Diffusing Wave Spectroscopy Research Articles

A microstructural investigation of an industrial attractive gel at pressure and temperature.

Oil-continuous drilling fluids used in the oil and gas industry are formulated to be pseudoplastic with a relatively weak yield stress. These fluids are required to maintain their properties over wide temperature and pressure ranges yet there are few methods that can sensitively study the inherent structure and mechanical properties in the fluids under such conditions. Here we study a model oil-continuous drilling fluid formulation as a function of both temperature (up to 153 °C) and pressure (up to 1330 bar) with Diffusive Wave Spectroscopy (DWS). The system comprises a colloidal gel network of clay particles and trapped emulsion droplets. As a function of temperature the system undergoes local structural changes reflected in the DWS dynamics which are also consistent with macroscopic rheological measurements. On cycling to high pressure the system exhibits similar structural and dynamic changes with a strong hysteresis. Although multiple scattering in multicomponent non-ergodic samples does not directly yield self diffusion probe dynamics, the use of microrheology analysis here appears to be in good agreement with direct rheological measurements of the sample linear viscoelasticity at ambient pressure. Thus DWS microrheology succesfully probes irreversible changes in the structure and the mechanical response of the drilling fluid formulation under a high pressure cycle.

Microrheological Approach for Probing the Entanglement Properties of Polyelectrolyte Solutions.

The entanglement dynamics and viscoelasticity of polyelectrolyte solutions remain active research topics. Previous studies have reported conflicting experimental results when compared to Dobrynin's scaling predictions derived from the Doi-Edwards (DE) tube model for entangled polymers. Herein, by combining classical bulk shear rheometry with diffusing wave spectroscopy (DWS) microrheometry, we investigate how the key viscoelastic parameters (the specific viscosity ηsp, the plateau modulus Ge, and the ratio of the reptation time to the Rouse time of an entanglement strand τrep/τe) depend on the polymer concentration for semidilute entangled (SE) solutions containing poly(sodium styrenesulfonate) with high molecular weight. Our experimental measurements yield Ge ∝ c1.51±0.04, in good agreement with the scaling of Ge ∝ c1.5 predicted by Dobrynin's model for salt-free polyelectrolyte SE solutions, suggesting that the electrostatic interaction influences the viscoelastic properties of polyelectrolyte SE solutions. On the other hand, the deviation in the scaling exponent for ηsp ∝ c2.56±0.04 and τrep/τe ∝ c1.82±0.28 is observed between our DWS experiments and Dobrynin's model prediction (∝ c1.5), likely due to the fact that Dobrynin's scaling model does not account for mechanisms such as the contour length fluctuation, the constraint release, and the retardation of solvent dynamics, which are known to occur for SE solutions of neutral polymers. Our results demonstrate that DWS serves as a powerful rheological tool to study the entanglement dynamics of polyelectrolyte solutions. The scaling relationships obtained in this study provide new insights to the long-standing debate on the entanglement dynamics of polyelectrolyte solutions.

Spectral Properties of Foams and Emulsions.

The optical and spectral properties of foams and emulsions provide information about their micro-/nanostructures, chemical and time stability and molecular data of their components. Foams and emulsions are collections of different kinds of bubbles or drops with particular properties. A summary of various surfactant and emulsifier types is performed here, as well as an overview of methods for producing foams and emulsions. Absorption, reflectance, and vibrational spectroscopy (Fourier Transform Infrared spectroscopy-FTIR, Raman spectroscopy) studies are detailed in connection with the spectral characterization techniques of colloidal systems. Diffusing Wave Spectroscopy (DWS) data for foams and emulsions are likewise introduced. The utility of spectroscopic approaches has grown as processing power and analysis capabilities have improved. In addition, lasers offer advantages due to the specific properties of the emitted beams which allow focusing on very small volumes and enable accurate, fast, and high spatial resolution sample characterization. Emulsions and foams provide exceptional sensitive bases for measuring low concentrations of molecules down to the level of traces using spectroscopy techniques, thus opening new horizons in microfluidics.

