Behavior Mechanism And Theoretical Modeling Of Spontaneous Imbibition Of Paper-based Coating Materials

The transport of fluid like print ink in coating of paper is directly dependenton the spontaneous imbibition performance of coating materials. Many printingquality problems such as print mottle, color evenness commonly arise from thebad imbibition characteristics of coating materials. Due to the stochastic anddisorder structural characteristics of porous coating, it generates many technicaldifficulties when charactering and modeling the imbibition mechanism. Andespecially, some experimental phenomenon of imbibition on porous coatingmaterials usually contradict with classical imbibitions theories and theseconfusions cannot be explained with those theoretical models, so some implicitimbibition behaviors still need to explore further. Considering these, the intrinsicimbibition mechanism, imbibition model and dynamic driving force system ofcoating material of paper are in turn investigated and discussed by means ofsome modern measurement methods and mathematical theories. On the basis ofexperimental studies, structural measurements and the pore wall rugosity, thebehavioral mechanism of imbibition and wetting in porous media are thereforeproposed. Moreover, the equivalent capillary tube provided with roughness, theimbibition model based on wetting contact line and fractal structure model ofimbibition mechanism respectively are constructed eventually, and the matchingresults between imbibition models proposed and experimental imbibitionperformance are discussed and further verified finally. The specific researchwork and some conclusions are as follows:According to the traditional inertial mechanism, Bosanquet mechanism andLucas–Washburn mechanism, the driving force system of imbibition and therelationship of these three imbibition models are compared and researched. The transformation relationship of these models is then simulated and confirmed onthe Matlab platform. Then, the samples for imbibition experiment are preparedand the imbibition characteristics of samples are measured using a gravimetricmethod, which are summarized by the time regime (t) and root time regime (√t)respectively. The experimentally analytical results show that the initialimbibition follows the inertial regime and has a linear relationship withimbibition time, and the time exponent satisfied with the index of0.5underLucas–Washburn regime proves Lucas–Washburn equation is correct to someextent and can be applied on the coating materials. Interestingly, a separatedimbibition phenomenon against the Lucas–Washburn regime forms in thisimbibition experiment. To disclose the essence reason of this experimentalsituation, the scientific hypothesis is thus presented correspondingly, which isthat the morphology of pore wall inside porous media might change the wettingbehavior and wetting force which lead to form two different imbibition of initialshort timescale and afterward long timescale. Hence, the roughness surfaces areable to affect on imbibtion performance.Considering wetting behavior of fluid on roughness surface, a new wettingway, a hemi-wicking on a composite surface, is probed by the surface energytransfer, which prompts to form liquid film of wetting at the initial wetting phase.The formation condition is discussed adequately in a general wetting situation.The liquid film caused by capillary condensation develops a smoothing effectcovering the tiny pores wall roughness. The physical circumstance in detailsfollowing this effect like this: when the liquids wet the roughness surface, thecapillary condensation happens first on the pore wall rugosity, the smoothingeffect of liquid firm is formed then which erases the solid roughness and changesthe wetting characteristics of surface area. The whole wetting process is thusdivided two phases: the wetting behavior on roughness surface first and onsmooth area filled with liquid later. As the wetting contact angle on theroughness area is less than that of one on the smooth surface which can explainthe separated experimental imbibition phenomenon properly underLucas–Washburn regime. Due to some measurement difficulties on dynamiccontact angle, the wetting contact length is developed to equal the changes ofcontact angle during the process of wetting. Moreover, the imbibition model and mechanism based on the wetting contact length are consequently proposed andthe specific described equations for modeling are also showed in this paper.To explore the relationship between structure of coating materials and itsimbibition behavior, the all coating samples are measured by means of nitrogensorption analysis and mercury porosimetry. The structural parameters of samplesas isotherm, the BET surface area, pore volume, pore area and pore sizedistribution in sequence are measured by the calculated models of BJH and DH.The sample structure suggests that:1) the data using BJH model and DH modelalmost are same and the only tiny deviation between them.2) The samples allgenerate the hysteresis loop at the different level which means the condensationhas happened in the adsorption/desorption process. The shape of all hysteresisloops is nearly same but the size is different and it decreases gradually becauseof the increase the styrene acrylic latex in samples which covers the some tinypores on pore wall.3) the certainty shape of