The strong shear induced by the injection of liquid sprays at high velocities induces turbulence in the surrounding medium. This, in turn, influences the motion of droplets as well as the mixing of air and vapor. Using fluorescence-based tracer particle image velocimetry, the velocity field surrounding 125–135 m/s sprays exiting a 200- μ m nozzle is analyzed. For the first time, the small- and large-scale turbulence characteristics of the gas phase surrounding a spray has been measured simultaneously, using a large eddy model to determine the sub-grid scales. This further allows the calculation of the Stokes numbers of droplets, which indicates the influence of turbulence on their motion. The measurements lead to an estimate of 2 −3 −4 the dissipation rate ≈ 35 m s , a microscale Reynolds number Re ≈ 170, and a Kolmogorov length scale of ≈ 10 m. Using these dissipation rates to convert a droplet size distribution to a distribution of Stokes numbers, we show that only the large scale motion of turbulence disperses the droplet in the current case, but the small scales will grow in importance with increasing levels of atomization and ambient pressures. 1 Introduction small-scale turbulence characteristics, such as the dissipa- tion rate, determine the influence of the gas-phase turbulence When a high-speed liquid jet breaks up into a spray, it drags on the motion and mixing of droplets in turbulence (Shaw along the air surrounding it, generating strong shear forces et al. 1998; Reveillon and Demoulin 2007). A dimensionless in the ambient gas. This shear can be the driving force for quantity called the Stokes number quantifies the response of generating turbulence. This turbulence, in turn, can influ- droplets to velocity fluctuations of the surrounding gas. It is ence the mixing and dispersion of the droplets in the spray the ratio of two time scales: the viscous response time over itself (Bharadwaj et al. 2009; Bocanegra Evans et al. 2016). the Kolmogorov time scale . A measurement of requires Little information exists on spray-induced turbulence, due a measurement of the turbulent energy dissipation rate . to the challenge of measuring the velocity field in such a This is an experimental challenge, as this requires measure- complex environment, as well as obtaining the number of ments at the resolution of the smallest length scales. In this measurements required to obtain statistical information. The paper a large-scale eddy approach is used in which proper- ties of small-scale motion are inferred from a measurement of large-scale velocity statistics (Pope 2000). * Dennis D. van der Voort One of the challenging aspects of obtaining gas-phase firstname.lastname@example.org velocities close to a spray is the inherent multi-phase envi- Nico J. Dam ronment. Hot-wire anemometers, often used for 1D measure- email@example.com ments of turbulence (Laufer 1954; Wyngaard 1968; Ligrani Herman J. H. Clercx and Bradshaw 1987), are influenced by impacting drop- firstname.lastname@example.org lets (Siebert et al. 2007) in both the processing and longev- Willem van de Water ity of the (fragile) probe. Direct-scattering techniques that email@example.com determine the displacement of small particles/droplets that follow the flow (tracers) using pulsed lasers, such as Particle Fluid Dynamics Laboratory, Applied Physics, Eindhoven university of Technology, Eindhoven, The Netherlands Image Velocimetry (PIV), are affected by the large range of scales, and are visualizing foremost the liquid phase of the J.M. Burgers centre for Fluid Dynamics, Delft, The Netherlands spray (Paulsen Husted et al. 2009; Cao et al. 2000). Present Address: Laboratory for Aero and Hydrodynamics, Delft University of Tehnology, Delft, The Netherlands Vol.:(0123456789) 1 3 110 Page 2 of 7 Experiments in Fluids (2018) 59:110 In the past, fluorescent tracers have been used to circum - continuous water or heptane spray, generated by a pressur- vent this problem (Lee et al. 2002; Zhu et al. 2012; Rot- ized straight single-hole nozzle capillary (see Figs. 1 and 2), tenkolber et al. 2002; Kosiwczuk et al. 2005; Driscoll et al. with a diameter of 200 μ m and a length of 2 mm. The noz- 2003; Zhang et al. 2014; Boëdec and Simoëns 2001). By zle is surrounded by a container ( 400 × 400 × 800 mm) to adding a fluorescent molecule to tracers in the ambient gas obtain a uniform dense seeding of the atomized tracers, with (μ m-sized droplets), the laser light scattered by the liquid optical access for the camera and laser sheet. The gas phase phase can be filtered from