ratholing powder flow. Many of these flow issues can be traced back to improper discharger or feeder designs. ratholing powder flow

 
 Many of these flow issues can be traced back to improper discharger or feeder designsratholing powder flow 4

a. The Circle Feeder can be used as a material feeder, large industrial feeder, laboratory feeder, powder. 6). hopper that gives mass flow with one powder may give core flow with another. Powder & Bulk Processing. Bridging or arching. In arching, the material forms an arch (or a bridge) above the outlet that prevents further flow. To mitigate process variations and disturbances caused by such risk scenarios, closed-loop feedback control is required. ) the powders are filled into closed cavities; this is followed by compaction using rigid punches and finally the product is ejected from the die. 4. The 2-in. Flow and potential rathole formation in conical hoppers. The API AeroFlow® automated flowability analyzer was tested using 6 pharmaceutical excipients. The. These problems lead to losses worth thousands of dollars at. Silo: A tall bin, where H > 1. m. 2. The corresponding control schemes at different levels for the feeding-blending system are provided in Table 6. 2. Silo design for gravity flow; most economic. Powder flow can also vary from lot-to-lot, which needs to be understood during R&D. In order to achieve mass flow, tion hoppers) are shown in Figures 5 and 6, respectively. These problems can result in limited live capacity. Major Testing: Bulk Density Measurement [ USP<616>] Tapped Density. Flow function test. 9b, although the variation of the blend flow was larger compared to the total powder flow in case study 1. 3b) occurs in case of funnel flow if only the bulk solid above the outlet is flowing out, and the remaining bulk solid - the stagnant zones – is consolidated and forms the rathole. Let us explain how the use of vibration or sudden large blasts of air solve material flow problems. The Circle Feeder can be manufactured with several outlets for “one. More. 10. To find out more about Rotoflo, contact rotoflo@severfield. A powder flow analysis is an indicator of how well formulation will release from the hopper during the tableting. 2. Researchers at Purdue University have developed a new technology that solves the caking, bridging, and ratholing that occurs in powder flow from hoppers and bins in agriculture. Flow rate evaluationThe model elucidated the impact of the material descriptors for density; powder flow; particle size; compressibility; permeability and wall friction angle on the feeding process. 2. In a silo, hopper or bin, the powder is exposed to various pressure. com. Particle size distribution (PSD) estimation by sieving of the two powders was performed according to Ph. The material that is. caking and powder flow speed dependency (PFSD) test, of spray-dried bee pollen enriched milk powder (packed in ALP, BOPP/LDPE, and PET/Al. 5mm are the only two that so far have had this problem. Options for explosion proof and pneumatic vibrators for hazardous. This method may be used for all powders, dairy and non-dairy products. ‘Rat-holing’ (shown in Figure 2a) is the principle flow obstruction in a core-flow vessel where the powder in the flow-channel above the outlet discharges and leaves a stable. Prevent bridging and ratholing. Arching or bridging is a flow-arresting situation whereby the powder mass creates a structure (such as a dome or a bridge) above the outlet hole inhibiting flow completely. Powder-container design affects discharge rate, cleanability, and powder flow. powder becomes deaerated in the stagnant region of a funnel flow bin, it usually develops 2. Acceptable flow is required in powder transfer operations such as the emptying of tumble bins and conveyance of powders by gravity or screw feeders. Jenike, who pioneered the theory of bulk solids flow at the University of Utah in Salt. Valves & Actuators. A bridge forms when wall friction holds up the ends of the arch. Powder & Bulk Processing. A Brookfield Powder Flow Tester equipped with Powder Flow Pro software for automated instrument control and data acquisition was used to test brown gravy mix. The flow properties of a bulk solid can have a significant impact on process efficiency and the success of the end product. Bridging or ratholing in the silo can block the whole process and cause a discontinuity with high technical and financial consequences. Pivotal work on the development of the theory of bulk solids flow began in earnest in the early 1950s, when. The purposes of this investigation were to develop a method to evaluate flow properties of powders from avalanching tests and to detect similarities and relationships between these data and conventional powder flow properties. These flow problems can result in powder caking, production delays, increased operator intervention, or product losses. the types of flow problems that can occur and the flow patterns. include modifying the hopper, adding a bin insert, using a flow. Apparatus. A. How to prevent solids and powder flow stoppages with proper feeder design FREE | October 18,. The final potential issue is erratic flow, in which flow alternates between ratholing and arching (see Figure 1). . A brief introduction to the flow properties of bulk solids, and common instruments and tests used to measure them, is given first, followed by a detailed summary of the research works. 