Population balance modeling of polyurethane foam formation with pressure‐dependent growth kernel

AbstractPolyurethane foams are widely used materials often chosen for their useful characteristics such as low thermal conductivity, ease of application, and high strength‐to‐weight ratios. Computational models are needed to predict the dynamics of the flow and expansion, and the resulting material properties, to improve manufacturing processes. In this paper, a model for PMDI, a water‐blown polyurethane foam, is presented. By extending a kinetics‐based approach by adding bubble‐scale information via a population balance equation (PBE) using the quadrature method of moments, we can track bubble size distributions during foaming. We present results from a three‐dimensional computational fluid dynamics model using arbitrary Lagrangian–Eulerian interface tracking implemented in finite element software. The model compares favorably with experimental data, including dynamics, bubble distributions measured by both camera and diffusion wave spectroscopy, and post‐test bubble size from scanning electron microscopy and density measurements from x‐ray computed tomography.

Measuring mesoscopic scales in complex fluids embedded with giant cylindrical micelles with diffusing wave spectroscopy micro-rheology

This review paper presents a procedure for measuring the mesoscopic scales in micellar solutions embedded with giant cylindrical micelles using the mean square displacement determined with a quasi-elastic multiple light scattering method (diffusing wave spectroscopy) and theory. The mesoscopic scales of interest are the micelles’ total contour length, persistence and entanglement lengths, and the mesh size of the entangled micellar network. All of them depend on the physicochemical parameters of the solutions and determine the rheological behavior. We present an assessment of the whole procedure, the scattering experiments performance, the recovery of optical parameters, which includes dealing with the light absorption and its treatment, and how to develop the micro-rheology for obtaining the mesoscopic scales in these complex fluids.

Exploring the Utility of Diffusing Wave Spectroscopy (DWS) as a Novel Tool for Early Detection of Stability Issues in Cosmetic Emulsions

In the current cosmetic and personal care industry, it is of great importance to have a technique that detects instabilities quickly and effectively, as consumers are demanding more innovative and sustainable ingredients. Diffusing wave spectroscopy (DWS) is a potential solution as it is a modern optical technique that can measure the spatial movement of particles or droplets in an emulsion—i.e., the mean square displacement (MSD), as a function of time. In the current investigation, systematic visual and diffusion behavior emulsion stability studies over a 3-h period on jojoba and avocado oil emulsions containing varying equal percentages of cocamidopropyl betaine (CAPB) and sodium lauryl ether sulfate (SLES) were conducted. The turbid emulsions studied had differing stabilities with unknown instability mechanisms to further explore if diffusing wave spectroscopy can offer a fast and early identification of problem cosmetic formulations. It was observed that, for emulsions displaying instability from 4 to 123 h, the greater the change in the MSD values over a 3-h period, the greater the instability of the emulsion. For all systems, the MSD values lowered and shifted to the right from hour 0 to hour 3. We conjecture that the emulsion droplets began to aggregate, potentially growing and giving rise to larger particles. The increasing particle size was the cause for the slowing down of the dynamics and thus diffusion, giving rise to the lowering of the MSD values. Our findings indicate that by testing an emulsion over a 3-h period, it is possible to determine whether it will be a problem formulation using DWS. Studies into this technology should be continued on a wider range of emulsions with known instability mechanisms to further our understanding of using DWS as a vital emulsion instability detector.

Candelilla wax-based oleogels versus palm oil: evaluation of physical properties of innovative and conventional lipids using optical techniques.

The widespread use of palm oil in food production affects high consumption of long-chain saturated fatty acids, which increases the risk of cardiovascular disease. Solid or semi-solid wax-based oleogels obtained as a result of edible oils structuring can be an alternative. Oleogels, obtained by structuring a mixture of refined rapeseed and linseed oils (1:1) with 30-80 g kg-1 candelilla wax (CW), were investigated using optical techniques: multi-speckle diffusing wave spectroscopy, centrifugal stability analysis, reflection method, and polarized light microscopy. Refined palm oil was a comparative sample. Increasing CW concentration resulted in an increase in values of L* parameter and opacity, a decrease in the Yellowness Index and a slight increase in the average crystal size. The microstructure of oleogels with 30 or 40 g kg-1 CW was least like the crystal network. Solidification of oleogels took place in two stages. Increase in CW concentration shortened solidification time and increased solidification temperature (greater elasticity of oleogels). Palm oil solidified the longest (497.1min) and at the lowest temperature (29.3°C). It showed lower resistance to centrifugal force than oleogels at 20 and 30 °C. All oleogels were stable (no oil release occurred) at 20 °C. Optical methods allow for an objective and detailed analysis of physical properties of palm oil and oleogels, as well as identification and tracking changes at the microstructural level over time. It has great potential in the edible lipid quality control at various stages of processing or storage. © 2021 Society of Chemical Industry.