the images, and only the lumines- is set in motion through the heptane and water spray, which cent gas phase is then recorded. In this way, the velocity field mixes the fluorescein-doped micro-droplets into the spray of the gas-phase can be determined independently, and the surroundings. A double-pulsed Nd:YAG laser (PIV-300, applied method is commonly referred to as Laser-Induced Spectra Physics) is custom-fitted to generate third harmonic Fluorescence PIV (LIF-PIV). These investigations often (355 nm) pulses at a repetition rate of 10 Hz and a time focus on visualizing large-scale flow structures (Rottenkol- delay between the pulses of 60 μ s. These pulses are formed ber et al. 2002; Kosiwczuk et al. 2005; Lee et al. 2002) or into a sheet with a thickness of approximately 100 μ m and a measuring the mean velocity induced by sprays (Zhu et al. fluence of 300 mJ/cm . Following a laser pulse, the lumines- 2012; Zhang et al. 2014). cent micro-droplets are recorded through a high-pass 420 nm A measurement of the statistical properties of the tur- filter (Schott, GG420) using a PIV camera (Redlake) with a bulent flow induced by the breaking jet aims to measure resolution of 1600 × 1200 pixels and at a magnification of its small- and large-scale properties. The first is character - 10.4 μ m per pixel. The sprays are continuously generated ized by the dissipation rate , which sets the length and by pressurizing the liquid reservoir connected to the nozzle 3 1∕4 the timescale of the smallest vortices, =( ∕) with a pressure of 10 MPa (surrounded by air at atmospheric 1∕2 and =(∕) , respectively, where is the kinematic pressures). This is done for approximately 1–2 min, leading viscosity of the surrounding gas. A value of the droplet to approximately 200–300 image pairs. This measurement is Stokes number St ≪ 1 signifies that droplets can follow the turbulent velocity fluctuations at the smallest scale (and thus also at all larger scales). The turbulent velocity 2 1∕2 u ()= ⟨(u(, t)− u()) ⟩ , wit h the position in space rms and u the mean velocity u()= ⟨u(, t)⟩ , where ⟨⟩ indicates an average over time, determines the dispersion of droplets that follow the flow exactly ( St ≤ 1). As the droplets predom- inantly behave like passive tracers down to the Kolmogorov scale their dispersion should behave like those of fluid ele- ments. At times much shorter than the large eddy turnover time T, droplets disperse in a ballistic manner, with the mean 2 2 2 separation between droplets increasing as ⟨ (t)⟩ = u t . rms However, at times much larger than T, the droplets disperse 2 2 diffusively, as ⟨ (t)⟩ = Tu t . Therefore, to obtain an accu- rms rate picture of the mixing and dispersion of droplets, the cor- relation properties of the velocity field have to be measured in addition to the turbulent velocity. 2 Experimental setup The fluorescent tracer agent used in this work is Fluorescein sodium salt (Sigma-Aldrich), an organic compound with a broadband absorption in the ultraviolet and a peak lumi- nescence at 521 nm. The compound is dissolved in water in near-saturated concentrations to ensure high luminescence yield. To follow the motion of the air precisely, the fluores- Fig. 1 Schematic of the experimental spray setup. Micro-droplets cent dye is atomized to droplets with a mean diameter of containing fluorescent tracers are added to a chamber containing a 0.3 μ m with a geometric standard deviation of less than 2.0, spray mount. A double-pulsed ultraviolet laser sheet is used to excite using a six-jet atomizer (Model 9306, TSI). The atomized the micro-droplets surrounding the spray. The spray surroundings are visualized with a PIV camera tracers are injected 1000 nozzle diameters downstream of a 1 3 Experiments in Fluids (2018) 59:110 Page 3 of 7 110 Fig. 2 Diffuse background (DBI) image of the heptane spray at an injection pressure of P = 10 MPa. inj 2 −3 repeated up to three times, resulting in 700–900 image pairs dissipation rate of = 50 m s , these drops have a Stokes for both the water and heptane sprays. number of St ≈ 2 . Smaller drops are considered as tracers, The continuous nature of the spray may introduce recir- while the contribution of larger drops on the PIV correlation culated droplets in addition to the large (outlier) droplets is minimized by setting their intensity equal to the back- from the aerosol generator. The jet velocity was measured ground intensity sampled on a radius of d around them. thr using laser-induced phosphorescence (Voort et al. 2016a, b), The result is shown in Fig. 3c. This