363 14. Figure 1: Manufacturing pharmaceutical tablets and capsules involves several powder handling steps. described ratholing and powder bridging in a small-scale feeder for fine, cohesive and compressible powders (Santos et al. (For an illustration of arching and ratholing, see the online version of this article at If a stable rathole forms in a hopper,They also prevent ratholing of hoppers and prevent lump formation. Discharge of powder from a hopper or bin is a common operation in solid dosage form manufacture. 2. Case Studies Keep product moving by preventing buildup, bridging and ratholing. This article describes a study scientists conducted to resolve a powder-binding problem that developed during the scale-up—from proof-of-concept scale to pilot. They all refer. 8 feet 12. Hoppers designed for mass flow with high quality surface finishes can address these issues. Typical powder flow issues found in the hopper are ratholing, bridging and segregation. outlet dimensions to avoid arching and ratholing. The reason for this is that when a result in a flooding condition at the outlet. TheWolfenbuttel, Germany) is used for measuring the flow properties of bulk solids or powder ( fig. Arches come in two types: interlocking arches, built up of large, mechanically. Scope. The field of bulk solids handling was developed due mainly to the work of Dr. Material Flow Solutions engineers offer scientifically-based solutions for your powder flow issues. g. , and J. Again, this impacts powder bowl depth, evenness and weight control. Our pneumatic and electric chute and pipe vibrators and vibratory equipment will: Unload dry or semi dry bulk material. His first conference session, “Design Theory: Best Bets for Hoppers, Silos, and Feeders”, will focus on the fundamentals to ensure reliable material flow and will. Eliminate bridging, rat holes, and stuck material. It is therefore imperative to know your powder properties in order to design the desired silo. It is mainly used clinically as an adaptogen, but antihypertensive effects have been reported for the. g. 89-0. A high fat powder (HFP) with 73% milk fat content, whey permeate powder (WPP) with 86% lactose, rennet casein powder (RCP) and sodium caseinate powder (SCP) were donated by Kerry Ltd. Traditional powder testing methods cannot force the bridging to occur in a repeatable manner and thus they cannot discriminate flow differences between powders. • Stable and strong thanks to high-quality Inox tube frame construction. A proven and practical scientific approach for designing bins and feeders based on a material’s flow properties. This type of flow pattern is indicative of uniform, first-in-first-out flow, where ratholing, erratic flow, segregation, and flooding problems are mitigated. 10). The powder flowability is defined as the ability of a material in the form of particles to flow in a desired manner when used in specific equipment [33]. Ratholing is influenced by the bin/hopper geometry and outlet size the material is being fed through. 125” to 0. Consequently, meas-urement of the wall friction characteristic of a. The hopper must be designed so the outlet diameter is larger than the outlet rathole critical diameter. Calculation of a Hopper Geometry for Mass Flow An organic solid powder has a bulk density of 22 lb/cu ft. Robert Sedlock. Flow problems, such as ratholing, arching, and erratic flow, can be eliminated with appropriate container geometry. Test results allow a formulator to determine required hopper outlet dimensions that will prevent flow stoppages, hopper angles necessary to prevent ratholing, and outlet sizes required to achieve. This can disrupt your production line. Discharge of powder from a hopper or bin is a common operation in solid dosage form manufacture. Of course the outlet of the hopper has to be large enough to prevent bridging above the feeder. Ratholing/ funneling 5 Inconsistent flow 3 Electrostatics Flowability Compaction . 4. Ratholing occurs when material in the center discharges completely while material nearer the walls of the hopper remains in place. Ratholing. Flow obstructions occur when the forces opposing motion exceed the forces promoting. 5). The principles discussed in this chapter can be applied to analyzing new or existing equipment designs. Ratholing is influenced by the bin/hopper geometry and outlet size the material is fed through. Ratholing: can occur in a bin when the powder empties through a central flow channel, but the material at the bin walls remains stagnant and leaves an empty hole (rathole) through the material, starting at the bin outlet (Fig. Segregation Ratholing (Fig. Mass-flow bin. Due to the pressure, some solids tend to be more cohesive , when powders become cohesive, they can form archs or rathole , 2 phenomena very detrimental to the flow of powder and. Attempts to initiate flow, such as use of vibration on hopper with rubber mallet or increasing powder paddle feeder, did not work. This can disrupt your production line. A key variable that will have an impact on the flow is its cohesive strength. Problems of powder flow a. 4. was used to control the flow of powder. 