Rheology Control Using Nonionic Cosurfactants and pH Titration in an Amino Acid-Derived Surfactant Composition.

Sulfate-based formulations can be easily thickened by adding salt or amphoteric cosurfactants. However, sulfate-free and amino acid-based surfactants cannot. We explored an alternative thickening mechanism by studying the thickening effect of adding nonionic cosurfactants to a mixture of an amino acid-based surfactant, sodium lauroyl sarcosinate (SLSar), and a zwitterionic cosurfactant, cocamidopropyl hydroxysultaine (CAHS) at a 6:9 weight ratio. To characterize the formulations, we combined traditional rheometry with a state-of-the-art mesoscopic analysis of micelle dynamics obtained via diffusing wave spectroscopy. In addition, the formulations were characterized by cross-polarized light microscopy and dynamic light scattering. The cosurfactants studied included fatty alcohols, alkanediols, a fatty acid, and fatty alcohol ethoxylates (CnE3 and CnE6). Adding the nonionic cosurfactants increased the zero-shear viscosity up to 350 times the viscosity of the no-additive system at neutral pH. When pH titration was incorporated as a second thickening mechanism, the viscosity maximum was lower than the no-additive mixture. Furthermore, the pH of the viscosity maximum was shifted to higher pH for all systems except for CnE6, which shifted the maximum to lower pH. The nonionic amphiphiles also broadened the viscosity maximum, particularly in the C10OH system. Consequently, the C10OH system had a more favorable profile for development as a practical thickening system for an amino acid-based cleanser. Analysis according to the Zou and Larson micelle dynamics model revealed that the broadening effect was associated with substantially longer breakage times for the C10OH system (4-208 ms) compared to the no-additive system (4-38 ms).

Multi-exposure interferometric diffusing wave spectroscopy.

We present multi-exposure interferometric diffusing wave spectroscopy (MiDWS), which measures brain blood flow index (BFI) continuously and non-invasively. MiDWS employs interferometry to detect low light levels, probing the optical field autocorrelation indirectly by varying the sensor exposure time. Here MiDWS is compared with conventional interferometric diffusing wave spectroscopy and speckle contrast optical spectroscopy in phantoms. Notably, the MiDWS approach enables the use of low frame rate, two-dimensional complementary metal-oxide semiconductor cameras in a short exposure time regime, where detector noise greatly exceeds the sample photon count. Finally, we show that MiDWS can monitor the BFI simultaneously at two source-collector separations (1 and 3 cm) on the adult human head on a single camera, enabling the use of superficial signal regression techniques to improve brain specificity.

Softness mapping of the concentration dependence of the dynamics in model soft colloidal systems

The dynamics of a series of soft colloids comprised of polystyrene cores with poly(N-isopropylacrylamide) (PNIPAM) coronas was investigated by diffusing wave spectroscopy (DWS). The modulus of the coronas was varied by changing the cross-link density and we were able to interpret the results within a hard-soft mapping framework. The soft, swellable particle properties were modeled using an extended Flory-Rehner theory and a Hertzian pair potential. Following volume fraction jumps, softness effects on the concentration dependence of dynamics were determined, with a ‘soft colloids make strong glass-forming liquid’-type of behavior observed close to the nominal glass transition volume fraction, φg. Such behavior from the current systems cannot be fully explained by the osmotic deswelling model alone. However, inspired by the soft-hard mapping from Schmiedeberg et al, [Europhys. Lett. 2011, 96(3), 36010] we estimated effective hard-sphere diameters and achieved a successful mapping of the α-relaxation times to a master curve below φg. Above φg, the curves no longer collapse but show strong deviations from a Vogel-Fulcher type of divergence onto soft jamming plateaux. Our results provide evidence that osmotic deswelling itself cannot fully explain the observed dynamics. Softness also plays an important role in the dynamics of soft, concentrated colloids.