hysteresis loops like that theadsorption volume increases slowly with relatively pressure increase at lowpressure field and becomes faster at mid-pressure area, reaches to a quickincrease at high pressure region which is similar to that of standard hysteresisloop of H3.The pore size calculated by adsorption curve is greater than that ofusing desorption one. Therefore, the ink-bottle stacking pore should exist insidethe samples extensively, which has a great performance of capillarycondensation.4) the pore structure of materials consists of mesopores andnanoscale pores, which the former provides the main bulk volume and the latterforms the major BET surface area on samples. It indicates that many tiny poreslike rugosity are embedded over larger pores (nanoscale pores) where are liableto form capillary condensation. In addition, the saturated imbibition volume isassessed using mercury porosimetry and the experimental data are furthermodified when considering the penetrometer expansion, mercury and sampleskeletal compression, which can decrease affect on physical structure of samples.In order to verify the imbibition model based on wetting contact line andcheck the role of smooth effect of liquid film, the experimental contact wettingline is defined in light of the roughness surface area (S) measured by capillarycondensation area and the equivalent length of imbibitions(L) obtained byexperimental imbibition over the smooth surface. The wetting contact line length of all samples is examined by this definition. The imbibition rate of modelmatching with experimental data is discussed and analyzed.The matching resultsindicate that the calculated imbibition gradient of initial phase is agree with theexperimental results very well. The matching results using adsorption dispatch ofthe samples like GCC0A，GCC0B，GCC2，GCC6B is more correspondent withthe measured results than that of calculating by desorption curve. By contrast,the conversed matching situation is demonstrated on the samples of GCC4，GCC6A. Despite the matching results calculated by desorption are more close totested results on the samples of GCC4，GCC6A, there is only tiny deviationbetween adsorption curve and desorption curve. As a whole, the wetting contactlength though adsorption curve is better than desorption to match experiment.The whole process proves the positive role of surface roughness on theimbibition process, and the theoretical model using the wetting line length also isverified and confirmed eventually.To characterize the physical structure of porous coating materials andfurther probe the relationship of material structure with imbibition performance,the fractal characterization of coating materials and the fractal structure ofwetting contact line are investigated using a fractal theory of the non-Euclideangeometry in this section. The fractal structure of coating materials and fractaldimension are tested and calculated using the classical FHH model of multilayernitrogen sorption which is testified as a robust method to measure the fractaldimension of porous media in practice. Then, the fractal structure of wettingcontact line, half-pipe growth model, is constructed by the generation method ofsome typical fractal structures of line shape, which can generate two forms ofstructure: external growth model and internal growth model, and the specificcalculation formula are also deduced. Additionally, the fractal imbibition modelis proposed by combining the fractal structure and prior imbibition model ofwetting contact line. The new matching between fractal model and experimentalimbibition is executed in a same way as above. The matching results demonstratethat although the both fractal structures all coincide with experiment data verywell mathematically, especially for the internal growth model, there still havesome discrepancies with common sense. For external growth model, the fractaldimension matched is nearly to reach to a limited value of2for line fractal and pore size also exceeds the common pore size. It can speculate that the externalgrowth has a serious defect in its structure and the half pipes overlap heavily toform some eccentric fractal structures. In contrast, the internal growth effectivelyavoids the overlapped situation and the matched fractal dimension lies over thenormal region, but the pore sizes forming the fractal structure are still out ofreasonable limitation and are unrealistic. Therefore, the pore size should belimited to that area of capillary condensation and matches again withexperimental imbibition. The corrected matching results exhibit that still has asizable deviation from experimental test, around two orders of magnitude.Aiming to these problems, the internal growth model is revised againconsidering the cumulative inertial effect in porous structure. And thecorresponding imbibition model and theoretical equations are explored and given.Another new matching is carried out on our new model modified. The resultssuggest that they are almost matching perfectly when now considering theinertial wetting term in the initial imbibition phase. The continuity of this plugflow phase is then related to the continuous rapid acceleration experienced in themesopores and nanoscale channels constituting the pore wall structure. They alsoverify the effective role of inertial force in porous structure and are to urge afaster imbibition at initial stage.