5). A commercial system to study avalanching in powders was first described by Kaye et al [18]. The bin activator works discharges not over the full covered area, but only in a small unpredictable area and coarse ratholing. Prevent segregation with mass flow. powder flow problems. k. Powder flow is critical to a range of pharmaceutical manufacturing processes. There are many consequences of flow problems. If the powder does not bind sufficiently to another material, it will separate through fluidization if aerated or allowed to free-fall. If you’re in supplement processing and need expert advice or equipment related to powder handling, supplement or food production, call Right Stuff Equipment at 303. Factors that affect the flow behavior are discussed. This is due to issues related to the flow pattern of most bulk solids: arching in the hopper occurs during mass flow when the arch builds sufficient strength to support the powder above it; ratholing in the storage vessel. Fluidization is commonly used with pulverized fuel handling, drying operations, reaction processes, and fine powder hopper discharge systems. Ratholing, another flow arresting situation, is when material directly above the outlet flows but the rest of the powder mass closest to the walls does not, creating a tunnel. Jenike & Johanson is presenting the following AIChE sponsored courses June 18-20 at the Canadian Management Centre in Toronto:Flow of Solids in Bins, Powder Bulk Solids is part of the Informa Markets Division of Informa PLCRat-holing problem: * is one of common powder flow problems * When powders are released via a butterfly or slide valve, flow takes place directly above the container outlet. the types of flow problems that can occur and the flow patterns. steeper than. Under those conditions, the product flow typically typically is last in, first out. m. Each measured yield locus is based on the individual consolidation stress or the major principal stress (σ 1 ). Here, flowability and magnetization were measured for a dual-phase steel powder in size fractions from 20 ⩽ D / μ m ⩽ 40 to > 200 µm. 5). These behaviours are related to the cohesive strength of the powder, which is a function of the applied consolidation pressure. The reason for this is that when a powder becomes deaerated in the stagnant region of a funnel flow bin, it usually develops Ratholing: can occur in a bin when the powder empties through a central flow channel, but the material at the bin walls remains stagnant and leaves an empty hole (rathole) through the material, starting at the bin outlet (Fig. 24hr Emergency Service. As the level of fly ash in the flow channel drops, a resistance to further flow into this channel occurs due to. At the heart of our Powder Handling System is an IBC fitted with our patented Cone Valve Technology, a unique discharge valve that eliminates typical powder flow problems. 0”. Mass Flow also allows the most efficient outlet. piping or ratholing may occur. Unstick material and promote even flow. When you have buildup in the silo, the loads associated with asymmetric flow can be detrimental to the structural integrity of the silo as they can lead to wall failure and total silo failure. The material forms a narrow passageway above the feed auger or outlet, while the remaining materials in the storage structure are stationary and can begin caking to. In addition, poor flowability can also cause content uniformity concern because of insufficient mixing. The technology is a microcontroller actuated portable device that can be remotely controlled. Flow aids are used to return to a more regulated flow pattern and are relatively inexpensive. The unique design can feed sticky, fluffy, lumpy, flaky, and fibrous materials without issues of bridging and ratholing in the hopper. It is critical to understand the type of hang-up that you may be experiencing. Problems associated with ratholing are flooding, substantial variation of density in product, and eventually no-flow. 1. 1. 2. Powder has a natural ability to move and fall when it is stored in a silo or a hopper. It is a superb discharging device overcoming all manner of powder flow problems. flowability. The hopper design can play a role in this as those with sharp angles and rough surfaces can inhibit powder flow. 8 9 Dissolution can be improved by improved. powder flow is uncontrolled due to randomly collapsing of rathole (Royal and Carson. Visually detectable local ratholing and cratering in the fluid bed: Compressed air too moist, contains oil; relative humidity is too high inside the room in which the powder is processed. To improve the flowability of powders, flow aids or lubricants such as magnesium stearate are often incorporated in. "Rotoflo is the best silo discharger! Mass flow develops when all the material in a silo is in motion whenever any is withdrawn. The total powder flow can be controlled in the level 1 closed-loop operation as indicated in Fig. 1 Funnel flow bins When a fine powder is stored in and discharged from a bin having a funnel flow pattern, ratholing and flooding problems are almost inevitable. Figure 3: Stagnant, cohesive powders can form a stable rathole in funnel flow. Powder flow characteristics and vessel design vary tremendously. The typical problems encountered are either a cohesive arch or ratholing. 