mechanism of nanoparticles-catalyzed piperidinolysis of anionic phenyl salicylate

The values of the relative counterion (X) binding constant R(X)(Br) (=K(X)/K(Br), where K(X) and K(Br) represent cetyltrimethylammonium bromide, CTABr, micellar binding constants of X(v-) (in non-spherical micelles), v = 1,2, and Br(-) (in spherical micelles)) are 58, 68, 127, and 125 for X(v-) = 1(-), 1(2-), 2(-), and 2(2-), respectively. The values of 15 mM CTABr/[Na(v)X] nanoparticles-catalyzed apparent second-order rate constants for piperidinolysis of ionized phenyl salicylate at 35 °C are 0.417, 0.488, 0.926, and 0.891 M(-1) s(-1) for Na(v)X = Na1, Na2 1, Na2, and Na2 2, respectively. Almost entire catalytic effect of nanoparticles catalyst is due to the ability of nonreactive counterions, X(v-), to expel reactive counterions, 3(-), from nanoparticles to the bulk water phase.

Quantitative correlation between counterion-affinity to cationic micelles and counterion-induced micellar growth

The fascinating and serendipitous discovery, in 1976, of the characteristic viscoelastic behavior of wormlike micelles of cetyltrimethylammonium salicylate (CTASa) surfactant solution at ~2×10(-4) M CTASa became a catalyst for an increasing interest in both industrial application and mechanism of the origin of micellar growth of this and related wormlike micellar systems. It has been perceived for more than three decades, based upon qualitative evidence, that the extent of the strength of the counterion (X) binding to ionic micelles determines the counterion-induced micellar structural transition from spherical-to-small rodlike-to-linear long stiff/flexible rodlike/wormlike-to-entangled wormlike micelles. This perception predicts the presence of a possible quantitative correlation of counterionic micellar binding constants (KX) with counterion-induced micellar growth. The quantitative estimation of counterion binding affinity to cationic micelles, in terms of the values of the degree of counterion binding (βX), is concluded to be either inefficient or unreliable for moderately hydrophobic counterions (such as substituted benzoate ions). The values of KX, measured in terms of conventional ion exchange constants (KX(Y)), can provide a quantitative correlation between KX or KX(Y) (with a reference counterion Y=Cl(-) or Br(-)) and counterion-induced ionic micellar growth. A recent new semi-empirical kinetic (SEK) method provides the estimation of KX(Y) for Y=Br as well as ratio of counterionic micellar binding constants KX/KBr (= RX(Br)) where the values of KBr and KX have been derived from the kinetic parameters in the presence of cationic spherical and nonspherical micelles, respectively. The SEK method has been used to determine the values of KX(Br) or RX(Br) for X=2-, 3- and 4-ClC6H4CO2(-). Rheometric measurements on aqueous CTABr/MX (MX=2-,3- and 4-ClBzNa) solutions containing 0.015 M CTABr and varying values of [MX] reveal the presence of spherical micelles for MX=2-ClBzNa and long linear as well as entangled wormlike micelles for MX=3- and 4-ClBzNa. The respective values of KX(Br) or RX(Br) of 5.7, 50 and 48 for X=2-, 3- and 4-ClBz(-) give a quantitative correlation with the rheometric measurements of the structural features of micelles of 0.015 M CTABr solutions containing 2-, 3- and 4 ClBzNa.

An Advanced Method for the Preparation of Erucyl Dimethyl Amidopropyl Betaine and Acid Solution Properties

In this paper, an improved method for the preparation of erucyl dimethyl amidopropyl betaine (EDAB) was provided. The synthesis conditions were investigated. N,N-dimethyl-N′-erucyl-1,3-propylenediamine was synthesized by the reaction of erucic acid with N,N-dimethyl-1,3-propylenediamine at 170°C for 7 h, and then the intermediate was reacted with sodium chloroacetate in the mixture of methanol and water (3:7 v/v) at 60°C. The product was obtained after 6 h. The compounds were confirmed by IR and 1H-NMR. The properties of EDAB acid solution were also studied. The results indicated that viscosity of acid solution increased with decreasing hydrochloric acid concentration and was mainly controlled by surfactant concentration and temperature. The viscosity of an acid solution was maximum when the concentration of hydrochloric acid was at 15 wt%.

Smart wormlike micelles

A major scientific challenge of the past decade pertaining to the field of soft matter has been to craft 'adaptable' materials, inspired by nature, which can dynamically alter their structure and functionality on demand, in response to triggers produced by environmental changes. Amongst these, 'smart' surfactant wormlike micelles, responsive to external stimuli, are a particularly recent area of development, yet highly promising, given the versatility of the materials but simplicity of the design-relying on small amphiphilic molecules and their spontaneous self-assembly. The switching 'on' and 'off' of the micellar assembly structures has been reported using electrical, optical, thermal or pH triggers and is now envisaged for multiple stimuli. The structural changes, in turn, can induce major variations in the macroscopic characteristics, affecting properties such as viscosity and elasticity and sometimes even leading to a spontaneous and effective 'sol-gel' transition. These original smart materials based on wormlike micelles have been successfully used in the oil industry, and offer a significant potential in a wide range of other technological applications, including biomedicine, cleaning processes, drag reduction, template synthesis, to name but a few. This review will report results in this field published over the last few years, describe the potential and practical applications of stimuli-responsive wormlike micelles and point out future challenges.