Optimization of source-detector separation for non-invasive regional cerebral blood flow sensing

The detection of cerebral blood flow (CBF) has important clinical value for the diagnosis and treatment of ischemic cerebrovascular disease. The chronic changes of regional cerebral blood flow (rCBF) need long-term detection in specific cerebrovascular diseases such as Alzheimer's disease. In this paper, the optimal source-detector separation (SDS) in optical heterodyne detection combined with interferometric diffusing wave spectroscopy (OHD-iDWS) was studied. Changing the thickness of the skull and the absorption coefficient of the scalp layer, the Polarized Monte Carlo (PMC) method was used to analyze the influence of the average penetration depth and the number of polarized photons on SDS. In addition, the dynamic phantom experiments were used to evaluate the performance of the OHD-iDWS system. In this study, the system further explored the optimal SDS by distinguishing different flow rates, which provided an optimal method for SDS within 20 mm. Using PMC simulation and dynamic phantom experiments to find out the optimal SDS of rCBF sensing, it provides a theoretical basis for more effective detection of rCBF.

Effect of surface charge density of bacterial cellulose nanofibrils on the rheology property of O/W Pickering emulsions

In this study, the effect of surface charge density of bacterial cellulose nanofibrils (BCNF) on the rheological characteristics of O/W Pickering emulsions was investigated by regulating the fibril charge density. BCNFs with different carboxylate group contents (0.66, 0.90 and 1.16 mmol/g dry cellulose, representing as TOBC-a, -b, and -c) were obtained by 2,2,6,6-tetramethylpiperidine-nitrogen-oxide (TEMPO) oxidation. These oxidized products were used as Pickering stabilizers to prepare O/W Pickering emulsions. Diffusing wave spectroscopy (DWS)-based microrheology was utilized to reflect the rheological features of emulsions. TOBC-a stabilized emulsion had a lower macroscopic viscosity, lower elasticity, and better fluidity. It was because a weaker fiber network was formed in the continuous phase during the ultrasonication emulsification. The influences of pH and ionic strength on the rheological properties of high-charged TOBC-c stabilized emulsions were also investigated. The emulsion prepared at pH 3.0 exhibited the highest viscosity. It was probably because the inter-fibrils electrostatic repulsion was weakened by the addition of HCl, and the hydrogen bonding interaction became dominant due to the protonation of carbohydrate group. At pH 11, the emulsion viscosity was lowest, which was resulted from the destruction of the intra-fibrils hydrogen bonds. With the NaCl concentration increased, the emulsion viscosity and elasticity increased. It was induced by the fact that the charge shielding effect of NaCl facilitated the formation of a tighter fibrils network in the continuous phase. These results have the potential to provide a guide for developing emulsion-based products with appropriate fluidity to broaden the practical application of emulsion.

Phase stability of colloidal mixtures of spheres and rods.

We determined the phase boundaries of aqueous mixtures containing colloidal rod-like fd-viruses and polystyrene spheres using diffusing-wave spectroscopy and compared the results with free volume theory predictions. Excluded volume interactions in mixtures of colloidal rods and spheres lead to mediated depletion interactions. The strength and range of this attractive interaction depend on the concentrations of the particles, the length L and diameter D of the rods, and the radius R of the spheres. At strong enough attraction, this depletion interaction leads to phase separation. We experimentally determined the rod and sphere concentrations where these phase transitions occur by systematically varying the size ratios L/R and D/R and the aspect ratio L/D. This was done by using spheres with different radii and modifying the effective diameter of the rods through either the ionic strength of the buffer or anchoring a polymeric brush to the surface of the rods. The observed phase transitions were from a binary fluid to a colloidal gas/liquid phase coexistence that occurred already at very low concentrations due to the depletion efficiency of highly anisotropic rods. The experimentally measured phase transitions were compared to phase boundaries obtained using free volume theory (FVT), a well established theory for calculating the phase behavior of colloidal particles mixed with depletants. We find good correspondence between the experimental phase transitions and the theoretical FVT model where the excluded volume of the rod-like depletants was explicitly accounted for in both the reservoir and the system.