26. This is indicated in hopper calculations as “Free Flow” or “0. If you have material flow problems like arching, bridging, ratholing or material sticking to the sides of your bin, then a VIBCO Air Cannon can help! The VIBCO Air. It offers automatic and controlled discharge of virtually any powder type, winning where other systems. Consolidations can therefore be undone. Most times it does not present any problems such as ratholing, erratic flow, flooding and segregation, because the discharging material is not cohesive or has a small critical rat-hole dimension. This resulted in stagnation of the flow, especially after a weekend. Figure 1. Arching/Bridging & Ratholing. 3º Peschl 4 Inst Flow Function - Raw 0. Eur. UK-based powder flow solutions firm Freeman Technology offers this video on how particulate materials react when aerated, loosely packed or. The goal of the design process is the determination of the hopper wall inclination necessary for mass flow and the minimum outlet size to prevent flow problems due to arching or ratholing. com. Minor powder flow issues during R&D can turn into major headaches once scale-up to production begins. Chem Eng Sci. In powder technology, the flow conditions are from. This is different from avalanche testing where a rather unconsolidated powder bed rotates inside a rotating drum and therefore, the powder bed properties are evaluated in a practically free flow. The Circle Feeder has a variety of features but widely known for its ability to prevent material arching, bridging, and ratholing. The primary focus of this chapter is to provide guidance in designing bulk solids (powder) handling equipment to provide consistent, reliable flow, and the required product uniformity by minimizing segregation. Dense phase. To ensure issues don’t persist or escalate, it’s important to fix the issue as. 2 Flowability indicators used in industries 7 1. 1991; Holdich. Material hang-up (arching and/or ratholing) problems are generally caused by one of four things: cohesive forces between powder particles or granules, external forces, inter-particle locking, or elastic constraint issues. pharmaceutical tablets, detergents, ceramics, powder metallurgy etc. . 3. Keywords: live bottom, cohesive, powder, hopper design. Powder rheology is the study of the behaviour of powders as bulk assemblies, consisting of solids, liquids and gases. It can also cause storage and handling related problems including hopper/bin arching and ratholing, resulting in no flow. 3 Calculation of Minimum Required Outlet. That’s why. These issues are most likely due to improper storage, a poorly selected. Still, the material at the bin walls remains stagnant and leaves. size, form, elasticity, water content and temperature, which influence compressibility. , 1998,. The two most common flow problems experienced in a silo, bin or hopper are arching (bridging) and ratholing. The simplest way of explaining the flow function is with the uniaxial unconfined failure test shown in Figure 4, which measures the. Increase powder fluidity enables spreading. Ratholing is influenced by the bin/hopper geometry and outlet size the material is fed through. Breakthrough Products Awards. Its unique construction fulfills allows for quantitative dosing steadily and evenly. Arching occurs when large particles interlock to form an arch at a hopper outlet and stop flowing due to shape, pressure, moisture or temperature. The requirement that the funnel-flow bin be capable of self-cleaning can usually be met by making the hopper slope 15 deg. Process Control & Automation. The large open inlet exceeds most materials’ critical arching diameter, preventing bridging and ratholing. The way bulk powders flow impacts on the design of. 5D Bunker: A shallow bin, where H < 1. Bridging, ratholing, arching and comparable behaviors are the bane of powder handling and formulating. m. Also in the case of funnel flow, asymmetry is of no help when ratholing has to be avoided. . 