Synthesis and acid solution properties of a novel betaine zwitterionic surfactant

An effective and economic route was developed to synthesize a novel betaine zwitterionic surfactant gondoyl dimethyl amidopropyl betaine (GDAB) directly from natural fatty acid gondoic acid. The optimal processing conditions for synthesizing the intermediate and final product were probed: N,N-dimethyl-N′-gondoyl-1,3-propylenediamine was synthesized by the reaction of gondoic acid with N,N-dimethyl-1,3-propylenediamine at 160°C for 6 h, then the intermediate was reacted with sodium chloroacetate in methanol-water system (methanol/water:20% at 60°C and the product was obtained after 6h. The compounds were confirmed by IR and 1HNMR. The properties of GDAB acid solution were investigated and the results indicated that viscosity of acid solution increased with decreasing hydrochloric acid concentration and was mainly controlled by surfactant concentration and temperature. The viscosity of acid solution reached the maximum value when the concentration of hydrochloric acid was 2.28 mo L−1.

Studies on rheological and leaching characteristics of heavy metals through selective additive in high concentration ash slurry

The generation and disposal level of thermal power plant ash in India is a challenging task. The conventional mode of dilute phase ash slurry (10-20% solids by weight) transport through pipelines being practiced in majority of these plants not only consumes huge amount of precious water and pumping energy but also causes serious environmental problem at the disposal site. The present study investigates the rheological and leaching characteristics of an Indian ash samples at high solids concentrations (>50% by weight) using sodium silicate as an additive. The flow behaviour of ash slurry in the concentration range of 50-60% by weight is described by a Bingham-plastic model. It was indicated that the addition of sodium silicate (0.2-0.6% of the total solids) could able to reduce both the slurry viscosity and the yield stress. The analysis of the ash samples for the presence of heavy metals such as Fe, Cd, Ni, Pb, Zn, Cu, Co, As and Hg were carried out following Hansen and Fisher procedure. The addition of sodium silicate affected the leaching characteristics of the ash samples over a period of 300 days resulting in the reduction of leaching of heavy metals.

Wormlike micelles and solution properties of a C22-tailed amidosulfobetaine surfactant

Wormlike micelles have been observed and explained in a wide variety of different types of surfactants except sulfobetaine ones. Here, we first report branched worms formed by a C22-tailed amidosulfobetaine surfactant-3-(N-erucamidopropyl-N,N-dimethyl ammonium) propane sulfonate (EDAS). Increasing EDAS concentration in the semidilute region increases the viscosity by several orders of magnitude and forms viscoelastic micellar solution of entangled and branched worms. The intermicellar branching is proved by rheological methods and Cryo-TEM observation. Besides, the rheological experiments indicate that EDAS worms show some advantages such as low overlapping concentration, insensitive to inorganic salt, stable over the whole pH range.

Bis-urea-based supramolecular polymer: the first self-assembled drag reducer for hydrocarbon solvents

The hydrodynamic drag reduction phenomenon, also termed the Toms effect, is an unusual case involving macromolecules in solution in which the resistance to flow is reduced comparatively to that of the pure solvent. Although the effect is relatively well characterized, it is still unclear from the molecular viewpoint. The presence of some amount of a polymer with high molecular weight can produce large levels of drag reduction in turbulent flow as a result of the interactions of the long structures with the small vortices developed during the flow. For this reason, the effect is very attractive in the pumping process because a significant amount of energy can be saved. In aqueous systems, giant micelles can be spontaneously formed, driven by the hydrophobic effect, and are effective drag reducers. Giant micelles are interesting in promoting drag reduction because the noncovalent and reversible aggregation of the surfactant molecules avoids mechanical degradation, which typically occurs with classical polymers, due to irreversible scission of the backbone. In this letter, we present the first hydrodynamic drag reducer for hydrocarbons based on a self-assembled polymer formed from the reversible aggregation of bis-urea monomers. This system forms two competitive polymeric structures--the tube (T) and the filament (F) forms--which are in equilibrium with each other. Our rheology results in octane and toluene are fully consistent with calorimetry data and show that only the longest form, T, is able to promote the drag reduction effect.

Evaluation of the role of a cationic surfactant on the flow characteristics of fly ash slurry

Transportation of fly ash is a major problem in its efficient disposal. The main problem associated with fly ash transportation is that the particles settle down sooner than desired. The primary objective of this research is that not only the fly ash particles should remain floated till it reaches the end but also settle down after that. In this investigation the role of a drag-reducing cationic surfactant and a counter-ion has been evaluated to achieve the objectives. The experimental results show encouraging trends of surfactant helping fly ash particles to remain water-borne. The material exhibited Newtonian behavior. This paper describes these in term of shear rates, shear stress, temperature, concentration and viscosity. Rheological tests were conducted using Advanced Computerized Rheometer. Zeta potential was measured to test the stability of the colloidal fly ash particles using Malvern Zeta Sizer instrument. Surface tension was also measured to know the drag reduction behavior of the fly ash slurry by using Surface Tensiometer. The test results and flow diagrams were generated using Rheoplus software and are presented in this paper. Surfactant concentration of 0%, 0.1%, 0.2%, 0.3%, 0.4% and 0.5% by weight was mixed with equal amount of counter-ion and the slurry was prepared by adding fly ash with ordinary tap water to achieve the desired solid concentration of 20% (by weight).