elimination of droplets with v = 135 m/s for the heptane jet and v = 125 m/s for jet jet is based on their size, not directly on their intensity. The PIV the water jet. This leads to Reynolds Re = v d ∕ and correlations are done using DaVis PIV software (LaVision jet nozzle 2 4 Weber We = v d∕ numbers of Re ≃ 4.5 × 10 , W e ≃ 220 g GmbH, Germany), with 48 × 48 pixel interrogation win- jet 4 dows that started at 128 × 128 pixels. The planar velocity and Re ≃ 2.5 × 10 , W e ≃ 125 for the heptane and water jet, gradients, needed for the measurement of the dissipation respectively, with the kinematic viscosity, d the nozzle nozzle rate, were computed using central differences. As the PIV diameter, and the surface tension of the liquid. interrogation window size ≃ 5 , large eddy PIV implies a Figure 3a shows a single fluorescence image. Both the correction factor of ≃ 3.4, which multiplies with the standard fluorescent tracers and the direct scattering of the UV light value of the Smagorinsky constant C = 0.17 (Bertens et al. off the liquid phase (jet, drops) can be seen. Although the 2015). Statistics over 700–900 vector fields are computed observation of direct scattering is strongly suppressed by the over displacement vectors corresponding to correlation peak UV filter, additional image processing is necessary to reduce ratios larger than 1.15. Furthermore, the nozzle exit and jet the contribution of liquid drops to the PIV calculation. First, were obscured by a mask. Performing PIV in this multiphase the images are filtered using a 5 × 5 pixel binomial filter, environment is a challenge. However, we believe that we after which an 8 × 8 sliding minimum was subtracted. Next, have obtained a good estimate of the mean and turbulent all drops with a diameter d larger than 2 pixels (≈ 20μ m) thr flow magnitudes, and an order of magnitude estimate of the and intensity larger than an intensity threshold I = 100 thr small-scale turbulence properties. counts (see Fig. 3d) are located in the image. At a turbulent Fig. 3 Overview of the LIF (a) fluorescein image a surround- ing a ≈135 m/s heptane spray. b Enlargement (width 3 mm) of the image in (a) showing both fluorescent tracers and direct UV scattering of the liquid. After image processing c droplets larger than 20μ m are identified and replaced by the background intensity. The arrows in (b) and (c) point to the spot of a large liquid drop. (b) (c) (d) The intensity pdf (d) of the 0.1 images before (b) and after (c) image processing show a clear segmentation threshold for drops larger than d thr 0 100200 300 I (counts) 1 3 110 Page 4 of 7 Experiments in Fluids (2018) 59:110 3 Results Figure 4 shows the mean velocity field of the gas phase. There appears to be a net influx of mass into the measure- ment volume. This must be offset by a large downstream (upward) flow induced by the strong shear at the liquid–gas interface. This flow could not be visualized, as the current setup and imaging method cannot image close enough to the spray edge. Additionally, a small crossflow is antici- pated by the observed asymmetry of the pattern of radially inward flowing gas (compare left and right part of Fig. 4). This crossflow is orders of magnitude lower than the spray −1 2 velocity ( (10 ) vs (10 ) m/s), too weak to influence the breakup of the spray itself. While the mean velocity gives information on spray- induced entrainment, the velocity fluctuations are a meas- ure of the turbulence. The induced turbulence is strongest Fig. 4 The velocity magnitude of the gas-phase mean velocity field near the liquid–gas boundary, and is stronger for the heptane surrounding a 135 m/s heptane spray. The lines indicate the direction and magnitude of the velocity vector. A mask was placed over the jet than for the water jet, see Fig. 5. A possible explana- image to obscure the liquid jet tion is the different morphology of the jets: The heptane jet breaks up more atomized (more droplets, smaller core) than the water jet, and the liquid–gas interface will contain a larger number of droplets. The different structure of the root mean square (RMS) velocity for the left ( x < 0 ) side of the Fig. 5 The turbulent veloc- ity in the near-nozzle region of the spray, defined as � 2 2 1∕2 u =(⟨(u − u ̄) ⟩ + ⟨(v − v ̄) ⟩) . The lower graph shows the measured turbulent velocity u (x) at y = 5 mm. Few valid PIV vectors were obtained on the left side of the heptane jet, likely due to scattering of the laser sheet on the spray, leading to a large variation of u 1 3 Experiments in Fluids (2018) 59:110 Page 5 of 