2 Mass flow bins sufficient cohesive strength that its critical rathole diameter (the flow channel diameter at Flooding and ratholing problems can be which a rathole becomes. The most common and serious problem is no-flow, due to arching or ratholing [6], [7]. (For an illustration of arching and ratholing, see the online version of this article at If a stable rathole forms in a hopper,Powder flow is critical to a range of pharmaceutical manufacturing processes. Acceptable flow is required in powder transfer operations such as the emptying of tumble bins and conveyance of powders by gravity or screw feeders. For each bulk powder the low powder percentage retainedFlow and discharge of powders in process vessels are well known to give rise to significant handling problems in a range of processes, for example in the pharmaceutical, mineral, chemical and food industries. flow, including ratholing, erratic flow, flood-ing and segregation. A Brookfield Powder Flow Tester, equipped with Powder Flow Pro software for automated instrument control and data acquisition, was used to test this name brand baby formula. ), and dry, uniformly-sized larger materials will be free flowing. mechanical interlocking of large particles forming an arch 2. Such hoppers are sensitive to arching and ratholing. (Powder and Bulk Solids) (regular, part-time and distance learning) • PhD (Powder. Use the following guidelines for impacting vibrators: Wall Thickness of 0. Effective feeder design not only enhances the flow within bins, hoppers, and stockpiles but also. 36 3 Wall Friction Angle 24. Ratholing, and Poor Material Flow . Ratholing is a term used to describe extreme cases of funnel flow where the material nearer the walls is completely stationary and only the central material is discharged . Royal, T. flow rate through an orifice compressibility index and hausner ratio angle of repose shear cell. Ratholing is a flow obstruction is a no-flow condition obstruction that can cause erratic that prevents material discharge discharge. Pumps, Motors & Drives. Wall friction, internal friction and bridging properties determine the applicable hopper angle and opening diameter. For example, when conveying powders that tend to cake or pack, it will be necessary to feed the aeromechanical conveyor from an infeed hopper of steep-wall design that encourages material flow along the hopper walls and prevents bridging and ratholing of the material. the powder flows at the place of the smallest flow resistance. Use of Inverse Cones – A cone placed in the powder bowl can help fight the negative effect of poor flowing powders. If your effective is 20’ after 3 days at rest the rathole dimension is 18. Data were presented as mean. Material flow from a bin or silo is inextricably linked to how the feeder extracts the material from the bin outlet. A brief introduction to discrete elemental method (DEM) which computes and models powder. Check drain valve on drier is open: check oil and water separator : Poor fluidisation of the powderRatholing Ratholing is a condition in which the stored material does not slough into the central flow stream for discharge and instead forms a core. Purutyan H. aid, modifying the feeder, or using gas injection. Feeding, Weighing, Scaling 2. AirSweep breaks up material blocks and sweeps the vessel walls clean. The Circle Feeder is used to reliably discharge all types of granular materials. 6). The flow of powder out of a silo is stopping primarily for 2 reasons ; either formation of arches (arching, bridging) or ratholes. Hopper and feeder design is critical to ensuring proper material flow when handling and storing powders and bulk solid materials. Meet hygiene and safety requirements and remove the risk of cross-contamination. When working with bulk solids, especially in high-moisture environments, the material flow characteristics can change. If the coarser particles stick to the sides of the hopper they can get rancid and contaminate the next batch. Gravity Flow. The hopper design can play a role in this as those with sharp angles and rough surfaces can inhibit powder flow. For system manufacturers, process engineers, and operators: The timely application of flow enhancing solutions is recommended to prevent quality issues and production interruptions, such as bridging, ratholing and demixing. Bioprocess Equipment for biotech and pharmaceutical industries. Air displacement as the product flows from the container can cause segregation, leading to an inconsistent end product. In ratholing, a vertical flow channel develops above the hopper outlet and, once emptied, remains stable. The rest of powder compacts under vibration and get les flow-able in the time, so if a flow channel is established it will stay on the same place. Reduce costs in manual labor for unsticking materials from bins or hopper walls. Check drier is switched on. The primary measure of powder flowability is the powder flow function - which gives a measure of the amount of strength the material retains at a stress free surface following consolidation to a given stress level. The flow of powder from hoppers is usually assumed to take place in open atmosphere. Silo discharge solutions for powder bridging and ratholing. Provided here is a review of shear-cell testing and how the technique can be used to predict arching, ratholing and other behaviors. pub/extras. In: Brown CJ, Nielsen J (eds) Silos – fundamentals of theory, behaviour and design. Ratholes develop most often in conical hoppers that are not steep enough to produce flow at the walls. The flow