Self-motion and heterogeneous droplet dynamics in moderately attractive dense emulsions

We show that diffusing wave spectroscopy (DWS) is sensitive to the presence of a moderate short-range attraction between droplets in uniform fractionated colloidal emulsions near and below the jamming point associated with monodisperse hard spheres. This moderate interdroplet attraction, induced by micellar depletion, has an energy of about ∼2.4 k B T, only somewhat larger than thermal energy. Although changes in the mean free path of optical transport caused by this moderate depletion attraction are small, DWS clearly reveals an additional secondary decay-to-plateau in the intensity autocorrelation function at long times that is not present when droplet interactions are nearly hard. We hypothesize that this secondary decay-to-plateau does not reflect the average self-motion of individual droplets experiencing Brownian excitations, but instead results from heterogeneous dynamics involving a sub-population of droplets that still experience bound motion yet with significantly larger displacements than the average. By effectively removing the contribution of this secondary decay-to-plateau, which is linked to greater local heterogeneity in droplet structure caused by the moderate attraction, we obtain self-motion mean square displacements (MSDs) of droplets that reflect only the initial primary decay-to-plateau. Moreover, we show that droplet self-motion primary plateau MSDs can be interpreted using the generalized Stokes-Einstein relation of passive microrheology, yielding quantitative agreement with plateau elastic shear moduli measured mechanically.

Effect of pH on the Structure and Dynamics of Wormlike Micelles in an Amino Acid-Derived Surfactant Composition.

We studied the impact of pH as a thickening mechanism on the structure and dynamics of wormlike micelles in a mixture of sodium lauroyl sarcosinate (SLSar) and cocamidopropyl hydroxysultaine (CAHS). The viscoelastic properties were obtained using mechanical rheometry and diffusing wave spectroscopy, which provided access to a wide range of frequencies. By using a mesoscopic simulation method [Zou; Larson. J. Rheol. 2014, 58 (3), 681-721], characteristic micelle lengths and times were extracted including contour length, persistence length, entanglement length, reptation time, breakage time, breakage rate, and breakage rate constant. The interplay of pH-dependent reptation times (10-1000 ms) and breakage times (4-38 ms) leads to a minimum in the ratio of reptation time to breakage time of about 0.02 at pH 4.8. This minimum was closely associated with the sharp increase and decrease of the observed viscosity maximum at pH 4.8 in this system. These values may be contrasted with much longer breakage times (20-300 ms) that have been measured in more easily thickened sulfate-based systems. The low breakage times of the SLSar/CAHS system were attributed to the high and pH-sensitive breakage rate constants (0.01-0.17 ms-1 μm-1).

Acid-induced gelation of enzymatically cross-linked caseinates: Small and large deformation rheology in relation to water holding capacity and micro-rheological properties

Caseinate dissolved in different ionic milieus was used as model substrate for cross-linking by microbial transglutaminase and subsequent acid-induced gelation. The study follows up on previous research, where the molecular properties of cross-linked casein nanoparticles were linked to certain rheological characteristics of acid gels (Raak et al., 2019, Food Hydrocoll 86:43–49), and presents additional insight into physical gel properties. The frequency dependency of the storage modulus followed a power law relationship, with the exponent being linearly related to the phase angle. The frequency dependency of the loss factor could be fitted with a second-order polynomial function, the minimum of which was shifted to lower frequency at increasing cross-linking extent. Strain sweep experiments showed a less pronounced strain hardening behaviour and reduced fracture strain with increasing cross-linking extent, indicating lower flexibility of cross-linked casein nanoparticles and a lower number of non-covalent bonds, respectively. The water holding capacities of the gels were in a good relationship with the fracture properties, suggesting that the serum drainage during centrifugation was also affected by the strain hardening behaviour. Additionally, diffusing wave spectroscopy showed that the casein particles interacted already prior to the gelation onset, and that the presence of Ca2+ ions increases the particle size in both the caseinate solutions and gels

Scattering methods for determining structure and dynamics of polymer gels

Polymer gels are unique materials, which consist of a polymer network swollen in a solvent. The modulus and the overall state of the gel depend on thermodynamic parameters, such as strand length, structure, and chemical compatibility of the solvent. Scattering techniques have been used to study the gel structure and osmotic pressure and are discussed in this Tutorial pedagogically. These techniques are not always straightforward because of trapped inhomogeneities and complicated interactions. Nevertheless, there has been considerable progress in developing analytical tools to determine the internal structure and dynamics of polymer gels. In addition to these tools, we showcase modern spatially resolved techniques, such as Diffusing Wave Spectroscopy, and offer a perspective on similar methods such as Dynamic Small Angle Light Scattering and Differential Dynamic Microscopy, which can be used to study local and interface effects in gel systems as well as any anisotropy. These new tools can fundamentally advance our understanding of local gel dynamics, which have so far been too challenging to observe.