7 110 heptane spray can be explained by an increased scattering The correlation in the radial (x) direction is omitted due to of the laser sheet, reducing the signal-to-noise ratio (SNR). the inhomogeneity of the turbulent flow, but should be equal The size of the large-scale turbulent vortices is set by to C(r) in isotropic turbulence. The function C(r) is shown the integral scale, which quantifies the decay length of the in Fig. 6 for both the water and heptane jets. The exponen- −r∕L two-point correlation function. The longitudinal correla- tial decay of the C (r) correlation function, C (r)∼ e , yy yy tion function can be used to estimate the length scales in gives L ≈ 6 mm and L ≈ 8 mm. The magnitude y,water y,heptane the spray-induced turbulence. The longitudinal correlation of L demonstrates that the largest eddies are much smaller function (Pope 2000), averaged over all measurements and than the circulatory flow in this experiment, and are there- positions in the unmasked region of the flow, is fore generated by the shear at the liquid–gas interface. The smallest scales of the induced turbulence are C(r)= ⟨(v( + r), t)v(, t)⟩∕⟨v ⟩, determined by the turbulent dissipation rate . It is a chal- lenge to measure the dissipation rate because the veloc- where is the unity vector in the y-direction, and the aver- ity field is averaged over the PIV interrogation windows age ⟨⟩ is done over time and locations in the unmasked and the turbulence is inhomogeneous. In isotropic and region of the flow. For the computation of C (r), we correct homogeneous turbulence, the true dissipation rate can for the inhomogeneity of the velocity field u (x, t) by sub- be obtained using a large eddy correction of the meas- tracting the mean and dividing by the fluctuation velocity. ured velocity gradients (Bertens et al. 2015). In our case, while using the measured planar gradients, this would 3∕2 2 3∕2 result in = 2 (C Δ) ⟨S ⟩ , wit h C the Smagorinsky correction factor, Δ the PIV window size, and the strain 3 3 2 2 2 2 2 2 r ate S = ⟨( u) +( v) ⟩ + ⟨( u) +( v) ⟩ , wit h y x x y 2 4 u = u∕y , etc. Using this, we define a local () , wit h the understanding that the dissipation rate is the spatial average of () . In Bertens et al. (2015), we argue that the value of the constant C should depend on the ratio of Δ over the Kolmogorov length scale , the window overlap in the PIV calculations, and the discrete approximation of the derivatives. Figure 7 shows the local dissipation rate for the water and heptane case. Clearly, this local dissipation rate is very inhomogeneous, with a poorly defined average. 2 −3 The resulting averaged dissipation rates are = 50 m s hep 2 −3 and = 35 m s for the heptane and water jets, respec- wat tively. For the Kolmogorov length and time scales, this cor- −5 −4 −4 responds to ≈ 9 × 10 m, ≈ 6 × 10 s and ≈ 10 Fig. 6 The black and gray are C(r) for the heptane and water spray, −4 m, ≈ 7 × 10 s for the heptane and water sprays, respec- respectively. The dashed lines are a fit of C(r)∼ exp(−r∕L ) , with tively, with a lambda Reynolds number of 170 and 140. L ≈ 8 mm and L ≈ 6 mm. y,heptane y,water Fig. 7 Local dissipation field of the heptane (a) and water (b) case, computed from the velocity gradients, 3∕2 2 3∕2 = 2 (C Δ) ⟨S ⟩ , with 2 2 2 S = ⟨( u) + ( v) ⟩ + y x 2 2 2 ⟨( u) + ( v) ⟩ , with x y u = u∕y , etc., and Δ the interrogation window size, and the Smagorinsky constant C = 0.58 (in accordance with the large eddy correction) 1 3 110 Page 6 of 7 Experiments in Fluids (2018) 59:110 Whether the droplet dispersion is affected by the small- (a) scale turbulence induced by the jet depends on two prop- erties: The droplet Stokes number and the size of the tur- bulent velocity fluctuations as compared to the axial and radial release velocities at breakup. If the Stokes number is small ( St ≪ 1), the droplets will disperse with the tur- bulent air surrounding the spray. If the Stokes number is large ( St ≫1), they will mostly travel ballistically away from the spray with the radial velocity induced by the breakup of the ligament at the liquid–gas interface (which can be approximated from measurements of liquid dispersion van der Voort et al. 2016a). Using the measured and , and the individual fluid properties to determine the droplet response time = d ∕18 , with the viscosity of air, the droplet d d g g (b) Stokes number can now be determined. Taking the droplet size d from the size distribution of the droplets from the investigated sprays (measured with interferometric particle imaging), the size distribution can be translated to a distri- bution of Stokes numbers (see Fig. 8). The range of Stokes numbers indicates that these droplets will follow the turbu- lent eddies. 