properties that govern whether a powder is prone to ratholing include cohesive strength, wall fric-tion, and bulk density [1-5]. Follow this guidance to avoid common solids-handling issues, such as erratic flow and no flow. The primary design objective when determining the bin geometry is to ensure that bulk solid or powder will flow with the effects of gravity, and without flow obstructions occurring. Eliminate Bridging and Ratholing The Carman Vibrating Bin Discharger eliminates. It is critical to understand the type of hang-up that you may be experiencing. Unload and produce good faster in your production process. refilling) and unexpected events (e. pharmacopeial methods to characterise powder flow. Powder flow obstruction during hopper/bin discharge, such as arching or ratholing, remains an outstanding risk and cannot be reliably diagnosed using the existing flow function coefficient-based method. (USP 1-May-2024) Changes in flow rate as the container empties can also be. Powder rheology is used in a wide range of industries to. Unload and produce good faster in your production process. 1 Shear strength. • The particle size distribution – indicator of powder flow and the segregation potential • Bulk and tapped density – indicator of powder flow, mixing (fill volume) and tablet die filling. A better approach to predicting flow behavior is to take the characteristics of wall friction (φ w ). Discharging aids. Most flow problems are connected with the funnel flow pattern and can be avoided if the hopper is designed for mass flow (Johanson, 2002, Purutyan et al. While bulk solid and powder handling is extremely common in industry, even some of the most basic fundamentals of material handling remain poorly-understood – largely because our education generally only. A Brookfield Powder Flow Tester, equipped with Powder Flow Pro software for automated instrument control and data acquisition, was used to test this name brand baby formula. n 1. 71 Funnel / core flow. Are they steep enough to prevent ratholing when a powder having an FFC of 7. Bridging is the name given to the self- created arch that develops just above the outlet of a bulk material silo or hopper as it empties. 361 14. Native corn starch did not flow from the hopper, so tablets were not compressed and had a severe ratholing problem. readiness of a powder to flow -. 8 B), F > 63 and F > 90 had practically equal outlet diameters (1. Retrofit solutions. The orifice flow behaviours had thus corroborated with the powders' flow properties. Do you suffer from Bin Rash? When Material gets clogged in Bin, Hoppers and Silos, do you bang your hoppers with hammers? It is not a great solution and it c. bridging, ratholing and compacting. We can clean your silos, hoppers & vessels. For powders such as T100 and T100M which exhibit arching and. Preventing Arching and Ratholing. Typical powder flow issues found in the hopper are ratholing, bridging and segregation. . Larger particles are more likely to penetrate the surface than fine particles. POWDER FLOW DATA The equipment consisted of a custom-built laboratory scale hopper feeding material in a controlled manner onto a. Typical powder flow issues found in the hopper are ratholing, bridging and segregation. Bridging, ratholing, arching and comparable behaviors are the bane of powder handling and formulating. In this study, we showed that the major principal stress (σ1) at the bin outlet is required for. PHARMACEUTICAL ENGINEERING. In silos and hoppers it’s often the cause of flow problems like ratholing and bridging. ; the ratio of tapped bulk density to loose bulk density; where the greater the ratio, the more. 1. The gyrators also reduce particle segregation to make sure each bag is completely. The hopper to be designed is conical. Understanding the rheological properties of the. Avoid powder flow problems by gaining a better understanding of flow patterns and bin design. In some cases through the design procedure it is found that a. Magazine Events News & Notes Videos Podcasts Webinars White Papers Breakthrough Products Awards. Efficiency– As explained earlier ratholing powder flow can be likened to creating a “funnel effect”,meaning silos and hoppers cannot be used to their full storage capacity. Solve your powder handling problems, whether it is. m. Thus, it will not be separated. 4. The system is designed to help prevent powder bridging and ratholing in silos and hoppers. When your bottom line depends on moving product efficiently through your plant, obstructions. Pumps, Motors & Drives. High batch accuracy with difficult-to- handle material. Home; Blog; Case Studies; 770-255-1322. Aside from funnel flow, powder bridging is another undesirable flow issue which can occur in the hopper (Fig. Besides that, powder flow can be determine by the angle of repose make by the powder itself when poured onto a flat surface throughout the hopper. m. Minor powder flow issues during R&D can turn into major headaches once scale-up to industrial production begins. Angle of repose. and host "True or False: Bulk Solids Edition" from 1:29 p.