Symmetry breakdown in the sol-gel transition of a Guar gum transient physical network

The gelation of the mixture of guar gum and borax in an aqueous solution was studied by diffusing-wave spectroscopy microrheology. The Winter and Chambon power-law domain was evidenced at high-frequency range. The time-cure superposition was applied to the mean square displacement of the probe particles and the critical power-law behavior of the shifting factors was revealed close to the percolation threshold. Morphological characterization revealed the emergence of ribbon-like structures at high borax concentrations. The Rubinstein and Semenov plateau was demonstrated. The correlations between the critical exponents that govern the gelation of the transient networks were reviewed with regard to the scaling laws of both permanent and transient networks. Unlike permanent networks, the relation n+= n- was assumed as the unique condition to establish the hyperscaling laws in transient networks. Whereas, the symmetry breakdown of the longest relaxation time was found to be a common feature of the flowable gels.

Diffusing wave spectroscopy: A unified treatment on temporal sampling and speckle ensemble methods

Diffusing wave spectroscopy (DWS) is a well-known set of methods to measure the temporal dynamics of dynamic samples. In DWS, dynamic samples scatter the incident coherent light, and the information of the temporal dynamics is encoded in the scattered light. To record and analyze the light signal, there exist two types of methods—temporal sampling methods and speckle ensemble methods. Temporal sampling methods, including diffuse correlation spectroscopy, use one or multiple large bandwidth detectors to sample well and analyze the temporal light signal to infer the sample temporal dynamics. Speckle ensemble methods, including speckle visibility spectroscopy, use a high-pixel-count camera sensor to capture a speckle pattern and use the speckle contrast to infer sample temporal dynamics. In this paper, we theoretically and experimentally demonstrate that the decorrelation time (τ) measurement accuracy or signal-to-noise ratio (SNR) of the two types of methods has a unified and similar fundamental expression based on the number of independent observables (NIO) and the photon flux. Given a time measurement duration, the NIO in temporal sampling methods is constrained by the measurement duration, while speckle ensemble methods can outperform by using simultaneous sampling channels to scale up the NIO significantly. In the case of optical brain monitoring, the interplay of these factors favors speckle ensemble methods. We illustrate that this important engineering consideration is consistent with the previous research on blood pulsatile flow measurements, where a speckle ensemble method operating at 100-fold lower photon flux than a conventional temporal sampling system can achieve a comparable SNR.

High-internal-phase emulsions (HIPEs) for co-encapsulation of probiotics and curcumin: enhanced survivability and controlled release.

Synergistic biological activities of probiotics and curcumin can be achieved based on the gut-brain axis. However, it is still a challenge for utilizing both of them in actual food products due to their high sensitivity to environmental conditions. In the present study, high-internal-phase emulsions (HIPEs) were fabricated to co-encapsulate the probiotics and curcumin in response to the customer demand for convenience. β-Lactoglobulin-propylene glycol alginate composite hydrogel particles (β-lgPPs) with proper size and intermediate wettability were prepared at β-lg to PGA mass ratio of 2 : 1 and employed as particulate emulsifiers. Stable HIPEs with a fixed oil fraction (φ = 0.8) could be formed within a wide range of β-lgPPs concentrations, ranging from 0.1 to 2.0 wt%. Confocal laser scanning microscopy (CLSM) images indicated that the interfacial structure of the oil droplets was composed of both β-lg nanoparticles and a PGA network, which jointly contributed to the gel-like structures in HIPEs. An increase in elasticity and gel strength, as well as centrifugal stability, could be achieved by elevating the particle concentration as determined by diffusing wave spectroscopy and Lumisizer analysis. HIPEs with high particle concentrations showed a high resistance against pasteurization since no obvious flocculation or coalescence could be observed in these emulsions. HIPEs also provoked a significant reduction in the death of LGG as well as the chemical degradation of curcumin: up to 7.91 log CFU cm-3 of LGG and 93.0% of curcumin were retained after pasteurization treatment. Moreover, the HIPEs could also retard the release of curcumin and protect the LGG in simulated gastrointestinal tract conditions. The results from this work provide useful information for developing a promising delivery system for the co-encapsulation of curcumin and probiotics.