4 Conclusions The Stokes number quantifies the response of the droplets in the spray environment to the smallest timescale (eddy Fig. 8 The PDF of the droplet size distribution (a) and Stokes distri- turnover time) of the spray-induced turbulence, estimated bution (b) for the heptane (red) and water (blue) sprays. The gray area −4 from the measured dissipation rate to be ≈ 6 × 10 s. indicates the cut-off, determined by the lower limit of the IPI droplet On the other hand, the estimate of the integral length scale sizing measurement range (van der Voort et al. 2016b) � −2 leads to a large eddy turnover time = L∕u ≈ 10 s, one order of magnitude larger than , corresponding to a tur- �2 −2 2 bulent diffusion rate D ≈ u ≈ 10 m ∕ s. From the turb L measured size distribution, we conclude that most droplets will be dispersed by turbulence. This includes the formation of large-scale clusters and voids (of recirculated droplets), as is illustrated in Fig. 9. However, the initial velocity of the droplets will determine if the dispersion will occur in the near-nozzle regime investigated in this work. A separation has to be made between the recirculated droplets already present in the spray environment (such as would occur in sprays in a confined environment, as piston engines), and the droplets newly generated by the jet itself. The average radial and longitudinal velocity of the liquid part of the spray was measured using laser-induced phospho- rescence, which tracks the displacement of a small lumines- Fig. 9 Complementary image of the post-processed PIV images, cent volume of liquid using molecular tracers and intensi- showing the locations of droplets with diameters ≥ 20 μm surround- ing the spray at a single instance of time. The variation in droplet fied high-speed cameras (Voort et al. 2016b). The distance density indicates turbulent clustering in the regions of strain between each droplet travels before it is adapted to the turbulent flow the turbulent eddies (droplet response length) is given by v , which is in the d jet order of 30 mm for 10 μ m droplets ( St ≈ 1). This distance is much larger than our interrogation area, and only reaches the investigated area for droplets < 5 μ m ( St <0.1), which is 1 3 Experiments in Fluids (2018) 59:110 Page 7 of 7 110 Lee J, Yamakawa M, Isshiki S, and Nishida K (2002) An analysis of outside of our droplet sizing measurement range. Under the droplets and ambient air interaction in d.i. gasoline spray using present conditions, the influence of turbulence on the disper - lif-piv technique. SAE International, pages 2002–01–0743 sion of spray droplets is small. However, if the atomization Ligrani PM, Bradshaw P (1987) Spatial resolution and measurement level is increased, by increasing ambient pressure, or chang- of turbulence in the viscous sublayer using subminiature hot-wire probes. Exp fluids 5:407–417 ing the liquid properties, the mean jet velocity will decrease Paulsen Husted B, Petersson P, Lund I, Holmstedt G, Holmstedt G while the turbulent fluctuations will grow stronger. This will (2009) Comparison of piv and pda droplet velocity measurement shift the droplet distribution towards smaller Stokes numbers techniques on two high-pressure water mist nozzles. Fire Saf J and shorter droplet response lengths. As the ratio of u to the 44:1030–1045 Pope SB (2000) Turbulent flows. Cambridge, Cambridge University radial release velocity becomes larger, and the distribution Press shifts towards smaller Stokes numbers, the spray-induced Reveillon J, Demoulin FX (2007) Effects of the preferential segregation turbulence becomes increasingly important in determining of droplets on evaporation and turbulent mixing. J Fluid Mech the droplet dispersion, and thus the mixing of spray and air. 583:273–302 Rottenkolber G, Gindele J, Raposo J, Dullenkopf K, Hentschel W, Wit- tig S, Spicher U, Merzkirch W (2002) Spray analysis of a gasoline Acknowledgements This work is part of the research programme of direct injector by means of two-phase PIV. Exp Fluids 32:710–721 the Dutch Organisation for Scientific Research (NWO). The authors Shaw RA, Raede WC, Collins LR, Verlinde J (1998) Preferential con- also thank Edwin Overmars for advice concerning PIV processing. centration of cloud droplets by turbulence: effects on the early evolution of cumulus cloud droplet spectra. 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